CHAPTER 4Think creativelyDemystifying creativity 66Don your creative cap 68Creative treats 70 CHAPTER 7Creative conundrums 72 The mind-body connectionSurviving the creative process 74 Healthy body, sturdy mind 144Doodle art 76 The physical recharge 146Thinking outside the box 78 Stress factor 148Matchstick mayhem 80 Exercise the Eastern way 150Original answers 84 T’ai Chi 152More creative conundrums 86 Yoga 154Optical illusions 90 Sleep and the brain 156 Brain food 158CHAPTER 5Numerical reasoningNumerical aptitude 94 CHAPTER 8 Test your new brainpowerQuick-ﬁre arithmetic test 96 Final workout 162Improving numeracy 98Visual math workout 100Sudoku 106 Solutions 172Samurai Sudoku 110Kakuro 112 Useful websites 186Logic ﬂies out of the window 114 Further reading 187Gambler’s fallacy 116 Index 188Unraveling numerical riddles 118Riddles to try 120 Acknowledgments 192CHAPTER 6Verbal reasoningTalk your way to success 124Quick-ﬁre vocabulary test 126Language and intelligence 128A workout with words 130Reading comprehension 136Words and pictures 138Build a story 140
6 ForewordForewordIt is the dream of everyone to have a brain that works better.You are holding in your hands a book that will help you makethat dream come true!Brain Training is one of the ﬁrst VISUAL guides to enhancingyour mental acumen. In this New Age of Intelligence, in whichthe human brain has to think intelligently about managingknowledge and processing the information it is bombardedwith, it’s vitally important that learning materials are brain-friendly. One of the reasons I was so enthusiastic about writingthe foreword for Brain Training is that this book has everythingyour brain needs: it is written in the brain’s own language—the“visual” language. It contains relevant images, plentiful color,excellent spatial design, clear associations, and lucid writing. It isa book about the brain that is friendly to the brain. In its physicalform, the book is entirely congruent with what the brain needs.In maximizing your brain it is also important for you to knowthat, for learning, the majority of people do not use their fullcognitive potential. This might sound like bad news, but isactually good news. It means that you have a lot of untappedbrainpower still left in the tank. All you need to do is learnhow to access it! Brain Training will allow you to do that,by introducing you to exciting and enjoyable games andexercises that will help you maximize your intelligence.In this groundbreaking book, you will learn about your brainand its remarkable structure and capacity. You will also beenlightened about the power of your visual and imaginativeprocesses. You will ﬁnd out about your memory and itsextraordinary capacities, your innate visual and creativecapabilities, and your ability with numbers. The book will
Foreword 7offer “visual” approaches to increase your verbal reasoningand word power. There is also a chapter that addresses thevitally important relationship between your brain and your body,and in which you will learn that the ancient adage: “HealthyBody Healthy Mind, Healthy Mind Healthy Body” is true. Byworking through the puzzles in Brain Training, you will improveyour focus and concentration, your memory, and your learningand creative powers. These are abilities that will signiﬁcantlyboost your conﬁdence and joy in life.By investing in the Brain Training program, you have investedin your own intellectual capital, and that capital is the mostvaluable capital in the world.Tony Buzan,Inventor of Mind Maps®
8 How to use this bookHow to use this bookStudies show that the sense of sight is the mostreceptive when it comes to learning. Therefore, Working through the bookthis program is visually led, and is ﬁlled with a The structure allows you to either work throughdiverse mix of popular cognitive exercises, which the book from cover to cover or to pick out aare divided into thematic chapters covering speciﬁc topic—for example, memory—and workmemory, visual reasoning and spatial awareness, on it alone. However you choose to approach thecreativity, numeracy, verbal reasoning, and the book, we encourage you to start with the ﬁrstmind-body connection. chapter (and the “Where are you at?” exercises) We open with a general introduction to the and ﬁnish with the ﬁnal workout in Chapter 8, sobrain, and to the concept of intelligence and you can gauge how you have improved over time.visual learning. This is followed by a range of For the majority of exercises we have providedexercises—“Where are you at?”—to gauge your answer boxes for you to ﬁll in. For the remainingcurrent mental agility. In the subsequent chapters exercises, we will instruct you to write yourwe concentrate on a speciﬁc brain function, such answer on a separate sheet of paper. Finally, inas memory or creativity. First, we explain how “The mind–body connection” chapter, we willit works and then we offer the most effective introduce you to the type of foods, exercise, andpuzzles to exercise that particular mental function. other physical pick-me-ups that raise brain power.Technique pages offer 36 Memory Technique: the journey method 37tips and strategies forimproving brain function The Journey Method 1 Front door: a bandaged dog sits on the front 2 A man sat on the park bench with 3 The pond in the park has a duck with The Journey Method or Method of Loci (to use doorstep stethoscope a bright its original name) is a technique for memorizing around his mohawk long lists of items. It has been practiced since the neck haircut. ancient Greek era, a time when long speeches had to be recited without recourse to notes because paper was such a luxury. The method is a type of mnemonic link system based on memorizing items along an imagined journey or series of locations (loci) that are familiar to you. You do this by associating the object with 4 A tree in the a point in the imagined location or journey. Since START YOUR park has been struck by lightning the human brain thinks more readily in pictures it MEMORY 14 Brain potential Introduction: picture the brain 15 TO DO LIST 1 Give dog medicine 2 Book doctor’s appointment Picture the brain These parts activate our emotions, appetites, the spinal cord. Specialized types of neurons, 3 Go to hair appointment 4 Pay electricity bill The brain looks a bit like a giant crinkled rubbery mushroom, instincts, pain and pleasure sensations, and other including sensory neurons and motor neurons, 5 Buy milk with the average adult brain weighing about 3 lbs 5 oz (1.5 kg). drives that are essential to survival. The amygdala allow us to feel and act respectively. All neurons 5 A teacher 6 Buy birthday card for Mom outside the school activates emotional responses, such as fear or respond to stimuli, and communicate the presence Cerebral cortex 7 Hang out washing is drawing a cow Frontal lobe Corpus callosum euphoria, while the hypothalamus is the control of stimuli to the central nervous system, and then on the blackboard 8 Mail letter Thalamus center for brain-to-body, body-to-brain messages, to the relevant part of the brain, which processes Parietal lobe causing, for example, blood pressure to rise when the information and sends responses to other parts we are agitated. The thalamus receives auditory of the body for action. Each neuron is connected to and visual sensory signals and relays them to approximately 10,000 others by frondlike tendrils. the outer layer of the brain, known as the The dendrites are the “receivers,” and axons, cerebral cortex, where the information is the “transmitters.” The neurons are not actually processed. The hippocampus is critical to learning joined together but touch each other. When and remembering spatial layouts. At the very back neurons communicate, the gaps at the touch points of the brain lies the cerebellum, which handles are ﬁlled with with neurotransmitters, chemicals that movement and balance and, along with the brain carry pulses or “electrical messages.” The myelin stem, is the part of the brain that evolved ﬁrst, sheath acts as an insulator and increases the Mega memory inherited from our primeval ancestors. It keeps speed and efﬁciency of the pulses. Memory experts believe that by us alive by controlling our involuntary body applying the Journey Method a Hypothalamus 6 The woman functions, including breathing and digestion. Dendrites person with ordinary memorization at the ﬂower capabilities, after establishing the Amygdala stall is wearing route stop-points of their own a birthday Hippocampus What are neurons? cake hat “Journey,” can use it to remember the sequence of a shufﬂed deck of cards Temporal lobe Neurons are the cells in the nervous system that Myelin sheath with less than an hour of practice. Occipital lobe transmit information by electrochemical signaling. Cerebellum They are the core components of the brain and Axon Your brain is divided into two hemispheres: the frontal lobes, left and the right. These are linked by a central which are considered the home of our personality. processing unit called the corpus callosum. The uppermost part of the frontal lobes is involved The sum of its parts Each half is split into four more compartments: in solving problems, activating spontaneous Each hemisphere deals with different types of mental activity. The responses, retrieving memories, applying left side deals with logic, numbers, language, lists, and analysis occipital lobe, which judgment, and controlling impulses. It also handles much of your visual sense. modulates our social and sexual behavior. This area is more developed in humans than in any —the so-called reasoning activities. The right side is more visual, and deals with imagination, color, spatial awareness, pattern, recognition, and making sense of the abstract. Fact ﬁle boxes reveal temporal lobes, which are involved in the organization of sound, other animals. Most people seem to have a dominant side. The crucial word here is “dominant." It’s a natural preference, and not an absolute. What this means is that when you’re learning something new, your fascinating facts about the memory, speech, and emotional responses. The limbic system parietal lobes, Inside the ridges and grooves of each hemisphere brain prefers to learn in a certain way. It is not so much that you are biologically right-brain- or left-brain-dominant, but that generally you’ve become comfortable with applying one side more than the workings of the brain as well which handle sensations, such as touch, body lie a set of structures forming what is known as the other. The truth is that in practice you are always using both sides of awareness, pain, pressure, and body temperature. They also help you with spatial orientation. limbic system. This system includes the amygdala, hypothalamus, thalamus, and hippocampus. the brain simply because most tasks demand it, so you shouldn’t get too hung up on this division. as the latest research ﬁndings
How to use this book 9Hints and strategies work with the material. There are also “fact ﬁle”We also include techniques throughout the book, boxes, which offer fascinating information aboutsuch as “The Journey Method” (see p.36) for the workings of the brain.improving memory or “The physical recharge” You can use all the tips and techniques you(see p.146) to increase mental alertness. These have learned to complete the mix of exercises inappear as discrete features between exercises, and the ﬁnal workout (Chapter 8). You may then wantcome complete with an example of how and why to return to the start and retest yourself againstyou might use the technique. We encourage you the puzzles in the “Where are you at?” sectionto learn and apply these to the relevant exercises to assess overall improvement.in the chapter. We might prompt you to use aspeciﬁc technique to complete an exercise so thatyou become familiar with applying it, which is an Solutionsimportant part of improving your brainpower. Finally, you can ﬁnd the solutions and/or explanationsAlso, try to learn the hints and tips we offer to the puzzles at the back of the book. Look forthroughout the book (denoted by the lightning the solutions arrow at the foot of the page, whichstrike icon), as these will enhance your ability to guides you to the speciﬁc page number. The colored band at the top of the page indicates puzzle pages Answer boxes to ﬁll in as you work through the puzzles 52 Visual reasoning and spatial awareness Exercises: visual teasers 53 Top tip boxes are indicated Visual teasers 6. Reversed digits 7. Quick-speed counting by a lightning strike icon The following puzzles have been designed to exercise your Circle the numbers below that have A: Count the number of times the number skills of image and pattern recognition. There are others that been reversed. “6” appears below. will hone your concentration and test your logical aptitude. B: At the same time, count the number of “3”s: times both “3”s and “7”s appear in the sequence below (don’t just count all the 2. Guess the picture “3”s, and then the “7”s). “7”s: What would you see in the picture if you assembled the Feature: thinking outside the box 79 pieces together? 1234467889974674657865876576576 3576573625432657346578436578342 2732188582735827456724687343828 Top tips Challenge assumptions—don’t just fall back on accepted ways of 7672878682768723682376783768267 thinking but question everything that 2647648823178346432764876774653 has been done or is known. Find focal objects—pick an object Description: 7436574386581483627868653873456 at random (or a word from a dictionary) and see what thoughts the The nine dot puzzle 1. The standard solution: You object or word inspires. run the pen outside the nine dot boundary to join the dots. Harvest ideas—when you’ve come 8. Largest circle up with as many new ideas as you If the circles represented by arcs can, begin the process of harvesting A, B, and C were completed, which by selecting the best ones. 3. Triangle test 4. Spot the ﬂipper 5. Cake for eight would have the greatest diameter? A Invent alternatives—allow yourself plenty of time to come up with new How many right-angled Take a look at the three shapes. Each one is How do you cut a cake into A B ideas, perhaps setting yourself a triangles can you create in exactly the same but one has been ﬂipped over 8 equal-sized pieces with this ﬁgure by connecting so that you can see the other side. For each only 3 cuts? Mozart effect: does it work? minimum (say, 50) before you begin So does listening to certain types of classical music your analysis. any 3 dots? question work out which shape has been ﬂipped. B C increase spatial reasoning and improve visual Provide provocation—deliberately B set up a wild counterpart to the A recognition? The “Mozart effect” was ﬁrst mooted C in the ﬁeld of childhood development in the early normally accepted idea, not as an end in itself, but as a possible pathway to 1990s. The term comes from a study that claimed that new ideas. since neurons ﬁring in speciﬁc patterns can lead to an 1 2 3 2. If you had a thick pencil, Shape concepts—look closely at 1 2 3 increase in intelligence, music could be used to activate you could join the dots with clusters of ideas that have sprung up those patterns because the brain responds to speciﬁc just three lines. and see whether you can group any sound frequencies. The researchers conducting the study together into concepts. maintained that when children receive musical stimulus Suspend judgment—don’t rush to 1 2 3 their brains form connections between neurons in judge any new ideas, however strange 1 2 3 patterns that also help them with spatial reasoning. they may appear at ﬁrst. D However, a number of followup studies have found no C such correlation. In fact, many cynics believe that the triangles Solutions on p.174 media has exaggerated and distorted the claims. Just go crazy! While thinking laterally, you are encouraged to consider trivial or ridiculous ideas. This is because you are 5. If you laid the paper on 4. Even with a thinner pencil, 3. Why stop at three lines? using the information not for its own the ground, you could draw You could still make do with Why not take a very thick value but for its knock-on effect. Each one long line, which circles the three lines by folding the paper pencil and do the job with idea is a stepping stone to another earth three times, joining one so that the dots were closer to just one line?Solutions arrows provide row of dots each time. each other. idea. You will probably head into many strange directions as you jump from one idea to another but at some stagepage references for answers you will reach an innovative solution.and explanations
12 Brain potentialBrain powerYour brain is the most sophisticated objectin the known universe. Millions of messagesare speeding through your nervous systemat any given moment, enabling your brainto receive, process, and store information,and to send instructions all over the body. Your brain is capable of so much morethan you might give it credit for. Just take amoment to consider all the things made byhuman beings. From the earliest tool, such asa pickax, to the modern skyscraper, and fromthe largest dam to the smallest microchip—thehuman brain is where all of these objects wereﬁrst conceived. Undoubtedly, the brain is themost powerful tool at mankind’s disposal. Your brain works around the clock. Itgenerates more electrical impulses each daythan all the mobile phones in the world. Youhave billions of tiny brain nerve cells interactingwith each other in permutations that havebeen estimated to equal 1 with 800 zerosbehind it. (To make that remotely graspable,the number of atoms in the world—one of thesmallest material things we can get a ﬁx on—is estimated to be 1.33 with 48 zeros after it.)Did you know?Your brain runs on less power than your refrigerator light.That’s about 12 watts of power. During the course of a dayyour brain uses the amount of energy contained in a smallchocolate bar, around 230 calories. Even though these factsmight make the brain sound efﬁcient, in relative terms, it isan energy hog. Your brain accounts for merely 2 percent of the body’s weight, but consumes 20 percent of the body’s total energy. Your brain requires a tenth of a calorie per minute merely to survive. Your brain consumes energy at ten times the rate of the rest of the body per gram of tissue. The majority of this energy goes into maintenance of the brain.
Introduction: brain power 13Strengths and weaknessesSo, if we have such a powerful brain, why arent can be proﬁcient when it comes to reading maps,we all good at everything? Why are some of us another might be more creative, and a third, moreforgetful? Why do some of us have trouble logical. Of course, this is a crude analogy becausereading maps? Why do some of us lack a sense the different areas of the brain function togetherof rhythm? Surely with all that “electrical” activity for most tasks and a speciﬁc area dominates, butgoing on inside our heads, we shouldn’t be faced it does illustrate how the brain differs from personwith these difﬁculties? to person. In short, it’s a question of education Think of the brain as a busy fairground with and genetics. So, don’t be too hard on yourselfan assortment of rides and attractions, each if you think you’re bad at math or terrible atrepresenting a different area of the brain, and languages. The chances are that you excel inthink of the people as the tiny nerve cells or another area.“neurons” (see p.15). Now, the popularity of However, this doesn’t mean you cannotthe various attractions tends to differ from one develop a mental ability that you consider weakerfairground to another; a ride in one fairground than another. It’s wrong to think that just becausemay draw more people than the same ride in you’re not naturally gifted in something, suchanother. In brain terms, the “popular rides” are as math or map-reading, that there’s no point inthe parts of the brain with lots of “nerve cell” trying to improve it. Your brain is similar to anyactivity and, hence, tend to be more developed. muscle in your body in that exercise will raise itsThis development is aided signiﬁcantly by the kind potency. You can always strive to improve andof education we receive as a child. One person expand your current mental aptitude.
14 Brain potentialPicture the brainThe brain looks a bit like a giant crinkled rubbery mushroom,with the average adult brain weighing about 3 lbs 5 oz (1.5 kg).Cerebral cortex Frontal lobe Corpus callosum ThalamusParietal lobe Hypothalamus Amygdala Temporal lobe Hippocampus Occipital lobe CerebellumYour brain is divided into two hemispheres: the frontal lobes,left and the right. These are linked by a central which are considered the home of our personality.processing unit called the corpus callosum. The uppermost part of the frontal lobes is involvedEach half is split into four more compartments: in solving problems, activating spontaneous responses, retrieving memories, applying occipital lobe, which judgment, and controlling impulses. It alsohandles much of your visual sense. modulates our social and sexual behavior. This area is more developed in humans than in any temporal lobes, other animals.which are involved in the organization of sound,memory, speech, and emotional responses. The limbic system parietal lobes, Inside the ridges and grooves of each hemispherewhich handle sensations, such as touch, body lie a set of structures forming what is known as theawareness, pain, pressure, and body temperature. limbic system. This system includes the amygdala,They also help you with spatial orientation. hypothalamus, thalamus, and hippocampus.
Introduction: picture the brain 15These parts activate our emotions, appetites, the spinal cord. Specialized types of neurons,instincts, pain and pleasure sensations, and other including sensory neurons and motor neurons,drives that are essential to survival. The amygdala allow us to feel and act respectively. All neuronsactivates emotional responses, such as fear or respond to stimuli, and communicate the presenceeuphoria, while the hypothalamus is the control of stimuli to the central nervous system, and thencenter for brain-to-body, body-to-brain messages, to the relevant part of the brain, which processescausing, for example, blood pressure to rise when the information and sends responses to other partswe are agitated. The thalamus receives auditory of the body for action. Each neuron is connected toand visual sensory signals and relays them to approximately 10,000 others by frondlike tendrils.the outer layer of the brain, known as the The dendrites are the “receivers,” and axons,cerebral cortex, where the information is the “transmitters.” The neurons are not actuallyprocessed. The hippocampus is critical to learning joined together but touch each other. Whenand remembering spatial layouts. At the very back neurons communicate, the gaps at the touch pointsof the brain lies the cerebellum, which handles are ﬁlled with with neurotransmitters, chemicals thatmovement and balance and, along with the brain carry pulses or “electrical messages.” The myelinstem, is the part of the brain that evolved ﬁrst, sheath acts as an insulator and increases theinherited from our primeval ancestors. It keeps speed and efﬁciency of the pulses.us alive by controlling our involuntary bodyfunctions, including breathing and digestion. DendritesWhat are neurons?Neurons are the cells in the nervous system that Myelin sheathtransmit information by electrochemical signaling.They are the core components of the brain and Axon The sum of its parts Each hemisphere deals with different types of mental activity. The left side deals with logic, numbers, language, lists, and analysis —the so-called reasoning activities. The right side is more visual, and deals with imagination, color, spatial awareness, pattern, recognition, and making sense of the abstract. Most people seem to have a dominant side. The crucial word here is “dominant." It’s a natural preference, and not an absolute. What this means is that when you’re learning something new, your brain prefers to learn in a certain way. It is not so much that you are biologically right-brain- or left-brain-dominant, but that generally you’ve become comfortable with applying one side more than the other. The truth is that in practice you are always using both sides of the brain simply because most tasks demand it, so you shouldn’t get too hung up on this division.
16 Brain potentialWhat is intelligence?Now that we’ve introduced the brain, let’s talk about intelligence or, morespeciﬁcally, what makes you intelligent. Intelligence is a difﬁcult term todeﬁne. It can mean different things to different people. In fact, the scientiﬁccommunity has been debating its meaning for a long time and there is stillcontroversy over its exact deﬁnition and the ways to measure it. The “IQ” test was once regarded as the best way to measure intelligence.However, there is now a general awareness ofits shortcomings, namely, that it only testsspeciﬁc branches of intelligence (seeopposite). The important thing to bearin mind is that being intelligent isnot only about excelling in a narrowacademic ﬁeld, or having a broadgeneral knowledge, or even beinggood at spelling or math. All thosethings require a degree of intelligencebut do not deﬁne intelligence. Rather,intelligence reﬂects a broader and deeperaptitude for understanding multiple thingsin one’s surroundings, for catching on,making sense of things, or ﬁguring outwhat to do in any given circumstance.It’s about possessing the ability toanalyze and evaluate, to imagine andinvent, and, in practical terms, beingable to apply and implementideas successfully.
Introduction: what is intelligence? 17Strands of intelligenceThere are innumerable strands of intelligence, such as thecapacities to reason, plan, solve problems, think abstractly,comprehend ideas, use language, and learn. People’sintelligence may also be characterized by their ability to adaptto a new environment, or their ability to form healthyrelationships, or their capacity for original and productivethought. Furthermore, one could point out more speciﬁc strandsof intelligence. For example, a person who excels in a speciﬁcsport is demonstrating a high level of kinesthetic intelligence,whereas a person who can manipulate melody and rhythmhas high musical intelligence. In that respect, both JohannSebastian Bach and David Beckham could be regardedas highly intelligent people in their respective ﬁelds.The IQ test Brain training and tient,IQ is the acronym for intelligence quo intelligence raland refers to a score given for seve According to research carried out by the University chstandardized intelligence tests. Fren of Michigan, a good brain-training program can the psychologist Alfred Binet developed improve working memory and boost general ﬁrst of these in 1905. He constructed d, problem-solving ability, which can raise general the IQ test, as it would later be calle intelligence. In the study, after recording the to determine which chil dren might need s. The subjects’ mental agility in a variety of cognitive additional help in scholarly pursuit tests, the researchers gave the subjects a series of modern-day IQ test is primarily based on g, brain-training exercises. This mental workout was three intelligences: verbal reasonin given to four groups, who repeated the exercises al numerical reasoning, and visual-spati for 8, 12, 17, or 19 days. After the training the on your reasoning. The system scores you researchers retested the subjects’ intelligence. simple understanding of everyday words, Although the performance arithmetical concep ts, and the ability to of the untrained group recognize shapes and interpret improved marginally, the representational pictures. trained subjects showed a signiﬁcant improvement, which increased with the amount of time spent training. This suggests that a good brain-training program is an effective way to boost intelligence.
18 Brain potentialLooking to learnHow much do you learn from your sense of sight? Well,in general, most experts agree that about 75 percent ofyour learning is through your visual sense. Take babies,for instance. With their inquisitive eyes they pick upbehavior traits by observing the things that peopledo around them; they process and interpret facialexpressions and physical gestures. From a singleglance, babies can tell when their mothers are happyor angry with them. It’s not something that everchanges. Consider two people who go out on a ﬁrstdate. How much attention are they really paying tothe conversation and how much attention are theyspending on reading each other’s body language? The fact that you pick up a great deal of information fromsight isn’t surprising since about 40 percent of your brain isdedicated to seeing and processing visual material. On average,most people know the names of approximately 10,000 objectsand can recognize them by their shapes alone.
Introduction: looking to learn 19Visual senseYour visual sense is key to interacting with the The ability to glean information from moreworld around you. By the time most children are abstract types of visuals, such as tables,six years old, it is estimated that they’ve already graphs, webs, maps, and illustrations, is uniquecommitted to memory the names of a ﬁfth of to the human race. By being able to interpretthe objects they will know in their lifetime. information from such sources, you are ableStudies have shown that visual stimulation helps to ﬁnd meaning, reorganize and group similarbrain development the most, and aids more things, and compare and analyze disparatesophisticated types of learning both when information. In learning, your visual sense isyou’re growing up and during adulthood. undoubtedly the most useful and widely used.Taking instructionThe amazing thing about the visual part of your brain is that once it seessomething a certain way, it tries to develop a memory of it. For example,if you’re trying to learn a dance sequence from watching someone elseperform, your brain will collect the visual information, process it, and thentry to memorize it. You can then use the memory to practice and developproﬁciency. Let’s stimulate your visual sense to learn something new.Seeing is believingTry this. What do you see in the image below? Take a look at the Of course, it’s a maple leaf—the motif image on the right.of the Canadian ﬂag. But look What do you see: theagain. Can you see the two face of a young womanmen who are clearly or a saxophonist playingriled, and head-butting his instrument? If youeach other? Look closely. study the picture for longTheir faces are formed by enough, eventually youthe outline of the top half of will be able to see boththe leaf. The men have very images, and your brain willpointed noses. develop a memory of both. From now on, every time you seethe Canadian ﬂag, your mind’s eyewill ﬂit between the picture of the A visual guide The puzzles and exercises throughout the book have amaple leaf and the two angry strong visual element. Following this principle, you willmen. You tend to learn ﬁnd that the brain-training program provides you withmore when your a constant interplay between words and images. Thispreconceptions have synergy will help you exercise your cognitive muscles thebeen challenged. If you most. In fact, one study showed that those who usedsee something you think you visual presentation tools to convey information wererecognize but it turns out to be 43 percent more successful than those who did not.something else, that’s memorable.
20 Brain potentialWhere are you at?Welcome to the Brain Training program. Before we introduce youto some of the tips and techniques for improving various mentalfaculties, let’s ﬁnd out your current mental agility. The following exercises will introduce you to the type of brainworkout that will primarily stimulate your visual sense, but we’vealso included some nonvisual tests to provide a contrast. You’ll begiven a score for each exercise you complete. Add up the score atthe end to ﬁnd out your current cognitive aptitude. 1. Home and away A: Try to memorize these 9 B: Now try to memorize these simple landmarks in order in 9 household objects in order in 1 minute. Then cover them 1 minute. Then cover them up up and see how many you and see how many you can can remember. remember. Window Radio Toothbrush Wastebasket Book Magazine Frame Plate Grand Canyon Cup Eiffel Tower Statue of Liberty Taj Mahal Acropolis Niagara Falls Egyptian Pyramids Great Wall of China Mount Rushmore 2. Number sequences Work out the next number in each of the following sequences. A: 3, 12, 48, 192 B: 1, 1, 2, 3, 5, 8 C: 2, 5, 10, 17, 26 D: 5, 13, 29, 61, 125 Solutions on p.172
Exercises: where are you at? 213. Building fences 4. Goat, cabbage, and wolfWhich pile of sticks was used to create the fence? A farmer needs to ferry a goat, a cabbage, and a wolf across a river. Besides the farmer himself, the boat A allows him to carry only one of them at a time. Without supervision, the goat will gobble up the cabbage and the wolf will not hesitate to feast on the goat. How can he ferry all of them safely to the other side? B C5. Mental arithmeticComplete this set of mental arithmetic questions in thefastest time possible.A: F K:B: G: L:C: H: M:D: I: N:E: J: O:6. A perfect circle?Is the inner shape a perfect circle, or just a little warped?Look closely. perfect circle warped Novelty factor What makes good mental stimulation? The answer is challenge, novelty, and variety. Don’t do only numerical exercises because that will only stimulate your number- crunching skills, and if you concentrate only on crosswords, it will ﬁre up only your aptitude for language. And if you only look at words and numbers, that won’t spark your visual and spatial awareness. Returning to the fairground not just the ones that you are good at or like the most.
22 Brain potential7. Personal diaryWrite down two speciﬁc things you did ... A: Yesterday B: C: D:Note: you’re not allowed to write the same things.8. Dog and bone 9. Light switches Solutions on p.172
Exercises: where are you at? 23 10. Speed reading Read out loud the following passage as fast as you can and try to articulate every word. Examining how you react in a give n situation You are deﬁnitely not saying might be a useful way to understa that “this is nd thoughts and what will happen under the feelings you ﬁnd difﬁcult to put into se circumstances," words. It might but you are holding it up as give you an insight into your own a mirror to yourself, deeper motives, and noting the sorts of beliefs and enlighten you to personal anxi , expectations, eties and frailties feelings, judgments, and anx that you might have not been cons ieties that you may cious of before. well ﬁnd yourself bringing to You can access these emotions by such a situation. creating or Putting something into this ﬁnding a story or parable that is clea framework makes rly ﬁctional, but it easier to describe your con nevertheless has some parallels to cern to others, and a real situation may increase the range of me you are facing. Ideally, you would taphors and images read it to yourself you can naturally use when (or you could draw your own pictu talking to others. re, whichever Should some areas of the sto you prefer doing). ry summon strong If you choose to create your own, negative feelings, this may you don’t suggest a need for have to be a good drawer or writer ﬁnding positive ways to han (stick ﬁgure dle similar feelings in drawings or amateur narration wou the real situation for instanc ld sufﬁce). It e, getting a colleague isn’t necessary for anyone else to to help you out in situations see or read your you may not handle work, although it is usually more prod too well. Similarly, if you ﬁnd uctive if you yourself being can get someone else’s perspective judgmental or negative abo or reaction. ut someone in your Because the story or picture is not story, you may need to dev a description elop ways to see such of your actual situation, you are at people more compassionate liberty to be ly. creative—you can make things hap In time, you may become aw pen as you wish are of cultural them to; you can present things in assumptions and expectatio particular ways ns—what “ought” or just because they “feel right." You “ought not” to happen by you can note what r (but perhaps not has to happen for you to feel com other people’s) conventions. fortable.Beneﬁts of reading aloudModern brain-scanning techniques such as fMRI (functional people don’t often do whenThere is intense activity in areas associated with articulation Children, in particular, should beand hearing the sound of the spoken response, which encouraged to read aloud becausestrengthens the connective structures of your brain cells for the brain is wired for learning through connections that are created by positiveconcentration. Reading aloud is also a good way to developyour oratory skills because it forces you to read each and and reading aloud.
24 Brain potential11. Spot the differenceStudy the picture on the left for 30 seconds. Then coverit up and circle the 6 alterations made to the samepicture on the right. = 3 points12. Numerical jigsaw 13. Visual logic test Look at the set of pictures below. Which one doesn’tsymbols. Rearrange these strips in the quickest time belong in each group?rows. In each equation, operations are done horizontally. AWrite the correct answers in the grid provided. A A B B B C C C D D D = 3 points correct answer
Exercises: where are you at? 2514. Manhole covers 15. Moving by degreesWhy is it better to have round manhole covers than If the hour hand on a clock movessquare ones? Look at the picture and think about it. It’s 1⁄60th of a degree every minute,not a trick question. There is more than one answer. then how many degrees will the hour hand move in one hour?16. Motorcycle parts 17. Straight lines?Which of the four options has exactly the right parts Are the two horizontal lines straight or curved?to complete the motorcycle? straight curved A B Did you know? Generally, it’s accepted that brain function naturally starts unlike athletes being at their physical peak and then having to work harder to keep ﬁt as they get older. The good news C D is that there’s no need to worry. The size and weight of your brain remains roughly the same until you reach 90, providing that you keep it active. In fact, there’s no reason to believe that you can’t keep your brain lively throughout your life by giving it new experiences, challenges, tests, and puzzles. These improve cell connections so that your brain’s overall function remains sound Solutions on p.172 regardless of your age.
26 Brain Potential18. Abstract artWhat you see on the right is theRey-Osterrieth Complex FigureTest. Neurologists commonly useit to assess a patient’s memoryand attention span. Look at the ﬁgure and copy iton a separate sheet of paper. Thisshould help you memorize thedetails. Then cover up the originaland the copy, and begin drawingit from memory on a piece ofpaper. You have 1 minute to drawas much of it as you can. Howmuch of it can you recall?19. Magic square 20. Color mazesThe numbers in all rows, columns, Find a path from the bottom left to the topand both diagonals of the grid add right that passes through an equal number of squares of each (nonwhite) color. To thenumbers 1 to 9; a number cannot right is a solved example.be repeated. We’ve ﬁlled threesquares. Fill in the missing numbers: Note: the line passes through two yellow squares, two red squares, and two blue squares. 6 A: B: C: 5 8
Exercises: where are you at? 27 21. A perfectly boiled egg You want to boil an egg for 15 minutes. However, you have only a 7-minute and an 11-minute egg timer at your disposal. How can you ensure that you boil the egg for exactly 15 minutes using only these two timers? Write your answer down on a separate sheet of paper. 22. Spot the odd picture In the list below, can you identify the picture that doesn’t belong in each of the groups? 23. Odd word out A bear cat tiger dog ﬁsh A B stream pond lagoon lake C cotton wood stool metal B D lawn thicket forest jungle E Chepre Cyprus Corfu Zypern C correct answer D How did you do? It’s time to add up your points. Turn to pages 172 and 173 for the answers and ﬁgure out your score. There is a total of 100 points up for grabs. YOUR SCORE: /100 E How well have you done so far? Has your score impressed you? Did you perform well in some areas and moderately in others? That’s only natural, because it’s uncommon for a person to be equally good at numerical reasoning and verbal reasoning, for example. Bringing all your brain activities up to the correct answer level of their highest potential is what this book is for. Now continue to ﬁnd out how to hone each mentalSolutions on p.173 faculty with tips, techniques, and more exercises.
30 MemoryAll about memoryDoes our memory play tricks on us? It might seem so when we canvividly recount a happy or poignant episode from our childhood, yetfail to remember the name of someone we met only yesterday. Orwe might be able to recall the entire lyrics of a song recorded by ourfavorite band, yet forget something as simple as which way to turna screw to loosen it. Why is our memory selective? Is it because ourmemory has a limited capacity, and so, consequently, we somehowprioritize what information to keep and what to discard? If this isthe case then is it possible to ﬁnd ways of boosting our memory?Perhaps we should address these questions once we ﬁnd out whatmemory actually is.What is memory?Memory forms a key component of your intelligence. Everythingyou learn in your lifetime is organized and stored in someway. The efﬁciency with which you access thisinformation is what deﬁnes whether you havea good or bad memory. Scientists have spent much time seeking thelocation in the brain where memories arestored, identifying the hippocampus andrhinal cortex as possible sites (see p.43).However, contrary to what many of usmight think, the latest research suggeststhat memory cannot be pinned down toany single part of the brain. In fact, it’sfalse to think of memory as a storagefacility crammed with everything youhave ever learned, and a place youdelve inside when you want toretrieve a piece of information. Memory isn’t a place, it’s an activity, anexperience: when you remember something you are actually reconstructing it from details youconsider important. Your memory is selective andinterpretive, and the mechanisms driving it are spreadthroughout the brain. Two people who witness thesame event can give entirely different accounts. Inshort, you remember more clearly what an eventmeans to you than the actual details.
Introduction: all about memory 31Can memory be boosted?Absolutely! Memory can be exercised, improved,and nurtured. The information your memoryretains is inﬂuenced by the meaning you attach toit. For example, you are more likely to remembersomething if it is linked to a personal experienceor emotion. You can boost your memory by givingthe information you wish to memorize strongermeaning and associations. Memory works by: making something memorable organizing and then storing that piece ofmemorable information retrieving it accurately at any given time.Memory mythThe myth we tend to hear most is that memory psychology author Tony Buzan reminds us:deteriorates as we get older. This is false. If the “senior moments are more to do with absentbrain is stimulated regularly, it can actually mindedness than absent memory.” The bestimprove with age. People in their 80s and 90s powers of recall do not necessarily belong to the can possess the young but to those who continue to hone their same memory cognitive skills throughout life. Older people power as people who engage in mentally taxing work, learn new half their age. skills, and keep physically active are likely to be in Brain cells don’t better mental shape than a younger person who die off as we get doesn’t do these things. Brain training offers a older. As good cognitive workout. So here’s your chance to exercise your brain and boost your memory. Turn over to learn some killer techniques.The memory champsAt the annual World Memory Championships, contestants the previous world record ofbattle it out to see who has the best memory. In truth, 31.16 seconds set by Andi Bell.these people are no smarter than you or me; they just take Two years earlier Dr. Guntherthe time and make the effort to memorize information Karsten from Germany memorized ausing a variety of mnemonics, or memory strategies (see 1,949 digit number in an hour—andp.33). For instance, by using the Journey Method (see recalled it in under two hours. Thesep.36), memory champion, Ben Pridmore memorized a guys prove what the memory is capableshufﬂed deck of playing cards in 26.28 seconds, beating of if you apply the right techniques.
32 MemoryHow does memory work?Before we introduce you to the tips, let’s look at three types ofmemory you possess to receive and keep track of information.Sensory memoryYou receive information from thesenses, such as sight andhearing, and hold it forone or two secondswhile you process it anddecide what to do withit. What you ignorequickly fades andcannot be retrieved, much assound dissolves. Remember howyou can sometimes catch an echo of a sentence, or aglimpse of someone you sort of recognize when you’re notreally paying attention, but then, in an instant, it’s gone.Short-term memoryIf you pay attention to something, the details are thentransferred to the short-term memory, which can onlystore up to seven pieces of data at any one time. Forinstance, using this memory you can remember thedigits of an internet bank account or a pin code foronly as long as it takes for you to key it in. As soon asthe short-term memory is “full,” it only takes a new piece ofinformation to dislodge an old one because the neural mechanisms,(the meanings and associations) have not been created to allow you to recall the information later on. Some scientists believe that evolution has shaped this memory to have a limited capacity. Can you imagine if you were able to retain all the visual information you picked up in a day? What would happen if you kept a memory of every stranger you walked past and every sign you read? Well, your brain would eventually suffer from data overload. The advantage of a limited working memory is that it allows you to prioritize and focus on the task at hand.
Feature: how does memory work? 33Long-term memoryWhat makes information cross over to long-term memory? Any informationcan be committed to this memory through the process of rehearsal andmeaningful association. Once processed, the information can be recalledweeks, months, or even years later. To make this effective, you must make asmany links as possible to increase the number of starting points for retrievingthe memory. Links are established when you cogitate, review, and analyzeinformation. Association, in particular, relies on your visual memory (demonstrated with the Journey Method on p.36), which is an effective way of recalling a list of disparate items. One thing we do know about memory is that if it is linked to a personal experience or emotion it is more likely to be recalled. If you’re not convinced, then think of a birthday. Which do you remember: your 10th, 15th, 18th, or 21st? Chances are it’s your 18th or 21st because of the signiﬁcance. Memory aids the process the brain is very good at ﬁnding of forming mental connections is what our patterns and thinking to an order. The numbers brain naturally does to make sense of things. 7 1 9 3 11 5 might seem hard to remember, Information can be recalled more easily if you can but reorder them to 1 3 5 7 9 11 and it relate it to an idea or object that you are familiar becomes much easier because the brain spots with (association), or if you can create a mental the sequence order instantly. picture of it, as with Mind Maps (see p.62). use more of your senses than just without review, most people can sight: engage hearing, smell, taste, and touch only recall about 20 percent of selected to process information and make the memory material after a 24-hour period. Students can trace stronger and longer-lasting. signiﬁcantly improve their learning by simply it is easier for your memory reviewing material once after class to clarify to recall information if you create rhymes, and conﬁrm what they have heard, and once sentences, or bizarre imagery to jog your again later that day or evening. Reviewing memory. The ﬁve American Great Lakes for material regularly will transfer information example can be “HOMES”—Huron Ontario to your long-term memory. Michigan Erie Superior. of all memory techniques, these can be a good “explanation” works best. When possible, put way to memorize lists and the ordering of things into your own words. The combination things. For instance, to remember the planets of having the idea in your head and the words in our solar system, you might use the to express it is synergistic, creating a better following: My (Mercury) Very (Venus) Educated understanding of the information, and (Earth) Mother (Mars) Just (Jupiter) Served signiﬁcantly improving your ability to recall it. (Saturn) Us (Uranus) Noodles (Neptune).
34 MemoryMemory testersTry the following exercises. Notice how much you rely on yourvisual memory to answer the questions.1. This is your lifeThe following questions will test your long-termmemory. Answer as many as you can.A: What did you have for breakfast this morning?B: Where were you last Sunday afternoon?C: Where were you at midnight last New Year’s Eve?D: How did you celebrate your 21st birthday?E: What was the last movie you saw?F: Where were you when Barack Obama was declaredPresident of the USA?2. Attention to detail Photographic memoryMost of us are familiar with the enigmatic smile of Photographic, or eidetic, memory is a speciﬁc phenomenonthe Mona Lisa but can you answer the following: in which people can remember perfectly anything they have seen. This memory usually fades, but it can be so accurate as to enable somebody, after seeing a picture of 1,000 randomly A: What color are sprayed dots on a white sheet, to reproduce them perfectly. her eyebrows? For instance, a journalist called Shereshevsky noted that he could remember innumerable words and long number sequences after seeing them for only a few seconds. His memory appeared to be photographic and perfect. He could recall great chunks of information forwards or backwards even after a gap of 15 years. He used all his senses, as well B: In the pose, does as association and other mnemonic techniques to make the her right hand rest information he received meaningful. on her left hand or But it came at a price! Shereshevsky is it left over right? found it hard to hold down conversations and perform other tasks that required him to use his ﬂuid intelligence, because the information in his photographic memory set off an uncontrollable train of distracting associations. Solutions on p.173
Exercises: memory testers 353. Number recall How to never forget a faceStudy the numbers below for 1 minute and then Why do we forget someone’s name immediately after beingcover them up. Try to use ordering technique (see introduced to them? Think about it: “this is Nina Dawes.”p.33) to organize the information. How many numbers Taken in isolation these words are meaningless. In addition,can you recall? the name has no real “connection” to the face. For instance, if a person’s name was Mr. Buckteeth and he had large teeth, then it would be easy to remember. In times gone by, names were based on memory and association: 7 12 45 6 17 3 19 77 the man banging the anvil for your horse shoe was Mr. Blacksmith and the man selling you the leg of lamb was 11 9 97 68 21 55 Mr. Butcher. Today you have to recreate that image and association to store the name. So here are few tips to 34 83 24 67 87 help you remember: 5 37 84 90 increases memory capability 12 15 23 16 45 association. In our example, you could associate the ﬁrst name 79 “Nina” to the sound an ambulance makes and link the surname to the classic rock group The Doors, to help you remember it.4. Spot the changesStudy the picture on the left for 1 minute. Then coverit up and circle the 6 alterations made to the samepicture on the right.
36 MemoryThe Journey Method 1 Front door: a bandaged dog sits on the frontThe Journey Method or Method of Loci (to use doorstepits original name) is a technique for memorizinglong lists of items. It has been practiced since theancient Greek era, a time when long speecheshad to be recited without recourse to notesbecause paper was such a luxury. The method is a type of mnemonic link systembased on memorizing items along an imaginedjourney or series of locations (loci) that are familiarto you. You do this by associating the object witha point in the imagined location or journey. Since START YOURthe human brain thinks more readily in pictures, it MEMORYis able to recall a disparate list of items a lot easier JOURNEYthan if the information was memorized by rote,for instance. HEREHow does it work?Start by plotting out an imaginary journey withlandmark points along the route. Do bear in mind thatyou will need to have visualized the journey beforehand 8 The fountainto use this technique effectively. The landmarks (points is spraying outof reference) have to be crystal clear before you hook lettersany information on them. The characteristics of theimages you choose are very important for the techniqueto work. They should be unusual, vivid, striking, surreal,incongruous. The goal is to make a memorable picture. The diagram opposite is an example of a route.We have dotted items from the to do list at key pointsalong a stroll that starts outside a house. We pass apark bench, a pond, a large tree, a school, a ﬂowerstall, a bridge, and ﬁnally a fountain. These form thekey “landmark” points, which are immutable, althoughothers can be added as you become familiar with theroute. The list items have then been associated witha subject, an activity, or an object at the key points.For instance, the man on the park bench with thestethoscope is the mental trigger to book a doctor’s 7 A sailingappointment, a duck sporting a mohican relates to boat passesthe hair appointment, and so on. under bridge, sail stitched from itemsWhy not conceive your own journey and see how many of clothingitems you can recall from your own list of things to do?
Technique: the journey method 37 2 A man sat 3 The pond in on the park the park has a bench with duck with stethoscope a bright around his mohawk neck haircut. 4 A tree in the park has been struck by lightning TO DO LIST1 Give dog medicine2 Book doctor’s appointment3 Go to hair appointment4 Pay electricity bill5 Buy milk 5 A teacher6 Buy birthday card for Mom outside the school7 Hang out washing is drawing a cow8 Mail letter on the blackboard Mega memory Memory experts believe that by applying the Journey Method a 6 The woman person with ordinary memorization at the ﬂower capabilities, after establishing the stall is wearing route stop-points of their own a birthday “Journey,” can use it to remember the cake hat sequence of a shufﬂed deck of cards with less than an hour of practice.
38 MemoryExpanding visual memory5. Memory connectionsStudy the list of words below for 2 minutes and tryto memorize as many as you can: see if you can use theJourney Method to commit the words to memory. Thencover up the list. Book Hand And A: Now, on a blank piece of White Work Time paper, write down as many of the words as you can, and in the right order. If Candle Hold B: Can you remember the ﬁrst two words of column 1?Visual memory C: Can you recall the exactHow did you ﬁnd that exercise? Were central word spatially?some words easier to memorize thanothers? You might have found that itwas harder to remember words that D: Can you remember thewere not nouns because they were last word in the ﬁrst column?more abstract and did not lendthemselves to a visual translation. We E: Can you remember the lastare able to place in our visual memory word in the second column?information such as objects, places,animals, or people, and access themmore readily. A simple exercise such F: Were any words repeated?as this proves how effective our visualmemory is. Some psychologists referto it as the “mind’s eye.” Try the G: Can you remember theexercises on the ﬁrst word in the last column?next page, whichincorporate a visual H: What is the longest word?element, and seehow you do.
Exercises: expanding visual memory 396. Can you remember?Study the pictures below for 2 minutes and then coverthem up. Try to memorize as many as you can using the A: Can you remember the ﬁrst threeJourney Method (see p.36). images of column 1? B: Can you remember the central image? C: Can you remember the last image? D: How many animals do you remember seeing? E: Were any images repeated?7. Sporting chanceAllow yourself 1 minute to memorize the athletes, thencover up the pictures. Now answer the questions. A: Are the athletes facing left or right or both directions? B: How many sports shown involve water? C: What is directly above the basketball player? D: How many athletes are using equipment?
40 MemoryPegging 1. Light bulbPegging is a slightly different technique fromthe Journey Method. The link system of the 2. A wrapped presentJourney Method works brilliantly for somepeople but not as well for others. The problemfor some can be that if they forget a point inthe journey they break the chain link, lose 3. Bunch of ﬂowerstheir cue, and it is hard to continue. Thisdoesn’t occur with Pegging. Pegs, like those in 4. Model traina cloakroom with coats and hats hung onthem, have information hung on them, andthey are independent of each other. 5. Travel brochureA preference for pegsThe beneﬁt of pegs is that they provide anunmovable, stable support for whateveryou are trying to memorize. A peg can be 7. Bicycle pumpanything that you already know well andto which you can link new information. 8. CoatThese pegs are known as loci—a location hangerwhere you can mentally position a pieceof information you need to recall later. 6. EnvelopePegging pi (π)Let’s say you had to remember the number 31 41 5926 53 (the first 10 digits of pi (π), but it could equallybe a phone number or items on a list). Your first five 9. Printerloci could be things in your garden: Gate, Lawn,Path, Washing line, and Tree. You then convert thenumbers into other concepts using another memorytechnique: association. For instance, outside thegate you could have a bird (rotated “3”) landingon a perch “1.” The garden could have “4” childrenplaying with a toy shaped like the number one (1),and so on and so forth. This may sound ridiculous but with ﬁve strange butmemorable images you have learned pi to 10 decimalplaces. In our illustrated example, the pegs are partsof the body (something you’re unlikely to forget) but 10. Car engine oilthey could be objects within the rooms of a house(or just the rooms themselves).
Technique: pegging 41SHOPPING LIST Imagine Imagine wrapping your screwing a nose in brightly large light bulb colored paper. into the top of Maybe add a your head. bow on the end. Imagine lots Imagine a of ﬂowers necklace in the blooming on form of a railway your shoulders. track with a little Can you smell model train the sweet whizzing round it. fragrance? Imagine balancing Imagine a huge stack of wrapping your letters on each chest in holiday of your hands. Try brochures. not to drop any. Imagine the feeling of a bicycle pump Imagine coat pumping your hangers attached stomach up to your belt. through your belly button. Imagine the printer gripped between your Imagine you knees (hear the are standing noise it makes; in a pool of oil. see sheets of paper ﬂuttering to the ﬂoor).
42 MemoryMore memory games8. Peg that memoryLook at the illustrations below for one minute and try to memorize theitems. Then cover up the pictures and recall as many as you can. Try to usethe Pegging technique (see p.40) by imagining the items dotted around inyour favorite room.9. Noble tastesThe Knights of the Round Table are talking about their favorite vegetables.Study the diagram opposite for 2 minutes and then cover it up. Try to usean acronymic phrase to remember the knights (see p.33 for moreinformation on acronymic phrases). King Arthur AgravainA: How many knights are present? Lucan BedivereB: What is Sir Lucan’s favorite veg? broccoli cabbage parsnip pea Tristan CaradocC: Whose favorite is cabbage? carrot potatoD: Who is sitting to the right of the cauliﬂower turnipperson whose favorite vegetable is Dagonet Percivalcauliﬂower? zucchini spinach pumpkin cucumberE: Which two knights have names Lancelot Dinadanbeginning with D? Kay Galahad
Exercises: more memory games 4310. A sizable matter 11. Where was that?Below is a list of random objects. Study the list for Memorize the positioning of the arrows on the 4 x 41 minute and then cover it up. Try to use the ordering grid below for 20 seconds, then cover up the diagram.technique (see p.33) and recall them in terms of size,starting with the smallest. Skyscraper Dinosaur Bus Coffee mug Human being Laptop computer Helicopter Assuming the grid runs from 1–16, left to right, horizontally, where are the arrows placed? A: 3, 6, 9 B: 4, 6,11 C: 5, 10, 1212. Evocative sensesEngaging the other senses besides sight, study the images below for1 minute and try to memorize them. If it is a food item, recall how ittastes; if it is a musical instrument, remember the sound it makes. Now Memory and smellcover up the images and see how many you can recall. Smell is a highly effective prompt to tap forgotten memories. Have you ever caught a whiff of wood ﬁre or a perfume and found yourself transported to a time in your past completely out of the blue, or even remembered an old lover? Scientists believe that there is a cortex close to the limbic system that started out as a “smell brain” and evolved into an “emotional brain,” which is important for memory. It is called the rhinal cortex. Therefore, the connection between smell, emotion, and memory has an anatomical basis. Smell-evoked memories might seem clearer or more intense than other memories because they appear to be more “emotional” than memories triggered by visual, audio, or other types of cues. Studies suggest that while smells evoke memories that may feel more Solutions on p.173 powerful, they don’t help people recall more information, or speciﬁc details.
44 Memory 13. Sewing patterns Take 1 minute to memorize the pattern on each grid below. Then try to recreate it on the grid provided. How many strokes can you remember accurately?A: strokesB: strokes
Exercises: more memory games 45 14. Memory math 15. Olympic colors A C E B D =2 =4 =6A: A: D: E: + + =B: + + ÷ = Dreams: the perfect memory?C: + + × = 16. DIY dilemma Solutions on p.173
Chapter 3Visual reasoning and spatial awareness
48 Visual reasoning and spatial awarenessThinking in picturesJust consider the work your brain does when you walk to thelocal store to pick up a grocery item. Every step you take, youhave to use 3-D visualization to navigate the space to make sureyou don’t bump into other people or objects. The task becomeseven more complicated when you’re driving a car. Things movefaster and you have to use predictive vision to determine whereall the other road users might be at any given moment. You use visual and spatial reasoning within days of beingborn. Your visual cortex begins to adapt to light right after birthand, within weeks, you’re able to separate your parents’faces from the myriad colorsand shapes around you. Atthis stage, nothing fascinatesyou more than your mother’sface. Then, as you growolder, you play many gamesto develop your visual sense.For example, when you aretrying to complete a jigsawpuzzle you have to ﬁgureout how to put the piecestogether to recreate thepicture on the front of thebox. The way the differentshapes ﬁt together honesyour ability to reason,deduce, analyze, andsolve problems.Spatial awarenessVisual and spatial thinking is, of course, important inmemory—consider how taxi drivers navigate their waythrough the tangle of city streets. But it’s also a vital skillin many other professions. Any line of work that involvescomplex design and arrangement, such as architecture orurban planning, demands visual thinking. The peoplewho work in these ﬁelds rely on their ability to presentideas diagramatically. On a much smaller scale, if you’replanning a day outdoors and need to ﬁll a picnic hamper,you will have to visualize how to ﬁt the food, plates, andutensils into the conﬁned space before you begin loading.
Introduction: thinking in pictures 49Recognition factorSome people are blessed with these skills, others need to put moreeffort into sharpening that area of their brain. But there are ways inwhich visual and spatial intelligence can be developed. The ﬁrstthing the brain has to do with visual information is recognize it.1. Overlapped objectsBelow are pictures of three objects overlapping each other.Can you ﬁgure out what each of the images are?A: B:Objects: Objects:1 2 3 1 2 3C: D:Objects: Objects:1 2 3 1 2 3A camel’s head? Food trailDoes the shape on the right mean In ancient times visualanything to you? Could it be a camel’s intelligence used to behead, or the head of another animal? much more importantIf you recognized Africa tilted 90 to survival than verbaldegrees counterclockwise, intelligence. Forcongratulations—you’re in a minority. instance, the abilityBut if you didn’t, don’t worry—not to deduce thatmany people instantly identify shapes animal footprintsthat have been tilted away from their might lead to foodnormal axis. is a human trait that developed Solutions on p.174 during that time.
50 Visual reasoning and spatial awarenessSeeing is learningIn contrast to other types of reasoning—such as numerical andverbal reasoning—visual reasoning is not something directlyaddressed in most education systems. This may be because itis already used in a variety of subjects, such as art, sports, math,and music, so perhaps there seems little point in isolating it, asyou would do with verbal reasoning (languages) or numericalreasoning (math), to develop that particular mental faculty. Asa result, most people never learn how to realize their full visualthinking potential. What’s more, some psychologists suggest thatthe education system is at fault for labeling many visually giftedchildren as deﬁcient because they do not ﬁtinto a verbally geared education system.Enrich your spatialintelligence Bene of vi ﬁts sAlthough your spatial reasoning skills are thin ualcalled upon all the time, it is usually for kingtasks that you do repeatedly, such aswheeling the shopping cart throughthe aisles of the supermarket orperforming a parallel park on thefamiliar space of your driveway, and Visual thinking is a provenyou tend to operate on autopilot. method of organizing ideas In doing so, you rely on and ﬁnding coherentyour spatial memory rather than solutions to problems.stimulate your spatial intelligenceto tackle new spaces, shapes, Visual thinking techniquesforms, and dimensions. A simple improve memory, focus, organization, critical thinking,and efﬁcient way to improve your and problem solving.spatial intelligence is by doing a 3-Dmechanical puzzle, such as Rubik’s cube.In addition, research has shown thatplaying video games has a marked effecton overall spatial awareness (see p.55).For those of you who aren’t big on shoot‘em ups and racecar simulations, there are other simple ways to sharpen your spatial aptitude; see “Tips” opposite.
52 Visual reasoning and spatial awarenessVisual teasersThe following puzzles have been designed to exercise yourskills of image and pattern recognition. There are others thatwill hone your concentration and test your logical aptitude.2. Guess the pictureWhat would you see in the picture if you assembled thepieces together? Description:3. Triangle test 4. Spot the ﬂipper 5. Cake for eightHow many right-angled Take a look at the three shapes. Each one is How do you cut a cake intotriangles can you create in exactly the same but one has been ﬂipped over 8 equal-sized pieces withthis ﬁgure by connecting so that you can see the other side. For each only 3 cuts?any 3 dots? question work out which shape has been ﬂipped. B A 1 2 3 1 2 3 1 2 3 1 2 3 D C triangles Solutions on p.174
Exercises: visual teasers 536. Reversed digits 7. Quick-speed countingCircle the numbers below that have A: Count the number of times the numberbeen reversed. “6” appears below. B: At the same time, count the number of “3”s: times both “3”s and “7”s appear in the sequence below (don’t just count all the “7”s: “3”s, and then the “7”s). 1234467889974674657865876576576 3576573625432657346578436578342 2732188582735827456724687343828 7672878682768723682376783768267 2647648823178346432764876774653 3456 7436574386581483627868653878. Largest circleIf the circles represented by arcsA, B, and C were completed, whichwould have the greatest diameter? A A B Mozart effect: does it work? C So does listening to certain types of classical music B increase spatial reasoning and improve visual recognition? The “Mozart effect” was ﬁrst mooted C in the ﬁeld of childhood development in the early 1990s. The term comes from a study that claimed that since neurons ﬁring in speciﬁc patterns can lead to an increase in intelligence, music could be used to activate those patterns because the brain responds to speciﬁc sound frequencies. The researchers conducting the study maintained that when children receive musical stimulus their brains form connections between neurons in patterns that also help them with spatial reasoning. However, a number of followup studies have found no such correlation. In fact, many cynics believe that the media has exaggerated and distorted the claims.
54 Visual reasoning and spatial awareness9. Straight or crooked? 11. Largest parcel?Is the line across the corner of the cube straight Assuming that the shapes below areor crooked? 2-D, which of them has the largest surface area? A B C D EStraight: Crooked:10. Phony imageWhich 2 of the 6 cropped images donot belong to the picture below? A B C D E F
Exercises: visual teasers 5512. Sharp fox 14. Solitary snowﬂakeHow many triangles can you count All of these snowﬂakes appear twice except for one.in the picture of the fox? Circle the snowﬂake that only appears once. triangles13. Counting starsStudy these overlapping stars and then answer thequestions below. Video games Video games are excellent for developing visual awareness. For example, recent studies show that they can signiﬁcantly improve a surgeon’s dexterity when performing operations. Also, playing video games has been shown to increase short-term memory of subjects in test groups. The reason for this is that most games require players to distribute their attentionA: How many stars can you see? across the screen quickly in order to detect and react to changing events. In fact, playing videoB: How many triangles can you count? games may trigger previously inactive genes that are crucial for developing neural pathwaysC: How many stars does the largest star necessary for spatial attention. Researchoverlap? is now suggesting that playing video games could even increase attention Solutions on p.174 spans rather than reduce them.
56 Visual reasoning and spatial awarenessReading mapsMap-reading tests your spatial reasoning skills. It’s a step up from simplevisual recognition because not only do you have to identify symbols on a2-D surface but you also have to relate that information to the physicalspace the map is referring to. It’s a skill that combines reading, mentalrotation, and mathematics to improve your overall spatial awareness. When you’re reading a map the right hemisphere of your brain isactivated to help you stay oriented and navigate space. Studies haveshown that map-reading can increase the size of the hippocampus—akey area of the brain that is responsible for spatial memory (see p.14).It is no surprise then that the size of the hippocampus in taxi drivers Sharkis generally larger, and that size actually varies according to the time Islandthey have spent in the job. More crucially, these studies suggest that you can develop yourspatial reasoning skills. Even if you consider yourself inept when itcomes to reading maps, it is a skill you can master with practice. The C avesIf you work hard at developing your map-reading skill, in timeyou’ll be able to relate map symbols to terrain quickly, aswell as identify key information from the map to maneuverthrough unfamiliar surroundings. Equally, if you rely toomuch on satellite navigation systems, your hippocampus Palmwill not be activated and your spatial memory will not Beachhave a reason to develop.15. Find the treasureThis is a fun game to test your map-reading ability.The picture you see is of a treasure island. A treasure A B Cchest is buried somewhere on it. A map showing itslocation has been cut into nine pieces, which arerandomly distributed over the page. “X” marks theposition of each of the nine landmarks on the island, D E Fand the location of the treasure is marked with a coin.Your aim is to mentally assemble the pieces by squaringeach piece with the picture and drawing it into the grid. G H IYou’ll then be able to identify the square where thetreasure is located.
Feature: reading maps 57The A ncien t Fore st The V olcan o The L ighth ouse The V illage The R iver M outh The S hipwr eck Solution on p.174
58 Visual reasoning and spatial awarenessMental rotation puzzlesThe following puzzles and exercises are slightly more difﬁcult. Theywill not only test your visual recognition skills but also your ability toaccurately visualize objects in 3-D and perform mental rotation.16. Origami enigma 17. Shape shiftingIf you fold the image along the dotted line, which shape If you rotate this shape 90° in a clockwise direction,would you see? which of the four shapes would you see? A B A B C D C D18. Stacking mosaic tilesIf you placed these tiles on top of each other, starting withthe largest at the bottom, which image would you see?A B C D Solutions on p.174
Exercises: mental rotation puzzles 5919. Squaring up 21. False patternThese shapes have been cut out of a square. However, Look at the pattern on this teacup. Now look at the fouran extra shape has been added to the assortment. Can options below—which of them does not haveyou identify the rogue shape? the same pattern? A B C D A B F E C D20. The correct cubeIf you folded the template into a cube, which of the four Men and womenoptions underneath might you see? There are subtle differences in the way men and women mentally visualize objects in 3-D. Scientists have discovered that there is a region in the cerebral cortex called the inferior parietal lobule that is responsible for processing spatial information and is generally larger in men than in women. Does this mean that women have poor spatial awareness? Not at all. Many women are fantastic at math and physics. Only when you analyze large populations for slight but signiﬁcant trends do you see any difference.A B C D
60 Visual reasoning and spatial awareness22. Perfect ﬁt 23. On a rollIdentify the correct piece from the selection below that If you rotate this shape 90° in a clockwise direction,completes the cube. which of the four shapes will you see?A B C D A B C D24. The vanishing area 25. Spinning blossomWhen the same pieces are rearranged to form the When rotated 180º in a clockwise direction, what doessecond triangle, a gap emerges. Can you explain the the ﬂower head look like?change in the size of the surface area? A B C Solutions on p.175
Exercises: mental rotation puzzles 61Visual thinking and to create meaningful new ideas and methods. The practice of visual thinking to solve problems,the imagination work through issues, and communicate clearlyDon’t think of a pink elephant. You couldn’t has been fundamental to human progress in everyhelp it, could you? Our guess is that you’ve civilization. You don’t have to be an artist to thinkjust pictured a pink elephant. This is a simple visually. It’s all about paying closer attention to experiment to prove your inner eye, seeing beyond the obvious, two things: one, and entertaining brand new ideas. that imagination is synonymous with the mind’s eye, and two, we are all blessed with the ability to visualize beyond what is real.Creative thinkers, such as painters andﬁlmmakers, rely on their ability to generateconcepts in the visual form. They cast theirmind’s eye into the vast sea of endlesspossibilities and try to search for originalsolutions to old problems. This abilityto visualize allows them to transcendtraditional ideas and ingrained conventionsCapture the daydreamNext time you catch yourself daydreaming, try to grab What you will have done is echo thethe moment by writing down the details. You’ll ﬁnd that beginnings of the creative process. It isyou’re describing a series of images. Or, if you can, keep an example of the kind of visual thinkinga pen and some paper by your bed and, as soon as you that people working in creative industrieswake up, note down what you can remember of your often do. You too can get the most outdreams. You might ﬁnd yourself describing a set of of your imagination. Refer to Chapter 4 tosurreal pictures that make no logical sense. learn ways of boosting your creative thinking.
62 Visual reasoning and spatial awarenessMind MapsA Mind Map is a useful visual tool forexploring and examining an idea, a task, or aproblem. Invented by psychology author Tony Advantages?Buzan, it is a diagram that you produce bywriting down all the elements of the givenproblem, which branch out from a central keyword or idea. The aim is to organize disparatethoughts into a coherent whole.The beneﬁts of Mind MapsMind Maps offer ﬂexibility of thought, since you ?are visualizing a problem in a radial, graphical, ho Wand nonlinear manner. They also call on your logical and creative skills, thereby demanding work from both sides of your brain. In addition, a Mind Map allows you to see the whole picture at once on a single page. You’ll ﬁnd that your brain has a natural inclination to look for patterns and completion. at? WhHow does it work?The elements are arranged instinctively,according to what you consider important,and these sprawl out on the page via curvedbranches. A typical Mind Map starts with asingle word or idea placed in the center, towhich associated ideas are added. Although An exampleyou take a brainstorming approach, you place Philippa is considering a career change. She is thinkingall the ideas into speciﬁc groups. You can usedifferent colors to separate these groups. remains uncertain. She draws a Mind Map to help her make the right choice. Her central question is: Do I wantMost Mind Maps have three crucial parts:that carry collateral information
Feature: mind maps 63 Association: think of everything you canDis associate with any of the headings and write ad v them down along the branches. You’ll ﬁnd you ant start thinking of some related ideas. Start a sub-branch where you think it ﬁts best and put age ? Why down all these ideas as well. You might want s? to use a different colored pen for the new branch. Soon, you will ﬁnd your brain trying to make connections between all the ideas you write down. w? Ho Analysis: look at what you’ve drawn. Which branches ? contain more information? ere Wh Where are the uncertainties? Use the diagram to reﬂect on your thoughts. This may lead you to start another Mind Map. When ? Whatever action you decide to take, the process of Mind Mapping will have helped you generate and crystallize your ideas. There are two further stages to undergo before you master the technique: Application (continued practice) and Adaptation (personalizing the tool to suit your needs). If The ﬁve “A”s you begin to use Mind Maps The initial principle of Mind Mapping involves on a frequent basis, you will following the instructions of three of the ﬁve soon ﬁnd that there are no “A”s: Acceptance, Association, and Analysis. limitations to the variety of ways you can use the Acceptance: when you start a Mind Map you model, since there are should set aside any preconceptions about your no limits to the number own limitations, and look objectively at the of connections that problem. Write down the problem or goal in the your brain can make. center of the page and circle it. Draw eight lines For further information from this circle and write key headings, such as: you can visit www. buzanworld.com 1. Why? 5. What (to use)? 2. How? 6. Who (can help)? 3. Where? 7. Advantages? 4. When? 8. Disadvantages?
66 Think creativelyDemystifying creativitySo what do we mean by creativity? Fundamentally, it’sa mixture of original thinking, insight, ingenuity, andinnovation. Naturally, some people are born with agreater tendency to tap into their creativity (notehow many times artistic and musical talent seemto run in families), but much of that results fromencouragement and opportunity. A positive rolemodel always helps. So, if for some reason you thinkyou’re not creative, perhaps it’s the negative beliefthat is holding you back, or the lack of encouragement,rather than the level of your creative aptitude.The creative geniusesWhere does this creative spirit come from? The imagesof the English Romantic poets Shelley and Byron strikinga heroic pose on the rooftop in the midst of an electricalstorm have seduced the world into believing that allinspiration comes like a bolt of lightning. Dramatic perhaps,but it couldn’t be further from the truth. Archimedes maywell have jumped out of the bath and cried “Eureka!”the instant he worked out how to calculate the volume of an irregular shaped object, but we’re fairly sure that he’d visited the bathhouse fairly often before reaching that breakthrough moment. Mozart was writing symphonies at an astonishinglyyoung age, but is he remembered for any those earlycompositions? Of course not, because he had to servehis apprenticeship before he could fulﬁll his undoubtedgenius. And how many unworkable theorems did Einsteindevise before he thought up his Theory of Relativity? Thetruth of the matter is that whichever creative geniusyou can name, you can rest assured that his or hercreation not only took a lot of brainpower,but practice and patience as well.
Introduction: demystifying creativity 67The cogs of creativityCreativity is not a bolt from the blue but a process,a series of incremental steps that leads to the magic“Eureka!” moment. Social psychologist Graham Wallasproduced one of the earliest models of the creativeprocess in 1926, proposing that creative thinkinggoes through four distinct phases: 4. Veriﬁcation—the ﬁnal phase when the idea is worked into a form that can be proven and communicated to others. 3. Illumination—the1. Preparation—the period 2. Incubation—the stage moment when a solutionof research, when raw when the problem is laid presents itself, albeit in amaterial is gathered and to one side, allowing rough state.organized, to be in a intuition, emotion, andposition to start the the unconscious mindcreative act. to ponder over it.Right-brain = creative? over by some higher power during a creative act,As much as it is wrong to think that creative the science leans more toward the theory thatpeople are only those blessed with an innate novel ideas materialize when imagination andgenius, it is equally wrong to think that all analysis work side by side. Creativity is, therefore,creative people are naturally right-brained while whole-brained and only by integrating variousall left-brained people are analytical and orderly mental faculties can you maximize your untapped(see p.15). The statistics might suggest that creative potential. You can develop your abilitycreative people tend to have a more dominant to think creatively by learning a few popularright-sided brain, but that doesn’t mean that strategies described on the following pages.the rest of us can’t be creative. The truth iseveryone has the ability to be creative. In fact,creativity ﬂourishes best when you use bothsides of your brain. As proposed by Wallas’ Music as a musemodel (see above), creativity is not some This is a simple warm-up exercise to get your creativemagical state of mind but a series of actions juices ﬂowing. Listen to a piece of musicthat depend on logic and applied thinking as without lyrics. It can be classical, jazz, dance, any type—although the slower,well—processes that are largely performed by the better because it will help you relax.the left side of the brain. What’s more, brain Think about the story you imagine thescans have revealed that during creative music is telling you. Write down thethinking both hemispheres of the brain share story at the end of the piece, embellishthe task equally. So, while you may have heard it as much as you like; don’t concernstories of artists feeling that they were taken yourself with form or structure.
68 Think creativelyDon your creative capIt is essential for you to be in the right state of mind to realizeyour full creative potential. Although this may seem to beobvious, it is something that science has been researching fora long time. For example, several years ago, neuroscientists inAustralia claimed that they had found a way to “switch on”a person’s unconscious creative skills by magnetic stimulation.They argued that everyone possesses extraordinary creativepowers, but the problem is tapping into these reserves, forwhich one has to be intensely focused.Finding focusThe ability to focus greatly determines yourcreativity at any given time. For example,have you never become so engrossed inan activity, such as staring at a painting,that your mind has been transportedto a different time and place? Thinkabout the last time you were curledup with an amazing novel—a realpage-turner. As you became moreabsorbed in the story, your inner eyewent into a Zen-like state, conjuring upall sorts of images of faces and places.Admittedly, you were stimulated by the quality ofthe writer’s storytelling, but the images you fashionedwere unique—each the product of your creative mind. Notwo people reading the same novel visualize the details inthe same way, hence our occasional disappointment withTips ﬁgure. Concentrate on the image.you’ll realize that music is a great stimulus. Pretend you’re that person. put yourselfAnecdotal evidence suggests that classical into their shoes—what do you see,music helps logical thinking, rock music helps how do you feel, where might youboost energy, and dance music aids creative writing—the be heading, and how might yourelentless rhythms act as a strong stimuli over a short period. get there? Ask yourself as manyOf course, these are general assertions and you will have questions as you can and write theto ﬁnd for yourself what music works best for you. answers down.
Feature: don your creative cap 69 Zero in! For those of you who are easily distracted, concentration exercises can be an effective way to enter this state. Next time you are about to start something creative, try this warm-up: Find a quiet, comfortable place. Close your eyes and focus on your breathing ﬁrst. Do not think of anything else. Take your time. Once you feel relaxed, think of the most beautiful place you’ve ever been. This could be a vacation destination, such as a sun-kissed beach, the beautiful interior of a palatial building, or even the treehouse from your childhood. Use all your senses to imagine this ideal place: what do you see, what do you smell, what can you touch? Is there sand pushing between your toes, are the colors bright and dazzling, can you smell the green wilderness? Take as long as you need to picture the location in your mind.ﬁlm adaptations. Any creative task demands Then savor it, revel in all the minute details.your fullest attention. Somehow you must Imagine walking around the area, keep searching for new elements to add to thiseliminate any distractions so that you can mental composition, and focus on the newconcentrate only on the task. This will establish discovery. If it’s an object, such as a pebblea space in your mind where your creative spirit in the sand, imagine picking it up andcan roam free to be playful and inventive. turning it over—see all the marks on it. Once you are immersed in the picture, you should feel totally focused. You are now in the creative spirit. Your mind’s eye has been catapulted to a different time and place. Even though the location may have a basis in reality,for ﬁve minutes and see what images your mind forms. you’ll ﬁnd that you have createdThen use those images to write a short story. some of the details since memory is selective (see p.30) and you’vebe under a starry sky, try ﬁlled in the gaps by relying onto see what constellations your imagination. Who saidyou can form. You’ll be you’re not creative?surprised at what yourimagination conjures up.
70 Think creativelyCreative treats1. The hidden storyobject—the sort of thing that would sit at the center of a fantasyhow you would keep its secret if a master criminal was out to get to it.2. Striking similes Think of a simile to complete each of the following sentences. Try to think beyond clichés and continue on a separate sheet of paper if necessary: .
Exercises: creative treats 71 3. Mystery ﬁgure This is a game to play in groups of another person in the group. During four. Each of you starts with a fresh the next stage everyone draws the sheet of paper. body, folding the sheet once again Decide on a “name” to call the to hide the creation, and swaps it ﬁgure each of you is about to draw. again with another person. The This is the only stimulus that binds same is done with the legs and the you creatively to each other. Each feet. Once everyone is ﬁnished, person draws a head on their sheet unfold the drawings. You should of paper. The sheet is folded to hide have four completely different the drawing and is swapped with versions, all inspired by that name. 4. Imaginary biography This is a game to play in groups of two or more people. Write down an assortment of words relating to fame—these could include names of celebrities, famous landmarks, or famous historical events. Put all the words into a hat. Each person takes a turn to talk about their own life for one minute. At the 30-second mark, the person reaches into the hat and picks out a word at random. Whatever the word, the person has to include it in their biography for the next 30 seconds.Passion and purposeWeren’t these exercises a lot of fun? He argues persuasively that by tapping much fun, then itWhen was the last time you gave your into our creativity, we reinvigorate our might be becauseimagination free license in this way? passion, which breathes purpose back your creative skillsYou may not be used to thinking into our life. Robinson reminds us that are lying dormantcreatively in your day-to-day life, in the creative spirit is an essential part of and your brain iswhich case you are neglecting a key human nature and human progress, craving some kindmental faculty. One of the most ardent and we allow our creativity to be of change. Perhapsadvocates of the belief that we are not neglected at our peril. So, if you feel it’s time to ﬁndusing our creative resources properly is that you’re stuck in a rut, or you’re something creative to breathe passionthe Englishman Sir Kenneth Robinson. clock-watching all day and work isn’t and purpose back into your life?
72 Think creativelyCreative conundrumsThe following puzzles are designed to get you to thinkcreatively about a solution. This exercise isn’t aboutﬁnding the “right” answer because, occasionally,there might not be a deﬁnitive answer to a problem.It’s about ﬁnding a solution that you think answersthe problem. You may want to write your answer ona separate sheet of paper.5. Horsing aroundA man stands in the center of a ﬁeld. There are 4 horsesin the ﬁeld, one at each corner—a bay horse, a chestnuthorse, a white horse, and a black horse. The man has totether his horses so that they can’t bolt. If he must remainat the center of the ﬁeld while the horses stay at the4 corners, how can he ensure that his horses can’tescape using only 3 lassos? If you ﬁnd a solution quickly, try for another.There are at least 3 different solutions to the problem.6. Doubling thewindow sizeHow can a square windowbe made twice as largewithout increasing itsheight or width? Tryto think of as manysolutions as possible.7. Enough ﬁsh2 fathers and 2 sons wentﬁshing one day. Theyspent the wholeday ﬁshing andonly caught 3ﬁsh. One fathersaid, that is enough forall of us, we will haveone each. Explain howcan this be possible?
Exercises: creative conundrums 73 11. Crossing the bridge A rock band has a concert that starts in 17 minutes and its members must all cross a bridge to get there. All 4 men begin on the same side of the bridge. You must8. Drinking glasses help them across to the other side. It is night. There is 1 ﬂashlight. A maximum of 2 people can cross at one6 drinking glasses stand in a row, with the ﬁrst 3 time. Any pair or individual that crosses must have thefull of water and the next 3 empty. By handling ﬂashlight with them. The ﬂashlight must be walked backand moving only 1 glass at a time, how can you and forth, it cannot be thrown.arrange the 6 glasses so that no full glass stands Each band member walks at a different speed. Anext to another full glass, and no empty glass pair must walk together at the rate of the slower man’sstands next to another empty glass? What do pace: The singer: 1 minute to cross. The guitarist:you think is the minimum number of moves 2 minutes to cross. The keyboard player: 5 minutes torequired to solve this puzzle? cross. The drummer: 10 minutes to cross. For example, if the singer and the drummer walk across ﬁrst, 10 minutes have9. The elder twin elapsed when theyOne day Kerry celebrated get to the other sideher birthday. Two days of the bridge. If thelater her older twin drummer thenbrother, Terry, celebrated returns with thehis birthday. How come? ﬂashlight, a total of 20 minutes have passed and you have failed the mission.10. The swimmer in the forestDeep in the forest, the body of a man was foundwearing only swimming trunks, a snorkel, and goggles.The nearest lake was eight miles away and the sea was Note: there is no100 miles away. How had he died? trick behind this. It is the simple movement of resources in the appropriate order. There are two known answers to this problem. Note: this is supposedly based on a true incident. Solutions on p.175
74 Think creativelySurviving the creative processEntering the creative spirit is one thing, but what and upon which your brain has successfullyhappens when you’re in the middle of a creative relied to make sense of the world around you.task, such as making a birthday card, a collage, or Essentially, you are searching for multipleeven trying some creative writing? Does your solutions rather than settling for the ﬁrst ideacreativity come out in a continuous stream? Is the that comes to you. Fighting against this naturalprocess effortless from the moment you don your inclination can be frustrating but you have tocreative cap? Of course not! It’s not meant to be give yourself permission to be playful andan easy process, especially if you are striving for inquisitive, ﬂexible and versatile. Also, you haveoriginality. In fact, the product of any creativity to remember that the creative process isn’t aemerges only after you’ve fought a grueling battle serene boat ride. It is more like a rollercoaster,inside your head. You’re ﬁghting against existing ﬁlled with peaks and dips. For help in survivingmodes and conventions, ideas that are ingrained the creative process, see our tips: 3: Shift location. If you’re1: Acknowledge that 2: Embrace fear. Creativity working on a creative task fromcreativity comes in cycles. by deﬁnition asks you to your desk, your senses are ﬁxedYou might have the seed of venture into uncharted on the surroundings. This canan idea but it is not ready to territory. You’re bound to curb your creativity so changegerminate. Accept that there make wrong turns along the location from time to time.will be periods when your way and reach dead ends. Work in a different room, or gocreative brain might seem Each time, you’ll be stricken to a quiet café. Sometimes youdormant. If you remain by that familiar fear of can gain new perspective on acommitted to the task, you’ll failure, but reinterpret the problem by simply shifting theﬁnd that your idea will feeling as performance direction of your chair.suddenly blossom, or even energy and just keep going.shoot in an unexpecteddirection, and you’ll reap thefruits of your commitment. 4: Reconnect with your inner child. It will release you from the chains of adult sensibilities, allowing you to consider the seemingly “ridiculous” as an option. To get into this state of mind, try to delight in any childlike behavior before you begin your creative task.
Feature: surviving the creative process 755: Don’t try to be perfect!Perfection is an ideal. It’swhen the bar is set aboveand beyond your sightline.Aiming for the unattainablewill only prevent you frombeginning a creative taskin the ﬁrst place. 6: Keep envisioning your goal. Holding onto a mental image of what you seek to achieve is a powerful way of picking yourself up and moving 7: Note it down. Since forward even when your creative spirit seems to be your creative brain has a at its lowest. You can use visualization techniques to tendency to come up with reafﬁrm your desire to succeed. Remember, the best solutions without warning, creators are visionaries ﬁrst and foremost. keep a small notebook and pen with you. Use them to jot down sudden brainwaves, or even an innocuous strand of an The creative journey idea that might lead to a Creative thinking is chaotic. Eventually, you will ﬁnd a viable solution but breakthrough later on. Your your progress will be tumultuous. Psychologists refer to this as “loose notepad is your net because you’ll be surprised at how associative thinking.” It is a type of thinking that forsakes linearity for quickly an idea can slip something more “jumpy.” Psychologists say that the feeling of uncertainty is through your brain. necessary for the human mind to be able to come up with new ideas. They claim that comfort strangles associative thinking, often leading to an answer that is timeworn or banal. Leveraging uncertainty, riding it, and valuing it are all critical to developing creative ideas.8: Visit an art gallery or museum. If you’ve hit a brickwall, perhaps you need a bit of space from inside yourhead. Galleries and museums or any other “creative place”provide superb visual stimuli to kick-start an exhaustedmind. These are “play areas” where you can connect withan artist’s unique take on the world. This can help releasethe checks you’ve imposed on your own creativity.
76 Think creativelyDoodle artWe are fairly certain that the ﬁrst time you picked up a penor a pencil you didn’t write a sonnet or draw a masterpiece.You probably scribbled something that made no sense.However, encouraged by your parents and teachers, youkept doodling away and with time and practice, thesquiggles developed, and found a form—probably ofyour house, or mom and dad, or pet dog or cat. Doodling is one of the earliest ways in which youexpress your creativity. We believe that you’re nevertoo old to doodle because it can also help organizethoughts, feelings, and experiences. Like any creativeendeavor, doodling can be an outlet to express whatwords lack, and can even offer an answer when you feel creatively trapped. We have provided you with a set of randomscribbles. All you have to do is interpret what youthink each looks like—use your imagination—andbegin adding to the squiggle. Draw in details or thebackground to ﬂesh out your interpretation. Evenif you can’t think of anything, just begin addingto it until something tangible forms.Below is an example:
Feature: doodle art 77Breathing for inspirationHas your creativity ground to a halt? Instead of lettingfrustration get the better of you, try to sit back and takea few deep breaths. Did you know that drawing a deepbreath gives your creativity a boost by increasing thenegative ions in oxygen? The negatively charged oxygencirculates throughout the brain, refreshing the neuronsand, because these negative ions promote alpha wavesof longer amplitude in thebrain, which are associatedwith creative thinking,suddenly your creativityreceives a recharge. So, nexttime your creative spirit feelsdeﬂated, spend two minutestaking deep breaths, inhalingand exhaling every ﬁveseconds, and repeat thecycle at least 12 times.
78 Think creatively Lateral thinking:Thinking outside the box How many different ways areYou may have heard the expression “lateral thinking,” which is a there to join all nine dots in the square using a maximum ofmethod of getting us to think in unorthodox ways about a problem. four straight lines and withoutPsychologist Edward de Bono, who coined the phrase, believes that taking your pen off the paper?we tend to overuse logic and follow linear paths in our creativethinking, consequently ignoring the open spaces that ﬂow out tothe sides. In other words, “logic” then becomes counterproductive HERE AREbecause we box ourselves in and produce the same solution to a SOMEproblem, which, let’s face it, isn’t the least bit creative! EXAMPLES Lateral thinking relies on reasoning that is not immediatelyobvious, and encourages ideas that you may not think of byrelying on logic. Lateral thinking is concerned with the perceptionpart of thinking. It is about rewiring the way you approach aproblem. De Bono describes lateral thinking with this metaphor:“You cannot dig a hole in a different place by digging the samehole deeper.” Think about it. Trying harder in the same direction,especially if the direction is wrong, will not lead to any progress,and might actually hinder the chances of a breakthrough becauseyou will only be squandering precious creative energy. Lateralthinking asks you to dig as many holes as you can. Each time youdig a new hole you uncover a new possibility. It might work or itmight not. If it does, then great! If not, you simply dig another 6. And if that sounds a bithole and continue your search. far-fetched, you could do the same thing by rolling the paper into a cylinder.Lateral thinking in three steps:1. Identify the dominant ideas that prevent originalways of seeing the problem.2. Approach the same problem from different angles,regardless of how random the angle might seem.3. Put a stop to any doubts, preconceptions, andprejudices that might dismiss original thought. 5. If you laid the paper on the ground, you could draw one long line, which circles the earth three times, joining one row of dots each time.
Feature: thinking outside the box 79 Top tips Challenge assumptions—don’t just fall back on accepted ways of thinking but question everything that has been done or is known. Find focal objects—pick an object at random (or a word from a dictionary) and see what thoughts theThe nine dot puzzle 1. The standard solution: You object or word inspires. run the pen outside the nine dot boundary to join the dots. Harvest ideas—when you’ve come up with as many new ideas as you can, begin the process of harvesting by selecting the best ones. Invent alternatives—allow yourself plenty of time to come up with new ideas, perhaps setting yourself a minimum (say, 50) before you begin your analysis. Provide provocation—deliberately set up a wild counterpart to the normally accepted idea, not as an end in itself, but as a possible pathway to new ideas. 2. If you had a thick pencil, Shape concepts—look closely at you could join the dots with clusters of ideas that have sprung up just three lines. and see whether you can group any together into concepts. Suspend judgment—don’t rush to judge any new ideas, however strange they may appear at ﬁrst. Just go crazy! While thinking laterally, you are encouraged to consider trivial or ridiculous ideas. This is because you are4. Even with a thinner pencil, 3. Why stop at three lines? using the information not for its ownYou could still make do with Why not take a very thick value but for its knock-on effect. Eachthree lines by folding the paper pencil and do the job with idea is a stepping stone to anotherso that the dots were closer to just one line?each other. idea. You will probably head into many strange directions as you jump from one idea to another but at some stage you will reach an innovative solution.
80 Think creativelyMatchstick mayhemMatchstick puzzles offer an excellent way to exercise your lateral thinkingability. Why spend money on expensive games when you can occupy yourfree time by doing these fun puzzles? The puzzles are not all solved in thesame way. They require you to think outside the box and entertain myriadpossibilities. The puzzles encourage you to exercise different thinkingstyles. You will need a box of matches or toothpicks.12. The third square 13. Three for twoMove 4 matches to make 3 squares. Move 3 matches to make 2 squares. 15. Swimming ﬁsh Turn the ﬁsh by moving only 2 matches; no overlapping.14. Remove a squareMove 2 matches to new positionsto get only 4 squares, leaving nooverlapping or loose ends.
Exercises: matchstick mayhem 8116. Try for ﬁve 18. All the threesMove 6 matches so that 5 squares are formed. Move 3 matches so that 3 squares are formed.17. Even out 19. Total wipeoutMove 3 matches to new positions to get only 4 squares, Remove 9 matches, leaving no square (of any size),leaving no overlapping or loose ends. or any overlapping or loose ends. Solutions on p.176
82 Think creatively20. Equal divide 21. Find the extra triangleUse the 4 matches to divide the large square into 2 parts Move 3 matches to make 4 equilateral triangles, withoutof the same shape. Use the matches without breaking overlapping.or overlapping them.22. Break the wheel 23. More for lessMove 4 matches to form 3 equilateral triangles. Move 3 matches to add an equilateral triangle to the square and the rhomboid. Solutions on pp.176–7
Exercises: matchstick mayhem 8324. Ice in the glass 25. Doubling upMove 2 matchsticks and reform the glass in the same Move 1 match to make 4 triangles.shape so the ice is outside it.26. The elusive square 27. Two’s companyMove 1 match to make a square. Remove 2 matches to leave 2 squares.Sleeping on itDid some of these matchstick puzzles bafﬂe you? Perhaps what you should have doneis slept on it. Have you ever had the experience of falling asleep after worrying forhours about some seemingly intractable problem, only to wake up the next morningwith the perfect answer? Actually, the ability to sleep on a problem and solve it as ifby magic is a common human trait. How does it happen? It seems that as much as we need peacefulthinking time to create, our brain also appreciates the time to cogitateand deliver solutions while our consciousness is temporarily switchedoff. This may free the mind from the limitation imposed by ingrainedbeliefs. Sleep specialists don’t know exactly at what point this unconscioussearch takes place, but it seems likely that it occurs during Rapid EyeMovement (REM) sleep, the period that is also associated with dreaming,and the retention of memories and learning (see p.42).
84 Think creativelyOriginal answersA physics professor was about to give a universitystudent a zero for an answer to a question on atest paper. The student argued that he shouldreceive full credit, and blamed the system forrefusing to recognize how well-informed hisanswer was. Finally, the teacher and studentagreed to submit the paper to an impartial arbiter. The examination problem was: “Show how itis possible to determine the height of a tallbuilding using a barometer.” The student’s answer was: “Take the barometerto the top of the building, attach a long rope to it,and lower the barometer to the ground. Then,bring it back up, measuring the length of the ropeand the barometer. Add the two lengths and youwill get the height of the building.”Second attemptThe arbiter pointed out that although the studenthad answered the problem correctly, his answer didnot demonstrate any knowledge of physics so hecouldn’t be awarded any credit. He then suggestedthat the student make another attempt. He was given six minutes to answer the samequestion, with the warning that this time the answershould indicate some knowledge of physics. At theend of ﬁve minutes, the student claimed he hadseveral answers and was trying to select the bestone. He then dashed off the following answer:“Take the barometer to the top of the building.Lean over the edge of the roof, drop the barometer, and time its descent with a stopwatch. Then, using the formula S=½at², calculate the height of the building. The arbiter decided to award him a good mark since he had demonstrated some knowledge of physics.
Feature: original answers 85Alternative answersRecalling the student had mentioned having alternativeanswers, the arbiter then asked him what they were.The student replied:1. Take the barometer out on a sunny day and measurethe height of the barometer, the length of its shadow,and the length of the building’s shadow, then use simpleproportion to determine the height of the building.2. Take the barometer and begin to walk up the stairs. Asyou climb, mark off lengths of the barometer along thewall, then count the number of marks to get the heightof the building in barometer units.3. Tie the barometer to the end of a string, swing itand determine the value of the “gyromagnetic-factor.”The building’s height can be calculated from this value.4. Take the barometer to the basement and knock onthe owner’s door. Then offer the barometer as a gift 28. Polar exploreronly if the owner tells you the building’s height. Now that you know that there are many correct ways(Although this solution doesn’t show any knowledge of to answer a test question, try ﬁnding a solution tophysics, it does make use of the barometer.) the question below:Noticing that the arbiter wasn’t too impressed with the Scott Amundsen Peary, the extravagantly named Polarlast of those solutions, the student reluctantly admitted explorer, claimed that when he was in the far North,that he even knew the correct textbook answer: he could point his car north on an ordinary road, drive it for 1 mile, and without turning around, end up5. Measure the air pressure at the bottom and top 1 mile south of where he started. How did he do it?of the building and then apply the proper formula,illustrating that pressure decreases as height increases.However, the student told the arbiter that he was so fedup with college professors trying to teach him how tothink that he had decided to rebel. Solution on p.177
86 Think creativelyMore creative conundrumsAlthough the following riddles do have a deﬁnitive answer, whichcan be found in the solutions section at the back of the book, itdoesn’t mean that other explanations are not possible, if not moreplausible. Your imagination might actually take you in a totallydifferent direction. If so, run with it! See where your creativity takesyou. It might be that your explanation is a lot more interesting thanthe one we offer. What’s more, you might think the answer we’vegiven is, frankly, a bit silly.29. A son’s gratitudeA man locked his son out of the house.The son thanked him. Explain.30. Deadly shellThe ancient Greek playwright Aeschylus was killed by a tortoise. How?
Exercises: more creative conundrums 87 31. Foiled robbery A bank robber grabbed several thousand dollars from a bank teller and, although he was armed, he was captured within a few seconds before he could leave the bank. How? 32. Futile car chase A high-speed police car chases a much slower vehicle in which the criminals are making their getaway but the police fail to catch them. Why?33. Clever dunceWilliam was the least intelligent and laziestboy in a class of 30 students who took anexamination. Yet when the results wereannounced, William’s name was at the topof the list. Explain. Solutions on p.177
88 Think creatively 34. The fatal ﬂash There is a ﬂash of light and a man dies. The man is not killed by any other person, a bolt of lightning, nor does he die of any illness, such as a heart attack. It’s not suicide either. Can you suggest a plausible explanation?35. Lax borders 36. Strange detourAn ordinary American citizen, with A man lives on the 10th ﬂoor of ano passport, visits more than 30 building. Every day he takes theforeign countries in one day. He is elevator to the ﬁrst ﬂoor to go towelcomed into each country and work or to go shopping. When heleaves each one of his own volition. returns he takes the elevator to theHow is that possible? 7th ﬂoor and walks up the stairs to reach his apartment on the 10th ﬂoor. The man hates walking, so why does he do it? 37. Bottled money If you put a small coin into an empty wine bottle and replace the cork, how would you get the coin out of the bottle without taking out the cork or breaking the bottle?
Exercises: more creative conundrums 89 38. Separated at birth? A woman had two sons who were born on the same hour of the same day of the same year. But they were not twins. How could this be so? 39. Push that car A man pushed his car. He stopped when he reached a hotel, at which point he knew he was bankrupt. Why? 41. Nail on the tree When John was 6 years old he hammered a nail into his40. Newspaper divider favorite tree to mark hisTom and his younger sister were height. Ten years later, atﬁghting. Their mother decided to age 16, John returned topunish them by making them stand on see how much higher thethe same sheet of newspaper in such nail was. If the tree grewa way that they couldn’t touch each by 2 inches each year,other. How did she accomplish this? how much higher would the nail be? Solutions on p.177
90 Think creativelyOptical illusionsOptical illusions offer a great insight into how your creative mindworks. They prove that the eye doesn’t really see but merely collectsinformation that it passes down to the brain, where innumerableprocesses of analysis, association, and qualiﬁcation begin. Thereinlies your creative powerhouse. Making sense of an image is one of 43. Big-headed ﬂowerthe most creative acts the human brain engages in. Your brain By looking at the two ﬂower heads,essentially recreates the world on the canvas of your mind. In this can you guess which central circle iscreative process, the eyes are merely functionary. They simply deliver larger: the one on the left or thethe raw material to your brain. one on the right? That’s why the study of visual illusions and mental fallacies isuseful. While they point out the limits of perception, they also reveal 44. Confused creaturethe magic your creative consciousness is capable of. Some illusions What animal can you see, a duck orteach us to doubt and to question the many appearances of reality, a rabbit?while others, such as stereogram drawings (popularlyknown as Magic Eye), ask you to make sense ofseemingly random elements. Optical illusions can act as great creativestimulators because they arevisual, engage the right-handside of the brain, and forceyou to see things differentlyas you attempt to work outjust what is happening.42. The café wallAre the horizontal lines on the wallparallel to each other or tapering?
Feature: optical illusions 9145. Dotty or what?Can you see the dark dots at eachintersection? Are they really there?46. Look into my tie ...Concentrate your gaze on the picture.Do you see the pattern rolling? 47. Poles apart Are the tubular poles diverging at the top where the signposts are ﬁxed, or running parallel to each other? Explanations p.177–8
94 Numerical reasoningNumerical aptitudeNumbers are everywhere! But mentionmathematics and many of us cower. That maybe surprising since even babies and animals canregister some kind of rudimentary countingmechanism. Everyone has an innate degree ofnumerical aptitude. It’s built into our nature. Weare always handling numbers and performingmental exercises with them. Think about it. Whenwe wake up, it is usually because our alarm clockgoes off at a set time—a time that we interpretthrough reading numbers. When we buy “Everyone has an innate degreesomething, we quantify its value with the help of numerical aptitude. It’s builtof numbers. When we make our favorite dish into our nature. We are alwaysfollowing a recipe in a book, we use numbers handling numbers and performingto get the proportions of the ingredients right. mental exercises with them.”Numerical reasoning forms the cornerstone oflogic, rationality, argument, and proof. Yet, whenmany of us are asked whether we are any good atmath, we tend to answer in the negative becausethe word dredges up memories of struggling withformulas and fractions, geometry andtrigonometry. Why is this?NumerophobiaSome people have difﬁculty dealing with numbers anxiety requires an ongoing commitmentfrom a young age. Whether it’s caused by a fear to learning, to acknowledging fears andthat developed at school or is some kind of working through them.mental block, they cannot cope. If you’re one of You’ll be surprisedthem, you might be someone who suffers from how quickly the brainnumerophobia: literally, the fear of numbers—an learns new responsesirrational belief that your brain cannot process to enduring fears.mathematical problems (although math is aboutapplying logic and rationality, it is, paradoxically,affected by emotion). The truth is that eventhose of you who suffer from the phobia stillapply mathematical skills unconsciouslythroughout your daily life. Overcoming the
Introduction: numerical aptitude 95Visualizing mathNumerical reasoning becomes easier when youvisualize mathematical concepts. Einstein onceclaimed that his thinking process took placethrough visualization and that he very rarelythought in words at all. Crucially, brain scansshow that during calculations activity is notconﬁned to the left hemisphere, but is also presentin the visual, auditory, and motor areas of the brain.Furthermore, geometry and reading graphs bytheir nature require you to use your visual skillsto understand complex numerical data, whichimmediately involves regions of the right temporallobe. What we do know is that when a mathproblem is presented visually, it becomes clearerand more accessible, and the brain is more capableof recalling the knowledge later on. Number workout Did you know that doing numerical exercises gives your brain a workout similar to that which your body receives from a weight session at the gym? Here’s how it works. The nervous system of your brain contains neurons and, within them, axons, which are the nerve ﬁbers that transfer impulses between neurons (see p.15). The speed of this transfer determines how efﬁcient your brain is at processing information. Doing addition is one of the easiest ways of protecting the axons because the activity increases the insulation around them (also helped by diet), which fortiﬁes the connections between the neurons. Mental arithmetic helps speed and accuracy, while more sophisticated math boosts your problem-solving ability. Turn over to begin Brain Training’s numerical workout and get those neurons ﬁring!
96 Numerical reasoningQuick-ﬁre arithmetic testBelow are some problems to test your aptitude for basic arithmetic. Thekey is to do these in the quickest time possible without a calculator.Mental arithmetic is a robust mental exercise, accessing the powers ofyour short-term memory together with your ability to solve problems.1. 3 + 9 + 7 = 7. 120 ÷ 4 ÷ 6 = 13. Which of the 18. 195 ÷ 5 =a. 17 a. 7 following gives the a. 38b. 18 b. 5 answer 560? b. 39c. 19 c. 12 a. 20 x 30 – 30 c. 40 b. 20 x 25 + 602. 13 – 5 = 8. 329 + 457 = c. 20 x 29 – 25 19. 103 – 2.68 =a. 8 a. 786 a. 100.42b. 7 b. 820 14. 150 x 9 = b. 99.68c. 9 c. 790 a. 1532 c. 100.32 b. 13503. 25 – 16 = 9. 60 – (36 ÷ (3 x 4)) = c. 1575 20. 6¼ x 6 =a. 9 a. 98 a. 2⁄5b. 11 b. 57 15. 15% of 35 = b. 37½c. 8 c. 32 a. 6 c. 371⁄5 b. 6.54. 9 x 7 = 10. Which of the c. 5.25 21. In lowesta. 56 following gives the fraction termsb. 63 answer 510? 16. The answer to express 40c. 72 a. 5 x 2 x 43 this calculation in its minutes of three b. 2 x 5 x 51 x 7 lowest terms is: hours. c. 2 x 3 x 5 x 17 20 ⁄40 + 2⁄8 = a. 6⁄165. 9 x 8 x 2 = a. 3⁄4 b. 5⁄12a. 144 b. 1⁄8 c. 2⁄9b. 156 11. 50⁄250 reduced to its lowest fraction c. 12⁄3c. 125 term is: 22. 6% of 230 = a. 2⁄13 17. 4.6 + 0.23 + 1.96 = a. 1386. 66 ÷ 11 = b. 1⁄5 a. 1.46 b. 13.8a. 6 c. 3⁄7 b. 2.63 c. 1.38b. 9 c. 6.79c. 8 12. 6.6 ÷ 2.2 = 23. (-6) – (+3) = a. 3 a. 3 b. 3.3 b. -3 c. 2.2 c. -9
Exercises: quick-ﬁre arithmetic test 9724. 250 X 7 = 30. Which of the How did you do?a. 1750 following gives the This is math without any visual aidb. 1850 answer 1536? and you probably relied on the thingsc. 1950 a. 8 x 6 x 32 you’ve learned by rote to answer the b. 6 x 3 x 10 multiplication and division questions.25. 8% of 400 = c. 9 x 5 x 35 Basic arithmetic beneﬁts froma. 50 frequent practice and repetition. Turn over and learn someb. 52 31. 7.75 x 8 = killer tips to improvec. 32 a. 60 your numerical skills. b. 6126. 260 ÷ 5 = c. 62a. 50b. 52 32. 6% of 300 = Men and women So is it true that men perform betterc. 56 a. 16 at mathematical subjects than women? b. 18 Stereotypically, people tend to believe27. 15% of 70 = c. 20 that the answer is “yes.” However,a. 10.5 most statistics show that female students perform on average at exactlyb. 11 33. 5 x 6 x 3 ÷ 5 = the same level as their male counterpartsc. 9 a. 18 all the way through school, so the real b. 22 answer to the question is “no.”28. 168 x 9 = c. 24 Until, that is to say, you get abovea. 1512 and beyond higher education. Atb. 1550 34. (-9) + (-22) = this point, it is true that most of the mathematical geniuses tend to bec. 1580 a. -13 men: Archimedes, Newton, Einstein, b. 13 Hawking. You get the picture.29. 114 – 12.68 – 1.32 = c. -31 Why is this? Perhaps more mena. 100.42 choose to spend their adult livesb. 100 35. 60 x 3 + 20 ÷ 5 = reﬁning their aptitude for numeracy.c. 100.32 a. 50 Perhaps women have not been encouraged enough in the past so b. 45 it’s down to historical conditioning. c. 40 Perhaps now, with gender equality, we will see a few female mathematical geniuses join the ranks.Time taken: Nº. correct answers: All correct under 3 mins—excellent 3–4 mins—very good mins 35 over 4 mins—keep practicing Solutions on p.178
98 Numerical reasoningImproving numeracyThe key to improving your numerical skills is constant practice.The ﬁrst thing to do if you’re serious about improving yourgeneral mental arithmetic is to stop relying on your calculator.Of course, a calculator is a very useful and necessary tool. Thetrouble is that it allows such a large part of both sides of yourbrain to become just a little lazy. So if you want to improvearithmetic skills, you need to do without a calculator for allbasic arithmetic calculations. Another thing to remember is that improving yourmathematical skills gives you a great mental pay off—it produces an instant buzz. When you get it, you feelclever. Math beyond basic arithmetic, such as geometry,incorporates powerful visualization skills because you haveto use your mind’s eye to arrive at the answer. Keeppracticing and your ability to concentrate will become stronger.As a consequence, your overall capabilities in all other areas willimprove; you will become more focused, which is a key factorin becoming successful in life.Tips Take your time, especially different methods to arrive Once you understand aif you’re out of practice. at the answer. Opposite are concept, keep practicing.Think of it as a process to a few shortcuts that will be This is important since theimprove your aptitude helpful if you repeat the more you practice, the morerather than a test you need quick-ﬁre test. the concept will transferto pass in the quickest time. from your working brain toSpeed will come with To develop your ability to your long-term memory.practice and understanding perform quick calculations,the mathematical process. include numerical testers Visualize! It RC into your daily life. Add up is a natural M Be imaginative with math. grocery bills in your head as function of - MTry to see a problem in you go around the store. If the mind and ÷ + Mdifferent ways. This will you drive, calculate in your should be x √ head how much you’ll have applied to many Callow you to use a range of % 9 to pay for a quarter, half, mathematical tasks. CE three-quarters, and full tank Key concepts such as 8 6 N O of fuel. Next time you’re in division or place value 7 a restaurant with friends, (100s, 10s, and units) are 5 3 don’t use the calculator on often made clearer by using 4 . 2 your mobile phone; instead, pictorial explanations such use mental arithmetic to as graphs and tables. 00 1 ﬁgure out how much each of you will owe.
Techniques: improving numeracy 99 Shortcuts Multiplying by 9: if you Percentages: ﬁnd 7% of have to multiply a number 300. Sounds tricky? First of in your head by 9, let’s say all, think about the words, 168: multiply it by 10 (1,680) “percent”—it means per and take away 168, giving hundred. So, it follows that the answer: 1,512. 7 percent of 100 is 7; 8% of 100 = 8; 35.73% of 100 Adding big numbers: if = 35.73. But how is that you have to add some fairly useful? tricky numbers in your head, for example 329 and Back to the 7% of 300 457, round one of the question. 7% of the 1st numbers up (329 to 330), hundred is 7. 7% of the making a total of 787 easier 2nd hundred is also 7, to calculate, then subtract 1 and yes, 7% of the 3rd to get the answer of 786. hundred is also 7. So 7 + 7 + 7 = 21. If 8% of 100 is 8, it follows that 8% of 50 is “Dividing a large 15 percent tip: if you need half of 8, or 4. number by 5 is to leave a 15% tip after a meal at a restaurant, here’s actually very simple” an easy way to do it. Work Dividing by 5: dividing a out 10% (divide the number large number by 5 is actually by 10)—then add that very simple. All you do is number to half its value multiply the number by 2 and you have your answer. and move the decimal point: 15% of $35 = (10% of 35) 2978 ÷ 5. + ((10% of 35) ÷ 2) Step 1: 2978 x 2 = 5956 $3.50 + $1.75 = $5.25 Step 2: 595.6 Pie charts Pie charts are an easy way to visualize percentages. They are useful for analyzing polls Life before the mobile memory and statistics, and managing Can you recall the days when you had to keep a memory time or money. of all the phone numbers that were important to you?— Today it’s easy just to click on someone’s name, press the green button, and let the handset do the rest. But what + happens if you lose your handset and haven’t kept a= written record of the numbers? Yes, you’re stuck! Why not take yourself back to those days when people had to store numbers in their heads? Try to memorize as many phone numbers as you can. OK, it’s essentially a memory exercise, but you’ll be amazed how the constant calling to mind of different numbers improves your numerical skills, especially your aptitude for mental arithmetic.
100 Numerical reasoningVisual math workoutDifferent parts of your brain become active onceyou start making math visual, which leads to amore holistic brain workout. In addition, you learnto understand the language of mathematics byﬁnding ways to visualize its logical meaning. Thetruth is, many people are instantly put off by anumerical problem when it is presented with largenumbers and arcane symbols. So it stands to reasonthat adding a visual component to learning mathmakes it more engaging from the start. ? Below is an example to get you started. If yousimply read the problem, you might becomeconfused because of the information “overload”but the problem becomes much easier when youstudy the diagram below. Afterward, try the othervisual exercises on the next few pages.1. Under the bridgeAn aerial photograph was taken of a bus passing under 6 fta bridge. In the picture, part of the bus has traveled pastthe bridge. One half of the bus is yet to cross under thebridge. Two-thirds of the other half of the bus is directlyunder the bridge; and 9 ft of it has passed the bridge.How long is the bus? 9 ft ft 2. Casting shadows It is a sunny day. Steve, who is 6 ft tall, casts a shadow that is 9 ft long (see above). A: How tall is the building behind him if it casts a shadow that is ft 135 ft? B: Three hours later, Steve’s shadow increases to 13½ ft. What is the ft length of the shadow the building is casting now? Solutions on p.178
Exercises: visual math workout 101 Alma Lisa Emma Tara Size 8 J F M A M J J A S O N D3. Wedding ﬁtAlma, Lisa, Emma, and Tara are friends whose A: In which month did Alma andboyfriends proposed to them on the same day. They are Emma’s size differ the most?all getting married in 18 months’ time, and they wouldall like to ﬁt into a size-8 dress. They each diet and begin B: Whose weight was mostan exercise program. Their ﬁrst years’ progress toward consistent throughout the year?their ideal weight is shown above. C: Which bride will ﬁt into a size-8 dress after 12 months?4. Chance amourIn an art gallery, two strangers take a fancy to each other.They are 120 ft apart. The man walks toward the 5. Keen studentwoman at a rate of 9 ft/sec. The woman plays it cool, Jack walks to the bus stop to catch a busedging toward the man at 3 ft/sec. to his university. He then walks from the bus stop at the university to the studentHow long before they meet? center, arriving there at 9:35 am. secs A: How far does Jack walk in total? miles B: How far is he from the university student center at 9:20am? miles C: What is the average speed of the bus? mph 9 ft/sec 6 mi mph 120 ft walk 4 mi bus 2 mi walk 0 mi 3 ft/sec 9am 9:10 9:20 9:30 9:40
102 Numerical reasoning6. Carrying cupcakesPhilippa is holding a tea party in hergarden and is offering her hungryguests cupcakes on different sizetrays. The cupcakes she hasmade measure 2 x 2 in.How many cupcakescan she ﬁt side by sideon each of the traysillustrated in the picture?Small tray: cakes 12 in 16 in 16 in 8 in 10 in 12 inMedium tray: cakesLarge tray: cakes7. Land up for grabs a A: What is the totalFarmer Giles has decided to sell amount of land in feet ft² b that Farmer Giles owns?off his allotment. He divides theland into 3 different size plots: a c“a,” “b,” and “c.” The B: An interested client onlydimensions of his plots are a a wants to buy the “c” ft²shown below. plots. What is the total area of that land? a 12 x 12 ft b C: Another client opts to c buy all the “a” and “c” ft² plots. How much land is that in total? b 24 x 24 ft b D: The plots cost $2,000 a a per 900 ft². How much are $ all the “b” plots worth? E: A client offers to buy all c 36 x 36 ft the plots. What is the total price he’ll be asked to pay? $ Solutions on p.178
Exercises: visual math workout 1038. Bathroom makeoverA: Philip is tiling his bathroom wall.The diagram shows how much hehas completed. Write down as afraction in its lowest terms howmuch he has left to tile.B: The tiles come in packs of 8. Howmany packs will he need to tile the packswhite wall?C: Each pack costs $2.40. Howmuch will it cost him to tile the wall? $9. Computersales 800This graph gives the 700number of computers soldeach month (in hundreds) 600by 3 different computermanufacturers: 500Manufacturer 1 (in red)Manufacturer 2 (in blue) 400Manufacturer 3 (in green). 300 200 100 0 March April May June July A: Which month showed B: What percentage of C: How many units did the largest total decrease Manufacturer 2’s sales Manufacturer 3 sell over in PC sales since the was made in April (to the ﬁve months? previous month? the nearest percent? %Does faster equal smarter?If you’re able to think more quickly does that make you a managed to complete these exercises is an indication ofsmarter person than someone who takes more time? In your current numerical aptitude. The ability to processgeneral terms, we’d have to say it’s debatable. For example, information rapidly indicates there is more neuron activity inan artist may take years working on a masterpiece but does those areas of the brain. However, you should always takethat reﬂect on his or her intelligence? In numerical terms, enough time to ensure that the answers are correct. It’s nothowever, the answer is “yes.” The speed in which you very smart to make mistakes through sheer carelessness.
104 Numerical reasoning ﬁnish 8 3 6 7 8 7 5 210. The shortest route 7 8 7 6 5 5 8 7 1The objective is to create a path that 2 7 2 4 6 6 5 2starts in the lower left corner and 1 3 2 1 9 9 3 1 3ends in the upper right corner. Each 8 4 9 4 6 7 6 5number represents the distance in 4 6 5 4 3 3 5 2 4feet of the line it is on. 4 2 8 4 7 9 1 9Your goal is to ﬁnd the shortest path 5 7 7 6 4 4 6 3 4possible through the grid. We’ve given 9 8 7 3 8 2 4 5you a head start. Can you ﬁnish it? 5 8 8 7 5 5 6 3 3 2 3 3 1 7 3 6 8Your score: 4 7 7 6 5 4 5 1 1 9 2 4 4 3 9 5 9 2 5 6 5 3 2 3 8 7Time taken: 1 5 9 2 2 1 8 5 7 2 3 2 9 8 9 4 3 mins 3 1 7 2 4 5 5 4 start11. The brokencalculatorThis calculator fell out of yourbag and into a puddle, andis now experiencing a majormalfunction. Only the buttonshighlighted in the picture MCactually work. MR MSYour task is to compute M+ CEthe numbers 1 through Cto 15 with the limited 4means the calculator 5offers. For instance, x0.5 x 2 will give you 2“1”—the ﬁrst of the 315 digits. 0 =6 =11 . + =2 =7 =12Can you use =your mental =3 =8 =13arithmeticskills to ﬁgure =4 =9 =14out theremaining =5 =10 =15numbers? Solutions on p.179
Exercises: visual math workout 105 7 in12. Unfold the foldsA piece of paper has been folded 5 times with a singlestraight fold down the middle so that the edges line up. 4 inFolded, its dimensions measure 7 x 4 in.Calculate its original dimensions inHint: visualize the unfolding pattern.13. Triangle ratioA circle has an equilateral triangle touching its circumferenceon the outside and another equilateral triangle touchingits circumference on the inside, as pictured.What is the ratio of the areas ofthese two triangles? :14. Cross mathFill the empty cells with the correct number or function. Career with no math? 2 2 So you might be wondering how these 8 ÷ = 4 + math exercises could relate to your 3 everyday life. The familiar story is that 7 1 we leave school or college and consign + 4 x == 4 our math books to the attic, or even 9 x 8 = x 8 throw them away, thankful that we = 0 won’t have to do another calculation 1 1 + – 6 = 9 for the rest of our days. Think again! 5 2 2 + 0 5 ÷ Do you know how many jobs or careers exist where you won’t have x = 3 ÷ 3 to use what math you have learned? – = 3 = 4 5 ÷ = 5 On average, less than 10 percent = = x throughout the world (and even that 4 ÷ + 3 = 6 7 estimate is a very conservative one). 0 7 = The truth is that everybody needs = to use numerical skills at every stage, whether in personal or working lives, 1 2 – = and the more well-honed yours are, the better.
106 Numerical reasoningSudokuOver the last few years, Sudoku has become column, row, and subgrid. The whole puzzleone of the most popular games worldwide is based on what is known as a Latin square,for exercising your brain. Although popularized possibly a reference to the preferred Romanin Japan during the mid-1980s, it was actually military formation.invented by an American, Howard Garns, in Sudoku is a logic exercise. It uses numbers1979, and was then called Number Place. but the puzzle involves no arithmetic as such. It is a neat little puzzle consisting of nine Following the rules of the game, and using thesquares with nine spaces in each square, which numbers already given, you work out whatare so placed as to form one large square, with the other numbers must be through a processvertical and horizontal lines, each with nine of deduction. The great thing about Sudoku isspaces. The aim is to ﬁll in a 9 x 9 grid of 81 cells, that each successful step makes the next stepsubdivided into 3 x 3 subgrids, with the numbers easier by narrowing the possibilities. Every box1–9. Each digit can appear only once in each you solve offers a clue to ﬁll another box.Rules of Sudoku at a glance:the numbers 1 to 9, each appearing once only. 2 5 7 4 8 1 9 6 3 column 1 9 3 6 2 7 5 4 8 8 4 6 5 3 9 1 7 2 3 6 1 7 5 8 2 9 4 row 9 8 5 1 4 2 7 3 6 7 2 4 9 6 3 8 5 1 6 3 2 8 7 5 4 1 9 4 7 9 2 1 6 3 8 5 subgrid 5 1 8 3 9 4 6 2 7
Exercises: sudoku 107Easy SudokuThe grids below are for the Sudoku virgins. As with all The grids become progressively more difﬁcult on the nextnumerical reasoning games, you’ll be amazed how much page. Don’t worry though, we’ve given a few hints to helpa little practice will improve your problem-solving skills. you with these. They also become much easier with practice. All you experts will probably ﬁnd these starter You’ll soon understand why Sudoku is so popular,exercises a little easy. However, that doesn’t mean you especially if you are the kind of person who always likes toshould ignore them altogether. You might want to boost solve puzzles you begin—there’s deﬁnitely some comfort inyour conﬁdence by doing these puzzles ﬁrst and ﬁnishing knowing that there is always a right answer. So, what arethem in a ridiculously short time. you waiting for? Get started! Grid A 7 2 6 1 2 9 8 4 5 3 8 2 4 1 2 6 5 6 1 2 3 5 7 8 9 5 4 8 1 7 9 6 4 6 9 5 Grid B 1 2 4 9 3 2 9 7 5 1 2 4 9 3 2 6 5 4 2 2 8 5 1 3 8 5 4 4 3 6 8 7 9 2 6 8 Solutions on p.179
108 Numerical reasoningIntermediate SudokuHint: one of the best pieces of advice is to “eliminate”:look for spaces where numbers can’t go. For instance, ifa box has 4 unﬁlled spaces, but you see 3 of the remainingnumbers won’t go into one of those spaces, then the 4thnumber must go there. Grid C 4 8 9 1 6 8 5 8 1 4 3 9 5 4 8 7 3 2 7 8 3 5 3 4 7 6 6 2 9 9 8 3 Grid D 6 7 7 2 2 9 1 5 3 6 5 7 1 4 9 1 8 7 8 6 4 5 1 2 6 8 3 8 7 3 9 7 Solutions on p.179
Exercises: sudoku 109Hard SudokuHint: group possible numbers into pairs. If 2 will slot intoa couple of spaces but you’re not sure which goes where,pencil them in anyway. This might leave you a spacewhere another number must ﬁt through trial and error.These puzzles demand patience and perseverance. Grid E 8 3 4 2 3 6 4 7 1 5 2 8 3 9 2 3 5 1 3 4 6 7 9 4 2 7 Age-proof the brain The key to age-prooﬁng the brain is to keep your brain active and to build on this. Simple techniques, such as games like Sudoku and the range of exercises in this book, challenge your brain and help keep it active. Think broad—if your work requires you to do the same kind of thing every day, try to learn a new skill, so your brain doesn’t get lazy or inactive. (See Chapter 7 for more tips.)
110 Numerical reasoningSamurai SudokuThe Samurai Sudoku is the monster puzzle that any Sudoku addictwill, sooner or later, feel compelled to tackle. If you’ve enjoyed theSudoku exercises, these should offer an excellent progression. Thegame is essentially the same as normal Sudoku except that itconsists of ﬁve interlocking Sudoku grids, and will really call uponall your powers of concentration and deductive reasoning. And, ofcourse, you’ll get ﬁve times the satisfaction when you’ve solved thepuzzle. Rumor has it that geishas invented these exercises to whileaway the long hours waiting for their Samurai lords to return fromthe battleﬁeld—hence the name. Grid A 5 4 8 7 3 6 8 9 9 5 3 2 9 7 9 8 4 8 3 6 1 3 7 7 4 8 5 4 3 2 6 2 6 2 5 8 2 1 2 4 7 5 2 1 5 9 6 9 6 3 8 4 1 3 5 7 6 7 9 2 7 9 2 8 4 4 2 6 8 3 7 1 1 9 8 5 6 8 7 9 4 6 6 4 8 5 1 7 2 1 3 3 5 1 9 6 4 6 4 6 9 2 7 8 3 2 9 3 5 9 6 4 2
Exercises: samurai sudoku 111 Tips All normal rules for Sudoku apply: no number can be repeated in any row, column, or grid. The central grid is critical, since numbers in each of its four corners correspond to numbers in the corners of all the others. It’s best to work inward from the outside grids; don’t try to solve the central grid ﬁrst. Concentrate on each grid brieﬂy; keep moving clockwise before tackling the central grid. Don’t allow yourself to be overwhelmed by the sheer scale of the puzzle; keep repeating your clockwise deductions. 6 3 7 9 9 3 8 6 1 4 2 3 2 5 3 61 9 2 4 7 2 4 75 4 8 7 6 7 3 9 1 1 9 7 5 6 4 7 8 3 56 5 1 9 8 4 2 1 4 1 5 7 3 7 9 4 2 9 4 75 3 8 2 1 5 7 6 5 1 5 4 8 9 5 7 9 8 41 2 3 8 4 2 9 3 8 2 7 3 4 6 8 6 7 1 7 9 2 6 6 2 3 6 4 8 2 Solutions on p.180
112 Numerical reasoningKakuroKakuro is the second most popular logic-puzzle gameafter Sudoku in Japan, and is also rapidly gaining theattention of puzzle fans throughout the world. Kakuro is laid out slightly more like a crossword. Numbers,often called clues, are given in shaded squares, relating to thehorizontal or vertical lines of numbers. Although a number canbe used only once to make up each total sum, there is no suchrestriction over the puzzle as a whole, and consequentlyKakuro solutions are less uniform and provide greater varietythan those of Sudoku. Kakuro is a useful variant to Sudoku,since it not only tests your logical aptitude but also exercisesyour numerical reasoning skills because it demands that youuse mental arithmetic to solve the puzzle. It is this variety that tends to appeal to those who ﬁndSudoku a little one-dimensional. Although starting off withobvious total combinations (4 = 1 + 3, 17 = 9 + 8), theanswers have a greater impact upon each other, involvingmore combinations, and giving the ﬁnal grid a verydifferent feel. Since no numbers are ﬁlled in originally(unlike Sudoku), you often have to work out differentcombinations on a separate sheet, making it closer to themathematics we all studied (or are studying) at school.Rules of Kakuro at a glance:crossword, containing shaded squares and blanksquares, where you need to ﬁll in a number from 1–9.to the total stated for that column or row on the grid. 7 3 Numbers in the left lower part 6 4 2 of each square refer to the total sum of the vertical column 4 3 1 Numbers in the right upper corner refer to the total sum of the horizontal row
114 Numerical reasoningLogic ﬂies out of the windowOK, so you’re now feeling more conﬁdent about using numbersand applying logic, both as a stimulus to mental activityand as a yardstick in everyday situations. But isn’tthere some nagging feeling in your psychologicalmakeup that says: “Sure, these games may beuseful at certain times but when it comes tothings I know well, I’ve got my own trustedmethods, thank you very much”? If you feellike this, then you’re not alone.HeuristicsAt times, most of us resort to intelligentguesswork rather than logic which, in theﬁeld of psychology, is known as applyingheuristic knowledge. This is a perfectlynatural response to incomplete informationor a complex problem. Our brains have beenencoded with these generally efﬁcient rules,either learned or inherited, which enable us to ﬁll inthe gaps. This is what leads us to make educated guesses andintuitive judgments. In other words, we are applying commonsense. There’s only one slight ﬂaw—although our brains maylead us to the correct answer most of the time, they might alsolead us astray unless we stop, take a step back, and apply logic.However, in practice this is easier said than done! The trouble is that although we are in the wrong andbiased, we still believe that we’re in the right. It’s arecipe for trouble, which is why psychologists are sointerested in the uses and effects of heuristics. Have alook at these examples. What would you think or do? 16. Beer money You’re on your way to meet friends15. Lottery numbers and you ﬁnd a $50 bill lying in theYou go into the store to play the lottery because it’s a street. You pick it up and decide torollover month and the jackpot is mammoth. The lady in buy everyone a drink with thefront of you is also playing the lottery and money. In other words you’re goingshe’s marked down numbers: 1, 2, 3, to spend it on a whim. You attach4, 5, 6. You think she’s totally nuts less value to it than you would afor choosing those numbers because $50 bill that you earned. Why so? Isthey’ll never come up. Is she being it really worth any less?ridiculous, or are you being illogicalfor entertaining that thought? Solutions on pp.180–1
Exercises: logic ﬂies out of the window 11517. Bidding warYou’re at an antiques auction lookingfor new stock for your antiquesshop. You’ve been ﬂicking throughthe catalog and have spotted abeautiful carriage clock. When thelot comes up you start bidding,setting yourself a price limit. Asthe bidders fall away, there’sone person left who keepsoutbidding you. You glance over your shoulder to see 18. Expensive tastesthat it is your arch competitor. Suddenly the price limit An inexpensive bottle of cologneyou set yourself means very little. Why are you being so costs $30, whereas a designerillogical? Don’t you have a business to run? brand costs $60. The retailers increase the price of the cheaper scent to $65. Which do you think will sell more? Conclusion Turn to the back of the book for the explanations. You’ll see that the logic is simple, but in certain situations these common biases can easily creep into our minds. What conclusion can we draw from this? Well, occasionally it’s fair to say that the human brain seems to want to let logic ﬂy out of the window. It might even be the natural order of things. After all, it’s only logical that we behave like human beings.19. Bad luck?You are with your friend in Las Vegas at a roulette table.Your friend has just won for the sixth time in successionby putting her chips on the red. She’s becomingreally smug while you’re running out of chips.You challenge her to try again. She obligesand advises you to always put the chipson the red. You spite her and put yourremaining chip on the black. Whodo you think has a better chanceof winning?
116 Numerical reasoningGambler’s fallacyBet you haven’t heard examples of the gambler’smantra! Well, it goes like this: “the next horse isgoing to come ﬁrst,” or “the next card is going tobe an ace,” or “the next fruit is going to be thatelusive third cherry.” We all know that it doesn’treally make sense, but the gambler conspires tokid himself that the fact he lost last time meansthat he’s more likely to win next time. In reality,the dice are eternally loaded against us. Ourchances are the same as before—pretty low,unfortunately. But don’t tell that to the gambler.And certainly don’t tell the person in front ofyou in the line who is about to play the lottery,because the odds for them are even worse. Infact, the odds of matching all six of six numbersfrom 49 are 1 in 18,069,460! So, what makes us ﬂy in the face of commonsense? Why do gamblers play against the oddswhen they’re often intelligent people? Is itjust greed? Without going too deeply intopsychological matters (basically, the driving forceis being on the cusp of the unknown), the answeris that the lure of winning big overrides thegradual despondency of losing small—or even Looks good, sounds good,relatively large—over a period of time. feels good! The casinos and other gambling outlets are only too aware of this fallacy and do everything in their power to lure the gambler to part with that last coin rolling in his pocket. They resort to the theory of “affect heuristic” to inﬂuence the gambler’s decision. What we mean by “affect” is that they offer multiple stimuli to generate an involuntary response. Slot machines are a perfect example. Think about all those ﬂashing lights, the tantalizing colors, the pace at which the reels turn, the electronic sounds that imply you’re on the brink of winning big. Oh, and what about that near miss? It’s drawing you in, messing with your logic, and lowering your risk perception. It’s manipulating you through your visual and aural senses. No wonder Las Vegas is the city of neon lights.
Feature: gambler’s fallacy 117 Sly, subtle scents Did you know that many casino operators pump a scent into the air? This may sound rather bizarre, but in an experimental test the scent was shown to increase substantially the number of coins customers dropped into the slots—by about 45 percent!Law of averagesThe law of averages is the diametric opposite of Murphy’sLaw. Basically, Murphy’s Law states that if something can gowrong, it will, whereas the law of averages is usually invokedto say that if things haven’t been going right, they will now.“By the law of averages, Katherine Howard is deﬁnitely thewife for me,” said Henry VIII, the 16th-century king ofEngland, delighting over his ﬁfth marriage. Result: herexecution a few months later. The law does not take intoconsideration other circumstances that might affect theoutcome, and usually reﬂects bad statistics or wishfulthinking rather than any mathematical principle.20. Heads or tails?Take a coin, and toss it, then ﬂip it again, and so on.Write down how many times it comes down “heads”in the ﬁrst 10 tosses. What are the odds of it being“heads” next time? Don’t you dare fall for the heuristicimpulse—you should know better by now! Solution on p.181
118 Numerical reasoningUnraveling numericalriddlesRiddles are similar to logical fallacies (see pp.114–117)in that they make you employ false logic. Riddles areproblems that are usually expressed in metaphoricalor allegorical language, and are loaded withambiguity. They are designed to trip youup, so you have to think carefully inorder to ﬁnd the correct solution. The best riddles cause your brains toﬁll in the missing gaps without usingsound reasoning, and they use allsorts of methods to lead youastray. Remember, mathematicalriddles are abstract, so it’s crucialto pay particular attention toinformation that doesn’t seemimportant in the ﬁrst reading. Someof the more “vital” informationyou are given might be there tolead you away from looking at thetrue problem itself!Progression MisdirectionAnother common type of riddle involves numerical progression This is the standard ploy used in most riddles. Here’s anor a sequence of numbers. The tendency in the progression example: “I have three coins in my pocket, which totalseems to be drawing you toward one answer, but in fact the 60 cents. Two of the coins are not quarters. What areanswer lies elsewhere. Here’s an example: 1, 1, 2, 3, 5... the coins?” Now, your initial instinct might be to propose this The questioner invites you into all the byways of lateralsolution and the rest of the series of numbers based on thinking, but the answer depends on a trick. So before youprime numbers: 1, 1, 2, 3, 5, 7, 11, 13. start working out whether the question is referring to However, the correct answer is based on adding another currency or other complicated explanations, look attogether the last two numbers (known as the Fibonacci it again carefully.sequence, after its inventor): 1, 1, 2, 3, 5, 8, 13, 21. “Two of the coins are not quarters.” Sure, but the third In this instance, the riddle has deceived you as to the one is. The answer is two quarters and a dime.type of progression used.
Feature: unraveling numerical riddles 119Logical teasersWe also include some logical conundrums, which offerapparently quirky answers to seemingly innocuousquestions, brain teasers, and other mind twisters. Thisoffshoot of math relies on thought rather than numbers.It tests your ability to ﬁgure out certain givens andconnect them together until you arrive at the solution. Question: How do you get (exactly) 4 gallons of water out of a well if the only pieces of equipment you have are a 3-gallon bucket and a 5-gallon bucket? Answer: 1. Fill the 5-gallon bucket from the well. 2. Use the 5-gallon bucket to ﬁll up the 3-gallon bucket. This leaves 2 gallons in the 5-gallon bucket. 3. Empty the 3-gallon bucket into the well. 4. Pour the 2 gallons from the 5-gallon bucket into the 3-gallon bucket. 5. Fill up the 5-gallon bucket from the well. 6. Fill up the 3-gallon bucket using the 5-gallon bucket. The 3-gallon bucket already contains 2 gallons, so 1 gallon goes from the 5-gallon bucket to the 3-gallon bucket. 7. You have just removed 1 gallon from the 5-gallon bucket. Voila! That leaves you with 4 gallons.
120 Numerical reasoningRiddles to trySo, just for a bit of fun, take a look at these classic types of riddles.Don’t worry too much if you need to peek at the answers—some ofthese are pretty difﬁcult to solve. Of course, the more you practice,the easier they will become. 21. Number sequences A: Find the next number in the following sequence: 1, 11, 21, 1211, 111221, 312211, ... B: What’s the next number in the sequence? 31, 28, 31, 30, 31, ... C: Find the next number in the sequence: 1, 4, 1, 5, 9, 2, 6, ... D: Find the next number in the sequence: 6, 25, 64, 81, 32 ... Hint: just because you’re presented with numbers doesn’t mean that mathematical logic applies!22. Chasing carsConsider a road with 2 cars traveling the right car and ﬂies at a speed of What is the total distancetoward each other with a distance 80 mph. When it reaches the left car that the bird has traveledof 100 miles between them. The left it reverses direction, and when it at the moment the 2 cars milescar travels at a speed of 40 mph and reaches the right car it reverses have reached each other?the right car at a speed of 60 mph. again to the opposite, and so on.A bird starts at the same location as 80 mph 40 mph 60 mph 100 miles
Exercises: riddles to try 12123. The famous 3 doors conundrumYou’re appearing on a TV game show. The host showsyou 3 closed doors and tells you that there is a ﬂashynew red sportscar in a room behind one of them. Theother rooms are empty. If you choose the correct door,you win it. You pick a door at random. The host, whoknows where the car is, stops you, then opens anotherdoor and shows you an empty room. He asks if youwant to change your mind. Should you?yes no 24. Weighing marbles You have 10 bags with 10 marbles in each bag. All of the marbles weigh 1 oz except for the marbles in one bag, which weigh 0.9 oz. But you don’t know which bag these 0.9 oz marbles are in. You have to ﬁnd out by taking zero or more marbles from zero or more bags and putting them on weighing scales. After seeing the result of the weight, you should be able to tell which bag contains the marbles that weigh only 0.9 oz. How many marbles from which bags do you take to weigh? (You’ll need to work this out on a separate piece of paper.)25. The condemned prisoner 26. Break up timeconundrum Break this clock into (exactly) 5 pieces so that the sum of the numbers on each piece add up to 8, 10, 12, 14,You are one of 3 prisoners in the same cell condemned and 16.to death. The jailer capriciously decides that one of youmay be spared—the one who’s the ﬁrst to guesscorrectly the color of the disk afﬁxed to the back of hisor her head. Any wrong guesses will mean instant 11 12 1death. The jailer shows all 3 of you that he has 5 disks: Hint: you’re2 black, 3 white. He uses 3 of them and hides the other allowed to cut2. You can see that each of the other prisoners has a through double 10 2 digits!white disk. 9 3What is the color of yours? 8 4 7 6 5 Solutions on pp.181–2
124 Verbal reasoningTalk your way to successThere is a direct correlation between verbal aptitude and successin life. We’re not just talking about the ability to completecrosswords, unravel anagrams, or ﬁgure out antonyms, althoughall of those activities are great for exercising your verbal aptitude.We’re talking more generally about the ability to use words,to manipulate language so that you can communicateideas, thoughts, opinions, and feelings cogently.Arguably, politicians and lawyers utilize thisskill best, as do rap artists and talk showhosts, who are all adept at engaging a massaudience with the power of words, oftenusing them to inﬂuence an audience’s wayof thinking. In short, the better your verbalintelligence, the more conﬁdent you willbe at asserting your needs and wants.You will be better understood andwill be able to form closerrelationships. Whateverthe path you take in life,improving your verbalaptitude will have amarked effect onyour social progressand prosperity.Language and the visualScientists believe that by the age of ﬁve you may alreadyhave about 2,000 to 3,000 words in your vocabulary, butthat does not mean you know the exact meaning of thesewords. For example, a child seeing a ball might say “ball” buthe might also say “ball” pointing at a balloon, a chocolateegg, or a pebble. What this suggests is that on an instinctivelevel, the visual sense has an enormous inﬂuence on howlanguage develops. For instance, consider the ﬁrst alphabetbook a child looks at. An image is used to qualify and givemeaning to a character in an alphabet. For example, “A“ forApple, “B” for Bear, and so on, so it stands to reason that ayoung child uses the same word for similar-looking shapesuntil his vocabulary grows. And while you may think that thisreliance upon the “visual” is something you grow out of bythe time you get through school (having accumulated a
Introduction: talk your way to success 125How it works Arcuate fasciculus Wernicke’s areaThe ability to use words and tap into the vastpossibilities of the spoken and written language booststhe brain’s processing power by opening up additional Broca’s areaneuron pathways. Scans have traced activity throughoutthe brain and not just the left side, indicating that verbalreasoning is an extremely complex process. When you the correctengage in a conversation, a whole series of cognitive syntax, and sofunctions take place even before a sentence reaches on. Wernicke’sthe tip of your tongue. A thought lights up in your area, which ishead, your brain then reﬁnes it using all the sensory located in theassociations, sends this information to two key areas temporal lobe, is of the brain (see below), which then select the responsible for language necessary words to convey its meaning, and ﬁnally processing—unscrambling place the words into a grammatical framework. others’ sentences, analyzing them Only then are you ready to speak. for syntax and inﬂection, and extracting meaning from them. A connecting neural The language powerhouses pathway called the arcuate fasciculus runs between theThe two main powerhouses of the brain’s linguistic two so that the areas are always working together. Thissystem are called Wernicke’s area and Broca’s area, system taps into other areas of the brain, allowing younamed after the two scientists who discovered these not only to talk and to understand speech, but also toregions in the 1800s. Broca’s area, which is located read and write, and even make speech-associatedin the frontal lobe of the cortex, is responsible for gestures. It also gives you the power to understandlanguage production—putting together sentences, using complex thoughts, and acquire new knowledge.vocabulary of about 50,000 words),consider the use of analogies, metaphors,and similes (see p.70). Visual conceptsinﬂuence language throughout your life.For instance, public speakers and those inpositions of power know that they stand a greaterchance of keeping you engaged if they use wordsto tell a story that conjures up a “big picture.”Words might evaporate, but use them to conveyan image and the idea behind it will be morememorable. The great orators have always reliedon the “visual” to fashion speeches. ConsiderMartin Luther King’s famous address to thenation. The words “I have a dream...” instantlyopen a window to his vision of the future!
126 Verbal reasoningQuick-ﬁre vocabulary test 3: PRODUCT A. a person or thingWe’ve grouped together a number produced by or resultingof simple exercises to measure your from a process, such as acurrent vocabulary. This is an example 1. Dictionary natural, social, or historicalof the type of test a prospective corner one; resultemployer might use to gauge an B. a continuous action, Select the correct deﬁnitionapplicant’s intelligence (and which operation, or series of from the three options. changes taking place in aforms part of psychometric testing). 1: HOLLOW deﬁnite mannerAdmittedly, vocabulary exercises are a C. a building or group of A. having a space or cavitycrude method and only test a speciﬁc inside; empty buildings with facilities forbranch of crystallized intelligence (see B. barren or laid waste; the manufacture of goodsp.128), but since clear understanding devastatedand expression are necessary to most C. to make a hole or 4: SQUANDERcareers, any job selection process will opening A. to stake or risk money, or anything of value, oninevitably test your vocabulary. 2: ACTIVE the outcome of something If you’re not an avid reader or do involving chance A. without anxiety or worrynot work directly with words then you B. engaged in action; B. to spend or use (money,might be surprised by your limited characterized by energetic time) extravagantly orknowledge of vocabulary. However, work, participation wastefullywith constant practice, you can C. boldly assertive and C. to distribute orexpand your knowledge of words forward; pushy apportion by measure;and overall command of allot; dole outlanguage, which includes 5: FLOWERyour critical reasoning A. the blossom of a plantcapabilities. B. woody plant smaller than a tree, usually having multiple permanent stems branching from or near the ground C. a fertile and delightful spot or region 6: PLIANT A. smooth and agreeable to the touch; not hard or coarse B. a condition, a state, a situation, especially an unfavorable one C. bending readily, ﬂexible, supple; adaptable Solutions on p.182
Exercises: quick-ﬁre vocabulary test 1272. Like for likeSelect the correct synonym from the four options.1: EUPHORIC 9: MELODIOUS 3. Find the oppositeA. lively A. sweet Select the correct antonym from theB. surprised B. harmonic four options.C. engrossed C. raucousD. ecstatic D. soulful 1: SHARP 6: DAMAGE A. chubby A. weaken2: PIOUS 10: AMPLE B. blunt B. repairA. legal A. ornate C. boring C. medicationB. devout B. thriving D. bright D. evolveC. spirited C. plentifulD. lucky D. elegant 2: CONSENSUS 7: DECLINE A. disagreement A. hesitate3: TIRED 11: DODGE B. teamwork B. acceptA. inﬁrm A. disguise C. dissension C. delegateB. fatigued B. net D. permission D. spurnC. dazed C. provokeD. downbeat D. evade 3: SURVIVE 8: EXPAND A. nonexistent A. amplify4: AUTHENTIC 12: MELLOW B. cease B. reviseA. ancient A. lament C. extinct C. shortenB. vintage B. soft D. suffer D. skinnyC. genuine C. frigidD. lavish D. exhibitionist 4: WITHSTAND 9: FRIENDLY A. endure A. affable5: SMART 13: OPTIMISTIC B. survive B. evilA. intelligent A. reliable C. succumb C. concernedB. resolute B. righteous D. possess D. aloofC. subtle C. hopefulD. bullish D. bright 5: DAINTY 10: INQUISITIVE A. coarse A. curious6: PERCEPTIVE B. petite B. cleverA. adept C. superior C. meddlingB. insightful D. dirty D. indifferentC. assuredD. resourceful Men and women7: KNAVE It is widely believed that men outperform women in overallA. slayer spatial ability while women outperform men when it comesB. storyteller to verbal reasoning. But if recent studies are anything to goC. rogue by, it seems that any difference in verbal aptitude accordingD. bigot to gender is negligible. What’s more, if the verbal reasoning8: CONCUR test includes questions that require spatial processing—forA. defeat example, solving linear syllogisms (Bob is heavier than Bill,B. agree and Bill is heavier than John; who is heaviest?)—then menC. bolster tend to fare better. However, scientists concede that moreD. cooperate research is required.
128 Verbal reasoningLanguage andintelligenceFluid intelligence and crystallized intelligence arefactors of general intelligence. Fluid intelligence isthe ability to ﬁnd meaning in confusion and solvenew problems. Crystallized intelligence refers tothe knowledge and skills accumulated over alifetime and that you apply to do familiar tasks.How does language ﬁt into all this? Well, as achild, you use your ﬂuid intelligence to makesense of the language spoken by your parentsand, in turn, learn to communicate withthem. During puberty, the rules ofgrammar, syntax, and all theother nuances of languagebecome crystallized.At this point, thekey region of thebrain where youimprint new informationand skills becomes smaller.It’s the reason why learningany language is a lot easierwhen you are young.Develop a bilingual brainIt is not impossible to learn a new language inadulthood. In fact we encourage it because,along with taking up a musical instrument, it’sone of the best ways to ﬁre up your neuronsand keep the brain active. These activities arementally demanding because they force thebrain to process unfamiliar information andmake new connections. Learning a foreignlanguage can also help protect the brainagainst the ravages of aging. Researchsuggests that people whoare bilingual seem tosuffer less mental declinefrom aging than those whospeak only one language.
Feature: language and intelligence 129Tips and look them up in a dictionary later on. If you areHere’s a rundown of our tips for improving your really conscientious, answer the questions “who?”,verbal aptitude: “what?”, “where?”, “how?”, and “why?”at the end of each chapter. As your aptitude for comprehension people from all walks of life. improves you will naturally begin interacting with the Look beyond family members, friends, text and this will develop your critical thinking skills. and colleagues at work. Be curious. Ask Verbalizing thoughts not only questions. Thoughtful conversations exercises the left side of your brain but molds abstract boost your overall cognitive capacity concepts, metaphors, and other symbols into more because nanoconnections are happening concrete forms. as you converse. Again, it’s By writing a daily or another reason why verbal discourse weekly journal you will develop yourin the form of classroom discussions powers of expression, which willis a commonly used learning tool. have a knock-on effect on your overall verbal aptitude.such as lawyers or politicians.Concentrate on the thread of their Games and exercises such as solvingargument. These professionals anagrams, rebuses, verbal analogies, and crosswordstend to have a highly developed maintain your verbal aptitude (see pp.130–137). Mixthinking power based on their and match the games to give yourself a moremastery over language, and can holistic workout.put across a point effectively. over a random Stretch yourself by horoscope page. It can be any sign andchoosing challenging material. Pick it doesn’t matter whether or not youup a classic novel or poem that believe in it. Try to extract the mainwill introduce you to new words and points from the information anddifferent styles of writing and original summarize them. Be extremelyways of thinking. However, reading in analytical and ask yourselfitself is a passive activity, so make a whether the horoscope is revealingmental note of unfamiliar words anything concrete.Verbal ﬂuencyImproving your vocabulary raises your intelligence, plain andsimple. The average person’s spoken vocabulary is about 1,000words and the number of words available to feed the brain isover three million. So there’s a vast scope for improvement. Thebroader your vocabulary, the more it will stimulate the brain byﬁring cell interaction during conversation, reading, and writing.A broad vocabulary gives you an advantage in school, business,and social situations. This is because you are able to think aboutmore complex things precisely. Verbal ﬂuency will give you thedouble advantage of thinking more quickly under pressure andtalking more composedly under duress.
130 Verbal reasoningA workout with wordsHere is a selection of fun exercises to help sharpen yourverbal aptitude. They are designed to combine your visualsense with your verbal reasoning skills.4. Word associationThis is a game to play in pairs. Write random wordson scraps of paper, fold them, and put them into abox. Sit down and face each other. Take turns pickingout a word and let the word association game begin.For example, the word “boat” might inspire theword “sail,” “sea,” “oar,” and so on. Youare not allowed to pause, hesitate, or repeata word. See how far you can gountil someone breaks one of the rules.5. Colored wordsIn the fastest time possible, sayaloud the color the word isprinted in, trying not to read theword. This exercise works bothhemispheres of the brain, withneurons zapping between theverbal and visual sites as you yellotry to manage your attention, winhibiting one response in blackorder to say something else. blue oran ge red blue oran ge gree gree n seconds gree n red n black purp purp le le yello w oran ge
Exercises: a workout with words 1316. Scrambled sentencesUnscramble the following list of words to make a normal sentence. Noticehow your eyes keep stalling because the brain cannot make sense of thewords, which disrupts your natural reading rhythm. This is a harder exercisethan you might think. A: a teacher Margaret school is strict B: circulation improves to exercise Physical brain blood the C: brain of billion 100 consists Your about neurons D: exercise is brain-training a Sudoku good E: words average The reading 200–250 speed is minute a F: read You are you what G: reading experience eyes By another life through you by vicariously the of H: reasoning use ﬁnd assess candidate verbal out verbal tests well how a can logic to Interviewers Solution on p.182
132 Verbal reasoning 7. The word ladder Use association to get from the ﬁrst object to the last. This is more demanding than game 4 because you have to use your verbal aptitude to get to a ﬁxed destination.A: C: D: B: camera cake bird clockumbrella glasses chair bicycle 8. Word-play analogies Identify the correct analogy that would make each statement true. A: Come is to go B: Arm is to hand C: Right is to left D: Rose is to ﬂower as arrival is to ... as leg is to ... as below is to ... as dog is to ... terminus foot ground cat airport toe above human depot ankle ceiling animal departure sole cellar puppy
Exercises: a workout with words 133 A 9. Student lodgings A: Andrew, Bruce, Caroline, David, Emma, Fiona, F George, and Harriet are all friends who met at college. As students, they lived together in different groups. The diagram below shows how they were grouped. B G D E H A C B C 5. Which person/s remained in house 2 (blue) all year? D E 6. Which person/s lived in all three houses? G F 7. Who is the only person Bruce lived with this year? H 8. Which house held the most people? 1. Which person/s lived in all three houses? C: People moved once more in the ﬁnal year. The diagram below shows how they were grouped. 2. Which person/s lived in house 1 (green) and house 2 (blue) but not in house 3 (red)? A 3. Which person/s lived in house 1 (green) for the entire year? C H 4. Which person/s moved from house 1 D F (green) to house 3 (red)? G E B B: The following year people moved into different houses. The next diagram (above, right) shows how they were grouped. 9. Which person/s lived in all three houses? 10. Which person/s lived in house 2 (blue) and E: Love is to hate house 3 (red) but not in house 1 (green)? as heat is to ... warmth 11. Which person/s has Andrew lived with ice during all three years? burning cold 12. Which person/s has Andrew never lived with? Solutions on p.182Solutions on page 000
134 Verbal reasoning10. Odd one outWhich object is the odd one out?A: C: E: F:Car Tiger Tomato ClavichordBus Cheetah Carrot SpinetTrain Leopard Cabbage HarpsichordTruck Jaguar Spinach ClarionB: D:Bonnet RockFez LogCap BoulderStocking Pebble Onl y cor last ni rect ght was spe ,Ia ling rg “co comm “ of a uued w mit ited w it11. Spot the errors! ma te ” w ord: I h my ﬁ ke s d.” A hile said eIt’s easy today. Usually, when peo o ctu my the nd abo ple’ many elly I am friend cor ut twriting, you use a word processing thin gI sm s isst pelling surp insi rect sp he ake sted ellinprogram on a computer, equipped goo wa d fo nt to s th errors rised t gwith spellchecker software, which do ey .O hat that it spe lling r on es p is o feel cr ften w peop ’sautomatically corrects any misspelled spe . erso ffend itici hen lewords, or ﬂags them with a red lling I’ve al nal any zed. O you can bec erro so f dev bod f co pon am ou e y isquiggle. However, spotting a the e re rs som nd th lopem ; I jus arse, t t outspelling error is harder than you coll ally ep at i ent t th he def eop f yo in la bad ag u p to imp k it is stmight think. This is because you spe e I go ensive le just oin rov stud lling to i .Ia get t ou e thsee words as a complete pattern e ; si m em t pe erather than the sum of letter wo nts ho they a mplim realy bar rase aple re rng e to re d ent hap ’s and for raw ing py t d, oparts. To put it another way, any asess me r wo not pra tea wh ering u asu o repoyou tend to recognize words rld. par che at t p cl res rt th r to he a to aeven if some of the units and bad We sho then a e ign y read sses to tackle tmay not be correct. uld d ore cor tea bec aus thinkin , how equatl a stud rectly. chAnother reason for this me e yo ga eve y e I ans ur a re c r, re to go nt’s ba thinkis that you rely on spe is b om m ou d itscontextual information lling that y ad spe pletly embar r into spellin star . It ou ller sep tha the g, t wi nee doe e t wto help recognize not sendin ll reall dt sn’t rate is bad sp iderindividual words you g yo y m o wor ma sue s. Ju ellin get u’re ake kh ke y g ab ar o sduring ordinary an inte CV to e ig d der to u dum treading. rvie mp iffe im . Al w. loye rance prove l it Read the following rs a wh you s to en rpassage and try to pick wea youout all the mistakes. the r or
Exercises: a workout with words 13512. Fill in the blanksChoose the correct word from the list to complete the sentences A–G.1. Trouncing A: Jasper, our pet dog, C: If “Beauty is in the eye F: The team won by2. Fireman started barking when he of the beholder” then why ............. the opposition.3. Bombarding saw the ............ break the do magazines keep ……4. Extend lock and climb in through us with retouched images?5. Expand the window. Jasper had6. Scientist locked all of us out.7. Mesmerizing G: When Ian started out as a ........... he wore his D: It’s a fact that roosters lab coat with the buttons cannot crow if they cannot done up to his neck. B: The poet had an elegant voice. She was …………. their necks. .............. us with her beautifully written verses. E: We’ve been telling Jim to……..... his horizons.13. Wordy riddlesHave fun trying to tease out the answer from theabstract set of information. Consider all possibilities:A: I can be heard but am never seen. D: All things I devour, Once I come out I never go back in. birds, beasts, trees, and ﬂowers; If you recognize me you’ll know I gnaw through iron, and I bite where I’ve come from. What am I? through steel; I grind hard stones to meal; I slay kings, I lay waste to towns, I even bring high mountains down. What am I?B: If there are three cups of sugar and you take oneaway, how many do you have?C: A prisoner was found guilty and was due to besentenced. The judge decided to test his verbalreasoning powers and said to him, “You may make astatement. If it is true, I’ll sentence you to 4 years inprison. If it is false, I’ll sentence you to 6 years inprison.” After the prisoner had thought for a bit andmade his statement, the judge decided to let him gofree. What did the prisoner say? Solutions on pp.182–3
136 Verbal reasoningReading comprehensionReading comprehension is an essential partof language development. The ability tounderstand and interact with the text works 14. Summer jobyour brain in multiple ways, honing your Read the passage and give your answer to each questionperception, reason, problem solving, and other as either “true,” “false,” or “cannot say.”cognitive faculties. It is a fundamental skill towhich you are introduced as a child, develop Post ofﬁces ﬁnd it beneﬁcial to employ students overas a student, and then apply in your career as their vacations. Permanent members of the staff oftenwell as your everyday life. A typical reading wish to take their own vacations during this period.comprehension assessment usually involves Furthermore, it is not uncommon for post ofﬁces toanswering a series of questions relating to a experience peak workloads during the holiday periodgiven passage of writing. The exercise tests and so require extra staff. Holiday employment alsoyour ability to draw logical inferences from attracts students who may wish to return as qualiﬁed recruits to post ofﬁces once they have completed theirsimple life situations. Your answers indicate education. Ensuring that the students learn as much ashow well you interpret the material. possible about the post ofﬁce encourages interest in working on a permanent basis. Post ofﬁces pay students at a ﬁxed rate without the usual right to beneﬁts.An eye for readingComprehension requires good reading, which Statement A—It is possible thatdepends on your ability to recognize words permanent staff who are on vacation canrapidly and effortlessly. This is where your have their work carried out by students.eyes play a major role since the informationis transferred via the visual pathways. The Statement Baverage reading rate for a Roman-character- their vacation period given the same paidbased language is 200–220 words per minute. vacation beneﬁt as permanent staff.Anything less will interfere with your abilityto decode the meaning because you will be Statement Cputting more effort into reading individual post ofﬁce’s standard disciplinary andwords or sentences than trying to understand grievance procedures.the idea being expressed.Common strategies to tacklereading comprehension:gist without stopping in midﬂow.makes sense throughout.
Feature: reading comprehension 13715. The sounds in my lifeRead the passage and based on your understanding ofit, check the box that correctly completes each sentence.I was walking along the street of my villagewhen I heard the siren of a ﬁre engine soundingin the distance. As I turned, I saw two otherpeople turning to look in the same direction. 1. The sound of a ﬁre engine in the villageThe sound of any passing emergency vehicle is makes people … 5. The writer dislikesan instant attention-grabber in my village. A: think of a ﬁre the sound of a dog’s B: look at each other bark because …In contrast, people living in a city are exposed to C: pay attention to it A: it doesn’t affect herso many sounds that they become desensitized D: stop crossing the street B: it reminds her ofand don’t really pay much attention when they happier timeshear an emergency vehicle in the distance. 2. People in the city … C: it makes her feel tense A: don’t care about D: it is too loudI was the same when I used to work in the city emergenciesmany years ago. I hardly ever noticed any B: are used to sirens 6. The writer enjoys thesounds while sitting at my desk, even when the C: are attracted by sounds sound of …window was wide open. D: don’t hear loud noises A: a coin dropping on the pavementIt’s very different at home here in the village. If 3. The writer … B: her typewriter whenI’m in bed, the sound of an aircraft ﬂying high A: sleeps next to the she’s typingover the house can wake me up. window C: anything that attracts B: isn’t sure what causes her attentionIt’s the quieter sounds that affect me the most. the noises at night D: footstepsSometimes, in the middle of the night, I can C: believes in ghostshear scratching noises downstairs. I also hear D: is interested in aircraft 7. The writer thinks thelittle creaking noises, which my imagination sounds in her life are ...turns into footsteps. This has been going on for 4. The writer relates to A: making her miserablethe last 25 years. I’m not sure why I never hear sounds at night by … B: louder now becausethese sounds during the day. A: imagining sounds that she’s more attuned to do not exist themI have a good idea of sounds I like and sounds B: exaggerating quiet C: a general mixture ofthat I don’t. I no longer like the sound of a dog sounds good and badbarking. It never used to bother me but now C: imagining the sound of D: a lot better at nightit reminds me of the time I got bitten and doors shutting because they affect herwhenever I hear the sound, my palms begin to D: refusing to the mostsweat and my body tenses up. acknowledge themThe sound of the keys of my typewriter hittingthe paper is lovely. I often write so that I can Solutions on p.183listen to the sound my typewriter makes.
138 Verbal reasoningWords and picturesHistorians have traced the art of storytelling, late Will Eisner, a famous cartoonist, called themwhich uses a sequence of pictures, all the way “sequential art” as opposed to “comic strips.”back to the earliest human civilizations. However, Over the years many educational institutionsthe art form that combines words and pictures have used comic strip narratives to develop verbalevolved much later on. For example, it wasn’t reasoning and comprehension skills. We responduntil the American comic strip format arrived in more positively to the combination of wordsthe early 20th century that devices such as the and pictures. In a world overloaded with visualword balloon for speech, the symbol of the material we have become more image-savvy and,ﬂashing light bulb above a character’s head to therefore, comic strips offer a fun and effectiveindicate a bright idea, and speciﬁc typographical way to boost literacy. You can do a fun exercisesymbols to represent cursing were introduced. The by cutting up the comic strips into individualﬁrst comic books were anthologies collected from cells, shufﬂing them, and then trying to put themnewspapers, which ran adventure stories such back together. You might even ﬁnd an alternativeas Buck Rogers, Tarzan, The Phantom, and The way to piece the cells to construct a differentAdventures of TinTin in comic strip format. The story altogether! Solution on p.18316. Dog’s day outWe’ve removed the text from thespeech bubbles in the comic stripand listed it below. Using the visualcues, try to put the correct text intothe correct bubble so that thedialogue makes sense.
Feature: words and pictures 139Verbal or visual? Future research based on these ﬁndings may be able toA recent psychology study, using functional magnetic determine whether cognitive styles are something one isresonance imaging (fMRI) technology to scan the brain, predisposed to or can learn. Depending on the ﬂexibilityrevealed that those who regard themselves to be visual with which one canlearners, as opposed to verbal learners, have a natural adopt a style,tendency to convert linguistically presented information educators couldinto a visual mental representation. The more strongly cater to onean individual relied on the visual cognitive style, the style over another tomore that individual activated the visual cortex when improve learning.presented with any reading matter. It has long been According to the study, the opposite also appears thought that propensitiesto be the case. Those participants who considered for visual or verbalthemselves verbal learners were found under fMRI learning styles inﬂuenceto have brain activity in the region associated with how children acquirelanguage cognition when faced with a picture (see knowledge successfullyp.125), suggesting they have a tendency to convert and how adults reason inpictorial information into linguistic representations. everyday life.
140 Verbal reasoningBuild a storyStorytelling is an ancient oral art that demonstrates the power ofwords to express thoughts, ideas, and feelings. We have relied uponit for spreading news, imparting wisdom, and learning the culturalhistory of others and ourselves. Storytelling is a commonly used toolfor making connections with people of all ages and races. It is also a very powerful tool that develops and strengthensskills in the language areas of semantics (meaning of words), syntax(formation of words), phonology (speech sounds), and so on.Storytelling uses language artistically to develop all of the criticalcomponents involved in the communication process. Storytellingimproves listening skills, enhances verbal expression, increasescomprehension, creates mental images, and stimulates verbalreasoning. It is the most holistic way to hone your verbal aptitude. Taking our cue from this, we will end this chapter with twoexercises that will test your creative writing skills.17. A mini-adventureWrite a paragraph that is no longer than 60 words,referring to the 6 objects below in no particular order.Here are your 6 objects: Car Apple Boat Horse Water Stick
Feature: build a story 14118. The main featureThis is an extension of the ﬁrst exercise. This time we A: Group 1 Group 3have provided you with a larger array of objects. They B: Group 2have been separated into 3 groups. Your aim is to write C: Group 3a 250-word story each time, using the objects from the D: Groups 1+3following groups: E: Groups 2+3Group 1 Group 2Did you know?Human beings have a natural tendency to make stories “The circle is chasing theout of everything. It is part of a larger desire and need to triangles.” Many studies sinceput ourselves in another person’s shoes—to be able to then have conﬁrmed the humanempathize. It is crucial to social interaction and communal predilection to make charactersliving. Psychologists call this Theory of Mind. A classic 1944 and narratives out of whateverstudy clearly demonstrated this tendency. The psychologists we see in the world around us.showed people an animation of a pair of triangles and a Some psychologists believecircle moving around a square and asked the participants that the imaginary world of awhat was happening. The subjects described the scene as story may serve as a provingif the shapes had intentions and motivations—for example, ground for vital social skills.
144 The mind-body connectionHealthy body,sturdy mindWe all need some physical exercise to stay in shape.Nobody would disagree with that. But how does thebrain feature in all this? Well, there’s a famous Latin sayingfrom ancient Roman times: “mens sana in corpore sano,”meaning “a healthy mind in a healthy body.” It seems thatthe Romans were onto something here because, while we’veknown for a long time that physical exercise can maintaingeneral health and well-being, more research ﬁndings areindicating that exercise may also be one of the best ways topreserve brain health. Actually, even if successive scientiﬁc studies hadn’t revealed this, it would be astonishing if this were not the case. Any physical activity, even a ﬁve-minute jog in place at the start of each day, raises our heart rate, which in turn increases blood ﬂow throughout the body—including the brain. The positive effects of physical exercise are more noticeable the older you get. People in their 50s who exercise regularly generally have better memories and greater concentration spans than those who leadsedentary lives. What’s more, those people whokeep physically active into their 60s reduce thelikelihood of suffering mental decline becausesome age-related cognitive diseases resultfrom physical inactivity, as well as a lackof mental stimulation. How much exercise? Guidelines published by the WorldWhat is aerobic exercise? Health Organization (WHO) recommends at least 30 minutes of moderate-intensityIt’s any physical activity, such as walking, jogging, physical exercise, such as a gentle jog,or dancing, that increases the heart rate to 60–80 per day. However, the majority of healthpercent of its maximum capacity for a period of professionals agree that most people can15 minutes or longer. This allows the lungs to reap greater health beneﬁts by engagingdraw in more oxygen, which the heart pumps in activity that’s either more intense for athrough the vascular system. You should be able shorter burst of time, or less strenuous butto engage in a conversation while doing aerobic carried out over a longer period. You couldexercise. If you haven’t exercised in a while, we also add stretching for ﬂexibility, andadvise you to have a thorough physical checkup resistance exercises called “calisthenics”before you begin any exercise program. to improve muscle strength and tone.
Introduction: healthy body, sturdy mind 145 Let’s assess your exercise history—past and present Exercise four 4 times a week + Exercise three times a week 3 Exercise twice a week 2 Exercise once a week 1 No exercise 0 Teen–19 20–25 26–30 31–35 36–40 41–45 46–50 51–55 56–60 60+Plot the graph by giving yourself a rating between 0 and appropriate box. Complete the relevant4 to assess how much physical exercise you do (30 age sections. How do your scoresminutes +), or have done in the past. For example, if you compare over the different periods ofplayed tennis twice a week as a teenager, put a 2 in that your life? Many people tend to showbox. If you went jogging once a week, write in 1. If you a decline in their level of physicaldon’t do any exercise at the moment, put 0 in the activity with age, but you should try to keep exercising to maintain your physical and cognitive health.How exercise works the brain 2. Increasing the amount ofAny form of aerobic exercise is the best way to improve serotonin in the brain—this brainblood circulation to the brain. The increased blood ﬂow chemical helps cells multiply andhelps the frontal lobes, in particular (see p.14). The frontal induces positive moods.lobes control emotional activity and play a key role inmental sharpness. It is the region you use to process 3. Causing new tiny blood vessels calledthoughts to make decisions, pay attention, show initiative, capillaries to sprout and nourish brainﬁnd humor in things, and so on. Unfortunately, this is also cells that might otherwise wilt from thethe part of the brain that feels the brunt of the aging aging process.process, making people forgetful, slow on the uptake,and less verbally ﬂuent as they get older. 4. Boosting the growth of neural stem cells. Studies involving mice exercisedExercise combats this decline by: on treadmills for an hour a day1. Generating a chemical called BDNF (brain-derived against mice that were left sedentaryneurotrophic factor), which acts a bit like fertilizer for showed that the mice that werethe brain’s existing neurons, and encourages the growth exercised had twice the numberof new neurons and synapses. of cells, making them smarter.
146 The mind-body connectionThe physicalrechargeIt’s difﬁcult to sustain energy levels throughthe course of an entire working day. Atsome point fatigue might set in, or youmight feel as if your brain can nolonger think clearly. When thefeeling strikes, a lot of peopledrink coffee or reach for achocolate bar, relying on the caffeineor sugar spike to bring energy levelsback up. But this is both unhealthy and ashort-term solution. An alternative wayto boost energy is by engaging in asimple physical activity for a fewminutes, which improves bloodcirculation and instantly makes youmore alert. Here are some of the bestways to give yourself a physical charge.Warmups“Warming up” before playing anyphysical sport is normal. Athletes 1. Take a simplewarm up not just to preparephysically, but also to focus their walk ... or climbmind and access “muscle memory.” the stairsBy warming up in tennis, for A gentle walk is a goodexample, the body and mind pickup because it increasessynchronize to remember the blood circulation and the amount ofdifferent strokes and actions oxygen and glucose that reach your brain.required for a game. This Walking is not strenuous, so your leg muscles don’t take up extra oxygen andbrain-muscle synergy glucose, as they do during other formsdecreases the likelihood of a of exercise. Maybe this is why walking can “clear yourbad performance or injury. head.” If you don’t have the time for a stroll, then climbAnother important beneﬁt of some stairs. This gets your heart rate up quicker and boostswarming up is that it helps you blood circulation—a perfect pickup prior to entering arelax and hone concentration. meeting room or taking an examination.
Technique: the physical recharge 1472. Cross crawl warmup 3. Side-to-side warmup1. Walk or jog on the spot. 1. Raise left arm and right leg and2. Lift your left knee to your right elbow, sway slightly to the left.then repeat for a count of 5–10. 2. Then return to neutral position.3. Now lift your right knee to your left Change over by raising right armelbow and repeat the movement. and left leg and sway to the right.4. Keep a steady rhythm for 3. Repeat movement for onea minute. minute, keeping steady rhythm without straining too much.The cross crawl is a simple andpowerful energy technique to promoteaccess to both the right and left-brainhemispheres. The crossing over ofenergy helps you feel more balanced,think more clearly, and improvescoordination. 5. Massaging the K-27 points Place ﬁngers on your collarbone. Slide them inward toward the center and ﬁnd the bumps where they stop. Move your ﬁngers down about an inch. Most people have a slight indent here that their ﬁngers will drop into—these are the K-27 points. Cross your hands if you wish; tap and/or massage the K-27 points while breathing in through your nose and out through your mouth. Continue for about 20 seconds. If you’re using one hand, tap on both points with thumb and ﬁngers. When you massage the K-27 points on a regular basis, you should experience a slight energy surge, clearer thinking, and improved vision.4. JuggleJuggling may seem faintly ludicrous, but don’tunderestimate this dexterous pursuit as a wayto help take your mind off the stresses of the dailygrind. It will help improve hand-eye coordinationand, according to one university study, may also boostyour brainpower.
148 The mind-body connectionStress factorStress builds up when a person becomesoverwhelmed by the pressures of life and feelsunable to cope. The key word here is “feel,”because stress is about the perception of thedemands on the mind, which has a knock-oneffect on physical well-being. Stress weakenspowers of creativity and memory recall. Stress isn’tall bad—everyone needs to experience moderatelevels to maintain focus and feel stimulated—butwhen it becomes excessive and unmanageableits effect is counterproductive and, potentially,detrimental to our health. Chemicals calledglutamates are pumped into the brain, which canbe harmful. A person becomes frazzled by toomany demands, loses self-conﬁdence, and endsup feeling ﬂustered, and, as a result, may becomeforgetful, misplace things, misinterpretconversations, snap at others, and so on.Excessive stress causes both brain and body tobecome inefﬁcient.Mind-body checklistBefore we introduce you to a gentle de-stressing routine, complete thischecklist, checking the boxes that best describe your current physical state. Very tense Quite tense Quite relaxed Very relaxed Face Forehead Back of neck Shoulders Chest Back Stomach Groin Buttocks Legs Feet Arms Hands
Feature: stress factor 149The physical stress-busterIf you found that the majority of your checks fell starts to hurt—for about 20in the “very tense” or “quite tense” box, then seconds—and then let go.you need to ﬁnd a way to regulate your stress Blood rushes to the area,levels. Many people use a popular technique which creates a warm sensation, andcalled Progressive Muscle Relaxation (PMR). PMR the tension should then ﬂow away,is about exaggerating the feeling of tension to leaving a state of totalhelp the mind and body wind down. You tense calm. PMR can work as aeach muscle group of the body in turn until it sleep aid as well.The PMR programSit on a chair, with your back straight and both feet ﬂat on the ground.Do the exercises in the following order: (remember to tense for 20 seconds): 1. Right hand and forearm make a ﬁst, hold, then release 2. Right upper arm bend the arm and “ﬂex the bicep,” then release 3. Left hand and forearm make a ﬁst, hold, then release 4. Left upper arm bend the arm and “ﬂex the bicep,” then release 5. Forehead raise your eyebrows, then relax your face 6. Face squeeze the eyes, then relax; clench your teeth and pull the corners of the mouth back, then relax 7. Shoulders and neck lock your hands behind your neck and gently push your head back against this resistance (the head does not alter its position); raise your shoulders and press your head back against their resistance (horizontally, unlike when you look up); let your shoulders hang, relax 8. Chest and back inhale deeply and hold your breath, pufﬁng out your chest at the same time as letting your shoulders hang, then breathe normally 9. Belly tighten the abdominal muscles (or draw in the belly), then release 10. Right thigh push the right foot forward using the ﬂoor as resistance (just enough so the chair doesn’t rock back), then release 11. Right calf lift up the right heel, then release 12. Right foot crook the toes, then release 13. Left thigh push the left foot forward using the ﬂoor as resistance (just enough so the chair doesn’t rock back), then release 14. Left calf lift up the left heel, then release 15. Left foot crook the toes, then release
150 The mind-body connectionExercise the Eastern wayFor thousands of years in the East, people have harnessed awhole range of techniques to seek harmony between mind, body,and spirit. Although traditionally, Western medicine has beensceptical of Eastern therapies, such as Zen, T’ai Chi, and yoga,increasing evidence from scientiﬁc studies, especially using brainscanning techniques, indicates that the ancient Eastern monksreally knew ways of lowering blood pressure, slowingrespiration, releasing muscle tension, and decluttering themind. In today’s fast-pacedworld, people are exposed togreater pressures. The bodyusually reacts by releasingstress-response hormones suchas cortisol, which circulates thesystem and inadvertently blocksthe formation of new neurons in the hippocampus.We now know that any type of meditative exercisehelps the body regulate stress hormone levels. Zen meditation Zen meditation is a practice that lies at the core of Zen belief. The purpose is to focus the mind—sometimes through using a mantra, a sound, or the breath—and promote a state of absolute calm. Through sitting still and honing the attention on a simple chant, the meditator unclutters all the bric-a-brac he or she stores in the head, namely negative thoughts, emotions, and sensations. This state of mind is often called “mindfulness.” About 10 million people meditate every day in the West and while there are many different techniques, the primary objective is to become aware of the stream of thoughts, allowing them to arise and pass away without interference. Empirical evidence suggests that Zen meditation helps alleviate the symptoms of depression and also improves quality of sleep.
Technique: exercise the eastern way 151Enter the meditative stateIt is important to adopt a good posture whether anything else for that matter. For example, if youyou choose to sit or stand, always keeping the suddenly hear a noise, you just listen to it ratherback upright. The aim is to clear the mind of all than think about it. As soon as you enter thedistractions and reach a state of “no mind” or meditative state, your brainwave patterns should“nonthinking.” To achieve this you have to pay shift from the right frontal cortex to the calmer leftattention to the sensory experience, rather than to frontal cortex. This decreases the negative effectsyour thoughts about the sensory experience, or of stress, mild depression, and anxiety. Try this simple routine: 1. Find a quiet spot. 2. Sit on a chair, stool, or cushion with your back straight and unsupported. 3. Inhale and exhale slowly through your nose. 4. Close your eyes and relax your body (but keep your back relatively straight). Focus your mind 5. Listen to your breathing; lose yourself in the rhythm of You can also meditate by focusing the breath. your mind on an object, such as a candle ﬂame. By focusing all your 6. Start to hum or say “om” with each breath, keeping energies on a single object, the sound constant; think about the vibration of the hum. you are blocking out all the Alternatively, repeat a chant or phrase such as “don’t other stimuli that bring worry, be happy.” sensations, emotions, thoughts, daydreams, and 7. Whisper or say the word quietly in your mind. impressions. In other words, 8. Keep this going for 5 minutes. How do you feel now? your mind ceases to swing from branch to branch and comes to a tranquil state, which naturally destresses your entire system.
152 The mind-body connectionT’ai ChiT’ai Chi is an ancient martial art that combines physical exercisewith mental exercise. The emphasis on movement helps expandthe mind and channel the body’s energy. Focusing the mind onthe slow movements creates a state of mental calm and clarity.Medical studies support its effectiveness as a form of therapyfor managing stress. These studiesconclude that practicing T’ai Chiregularly will help you relax,stay focused, and be moreproductive in life.How does T’ai Chi work?T’ai Chi practitioners believe that the intenseconcentration and the slow movementsimprove the ﬂow of energy throughout thebody. They consider this to be positive energy, asopposed to the negative energy induced byanger, for example, which is damaging to health.Try this simple test:1. Sit down and think of a time when you werefrustrated or angry about something. It could be aninstance when a reckless driver cut into your lane, ora time when someone was being unreasonable to youat your workplace.2. Recall what happened, the people involved—you willfeel the anger and resentment returning.3. Notice how this makes your body tense up and howyour breathing rate increases.Dredging up an unpleasant memory from the pastaffects your body. Now, try this:1. Stand upright, relax your shoulders.2. Raise your hand in front of you and begin slowlyrotating your wrist clockwise, concentrating on themovement as well as your breathing. Do this for a minute.3. The tension should slowly abate and your breathingslow down.
Technique: T’ai Chi 153A sequence of T’ai Chi movesThe beneﬁts of practicing T’ai Chi are unlimited. Clinical good health, and/or to help with managing a speciﬁcstudies in the US report improved balance and peace ailment. It can also improve internal circulation. Studiesof mind after only eight weeks of a very simple set of suggest that patients who suffer from neurologicalmovements taken from a T’ai Chi routine. T’ai Chi can diseases, such as Parkinson’s or Alzheimer’s, might alsobe used as a preventive health measure, to maintain beneﬁt from practicing T’ai Chi on a regular basis.Acupuncture and the brainAcupuncture is an ancient Chinese treatment for decreased in certain areas of their brain withinmany illnesses, in which a practitioner inserts ﬁne seconds of undergoing an acupuncture session.needles in deﬁned points of a patient’s body Other studies have found acupuncture to bethrough which “Qi,” the vital energy, ﬂows. There helpful in treating depression, eating disorders,are more than 1,500 “acupoints” throughout the addictions, and pain, although critics believe thatbody. Acupuncture works by deactivating, or the positive results could easily be a result of“quieting down,” key regions of the brain, and is the placebo effect. There is general agreementused to alleviate acute mood states, pain, and that acupuncture is safe when administered bycravings. The science behind this is far from a qualiﬁed practitioner using sterile needles.understood, and clinical trials into acupuncture However, many physicians reject the treatmentremain inconclusive. However, several studies altogether because the idea of the “Qi” and itsinvolving volunteers who were monitored using various pathways does not reconcile with modernfMRI brain scans revealed that blood ﬂow biomedical knowledge.
154 The mind-body connectionYogaYoga is an ancient practice that originated in India and is more than5,000 years old. Similar to T’ai Chi, it combines breathing exerciseswith physical postures and meditation. However, whereas T’ai Chiis classiﬁed as a soft martial art, asking you to focus energy on theelegance of motion, yoga is more like a conventional body workout.It’s about holding speciﬁc postures and controlling breathing. Yogais thought to calm the nervous system and balance the body andmind. Some of its practitioners claim that yoga can preventcertain maladies by keeping the energy pathways open andlife-energy ﬂowing. The popularity of yoga has grown throughout theworld. Yoga has been used to lower blood pressure,reduce stress, and improve coordination, ﬂexibility,concentration, sleep, and digestion. One study hasfound that doing yoga regularly elevates brain gamma-aminobutyric acid levels (GABA)—an amino acid that plays animportant role in regulating neuronal excitability throughout thenervous system. It recommends that the practice of yoga be exploredas a possible treatment for depression and anxiety disordersassociated with low GABA levels.
Technique: yoga 155Yoga posesHere are three basic poses to try. If you haven’t exercised in a while, youmight need to ease yourself slowly to increase body ﬂexibility. We advisethat you start with a medical checkup or consult a yoga practitioner. Theposes are arranged in the approximate order of difﬁculty.Mountain poseThis pose promotesconﬁdence and a positivemental state, as well asimproving posture andcirculation. Downward dog Lotusyour feet together. Fan out This is one of the most popularyour toes and push your circulation and concentration. meditative postures. It promotesfeet against the ﬂoor as if balance and harmony by calmingto stretch them. the mind. tucking your toes under.upward and your kneecaps rise the soles of your feet turned upwarda little. toward your spine and lifting your and heels as close to your abdomen pelvis to form an inverted “V,” with as possible. Keep your spine straight. your body in the position illustrated.distributed. Draw in your abdomenand maintain a high chest so that palms up. Hold as long as you wish.you take deep, even breaths. Keep (if possible) and turn your armpits toyour arms at your sides. face each other. closed during this posture. back and down with your heels, with your breathing even and smooth.Brain training with meditationNeurologists have discovered that during meditative that meditating actually increases the thickness of theexercises, such as yoga and T’ai Chi, brainwave patterns prefrontal cortex, which is involved in attention and sensory processing. This is sound proof that people wholeft prefrontal cortex, an area just behind the left side mediate regularly actually alter their brain anatomy.of the forehead, has been identiﬁed as the place where Consistant meditators also develop a remarkable abilitybrain activity associated with meditation is especially to cultivate positive emotions, retain emotional stability, and engage in mindful behavior.
156 The mind-body connectionSleep and the brainThere is nothing as refreshing as a good night’s sleep.You wake up feeling revitalized and ready to face theday’s challenges. This is because during sleep, growthhormones are released to heal damaged tissue,including brain tissue. Sleep also oils the cogs of thecognitive system by “reviewing and recalling” the day’sexperiences, which helps transfer information into yourlong-term memory. Sleep regulates your body clock,known as the “circadian rhythm,” which is naturallyattuned with the daily cycle of light and darkness, and isdetected by your eyes. It is the reason why people sufferfrom jet lag after a long-haul ﬂight, and it takes awhile forthe body clock to readjust.How much sleep?The amount of sleep required varies from person toperson. Some people can get by with as little as ﬁvehours a night, while others need nine. It is importantto be aware of what your own “magic number” is and try to stickto that ﬁgure. Otherwise you risk inhibiting your productivity as wellas your ability to remember and process information. A lack of sleepputs an enormous strain on the brain. Studies have shown that asleep-deprived brain loses efﬁciency. An area usually active during aspeciﬁc task needs to be propped up by other parts of the brain. Itis like driving a vehicle with a ﬂat tire—your performance is severelyreduced. Sleep deprivation also increases stress hormone levels, whichreduces nerve cell production (neurogenesis) in the adult brain.
Feature: sleep and the brain 157Stages of sleepSleep can be divided into four separate brain of course, there’s the dream state which,stages. There’s the theta wave when we according to Freud, acts as a safety valve forsometimes rouse with a sudden jerk. Then there’s the overburdened brain.the delta wave activity, during which if awokenyou’d be totally disorientated. While asleep yougo back and forth through these two brainwavepatterns in 90-minute cycles. It is then that youalso enter REM sleep, where your eyelids showmovement of a seemingly alert mind. And then,Top tips for good sleep Establish regular times—get used to your body-clock even Don’t try to force sleep. If you can’t fall asleep withinon weekends, when you are tempted to sleep in. 15–20 minutes of going to bed, do something distracting. Avoid caffeine, alcohol, and nicotine before bedtime—all Get out of bed and make a cup of caffeine-free tea or readof which disrupt natural sleep patterns. a magazine. Finish eating at least three hours before regular bedtime. Exercise daily, although not too close to bedtime. Use relaxing bedtime rituals such as soaking in a hot tub,or scented candles; listen to soothing music an hour ormore before you aim to fall asleep. Keep your bedroom a bedroom, not a study or a TV room. Try to keep out light and noise. Make sure your mattress and pillows are comfortable.Nap for a mini brain boostIf you feel drowsy in the early afternoon, perhaps after lunch, take a 20-minutenap. It might be impractical in many circumstances but it will do your brain moregood than reaching for a cup of coffee. Daytime napping is healthy for the brain.You need it to refresh your brain cells and allow the different areas to recover.If your brain’s tired, your performance will slow down. A nap is also a goodde-stresser. Some researchers have even suggested that a six-minute nap canimprove performances in memory and problem-solving tests.
158 The mind-body connectionBrain foodThere is an American proverb that says: “We need brainmore than belly food,” and it couldn’t be more true. Aswe stated on page 12, a resting person’s brain uses 20percent of food energy even though it accounts for justtwo percent of the body’s weight. Your brain needsfuel, especially foods packed with brain-boostingnutrients. Here are some top brain-training foods:1. Salmon or other oily ﬁsh, which containthe omega-3 family of fatty acids, helpmaintain brain cells and build stronger andbetter connections between them.2. Brightly colored fruit and vegetables,notably blueberries and spinach, are high inantioxidants that can also maintain healthybrain cells and improve brain-cell connectivity.3. Avocado is one of the most easily digestiblesources of high-quality protein and healthy fats.Avocado also contains antioxidants, ﬁber, andfolate, among other nutrients.4. Nuts contain protein, complexcarbohydrates, and beneﬁcial fats.They also provide a good dose ofvitamin E, which promotes brainfunction. Almonds are the best nuts,followed by hazelnuts, cashews,pistachios, and walnuts.
Feature: brain food 159 Alcohol It’s common knowledge nowadays that a daily glass of wine helps you de-stress, but did you know about the study that revealed that drinking alcohol can actually boost your brainpower? The study, conducted by the Australian National University in Canberra, monitored 7,000 people in their early 20s, 40s, and 60s, and found that those who drank within safe limits (no more than two drinks per day for men and one drink per day for women) had better verbal skills, memory, and speed of thinking than those who either drank excessively or not at all. How might alcohol be boosting brainpower? Some experts believe that the cardiovascular beneﬁts of alcohol might extend to the brain. However, the researchers were quick to point out that although the results were surprising, they do not necessarily prove for certain that alcohol beneﬁts the brain, since the study did not consider all the potential reasons why the nondrinkers performed less well than the drinkers. Medical professionals do acknowledge the potential health beneﬁts of alcohol, but emphasize that it should be regarded as a double-edged sword because the risk of abuse is high and the consequences of binge-drinking and alcoholism are well documented throughout the world. 5. Oats promote healthy blood ﬂow to help your brain function better. They also contain ﬁber, protein, antioxidants, and some omega-3 acids. 6. Beans and legumes are loaded with ﬁber, vitamins, minerals, protein, and folic acid, and give your brain a slow, stable supply of glucose. Dark chocolate Dark chocolate is a beneﬁcial brain food! It contains magnesium, which increases the supply of oxygen to the brain, and high levels of polyphenols, an antioxidant chemical that reduces blood pressure. Raw cocoa has the highest antioxidant value of all the natural foods in the world—twice the antioxidants of red wine, and up to three times the antioxidants found in green tea. It also appears to regulate7. Eggs contain protein and fat and are levels of the feel-good chemical serotonin in the brain. Scientistsanother source of stable energy for your followed up an examination of 10 patients whobrain. The selenium in organic eggs has received 1.6 oz of dark chocolate dailybeen shown to help improve mood. for two months. Patients given the dark chocolate reported less ChronicCholine, also found in eggs, is a protein, Fatigue Syndrome (CFS) and claimeda building block of every cell, and has to feel the weariness return whenbeen linked to improved memory. they stopped taking it.
162 Test your new brainpowerFinal workout1. Number recallA: What total do you get C: E: What total do you getwhen you add up the when you add up theeven-numbered jerseys? numbers on all the jerseys?B: What total do you get D:when you add up the on the blue jersey?odd-numbered jerseys?2. The correct cube 3. Old mates “Oh, you have a daughter!” Smith says to his old pal. “Are you married then?” “Yes,” the schoolmate replies. “To whom?” “Someone you don’t know,” his friend replies. “And what’s the name of your daughter?” Smith asks. “It’s the same as her mother’s.” “Then this little girl must be called Lucy!” Smith concludes.A B C D “That’s right!”
Exercises: ﬁnal workout 1634. Number grid 6. Memory math =3 =8 =12 3 1 5 = 8 A 4 8 3 = 29 - + = 9 6 2 = 27 B x ÷ = 5 3 7 = 1 C 4 9 6 = 6 x - x = = = = 19 1 22 D x - x =5. Colored words blue yellow purple red purple brown black green red green orange blue Solutions on p.184
Exercises: ﬁnal workout 16510. The word ladder 11. Hungry lion rice ﬁght forest net storm hear child ﬂask12. Shooting arrowsA: 8 7B: 6 5 4C: 3D:
166 Test your new brainpower13. Scrambled sentencesUnscramble the words in each of the following to makea proper sentence:A: and memory Daily concentration exercises skills boostcanB: refrigerator brain light as about a energy much Youruses asC: ticklish tickle No how be you might you yourself can’tmatterD: instrument spatial Learning play improves tomusical reasoning aE: health and a brain good maintains exercise PhysicaldietF: vivid events intense memories Emotionally produceG: awareness feeling others of what depend are skills correct answerSocial the on14. Recall the ﬂagswrite the name of the country in the grid provided. Belgium India USA China UK Netherlands Germany France correct answer
Exercises: ﬁnal workout 16715. Stacking mosaic tiles 16 Quick-ﬁre riddlesIf you placed these shapes on top of each other, A: How many times canstarting with the largest at the bottom, which image you subtract the number 5would you see? from 25? B: What gets whiter the dirtier it gets? C: What do you possess each correct but other people use it answer more than you do?A B C D each correct17. Krazy Kakuro 18. Spot the errors answer Find the word that is spelled incorrectly in each sentence and write the correct spelling in the answer box. 12 9 10 12 17 A: The baby waeled throughout the church service. 21 21 16 16 23 17 36 36 4 B: He was an accessery to the crime. 12 9 12 17 6 6 4 4 25 10 11 11 11 11 18 12 C: They accomdated us really well during our vacation. 4 17 9 9 13 13 17 23 3 3 16 16 6 10 10 3 D: Phillip was deﬁnitely unaccusstomed to public speaking. 12 41 41 18 25 3 3 15 15 E: The weather looks very changgable. 6 10 17 10 3 F: The teacher was very dissappointed. completed grid G: The television was cheap but came without a guarantie. Solutions on p.185
168 Test your new brainpower19. A love of animalsAt a board meeting the 12 directors of a popular zoo A: What is Mr. Mukherjee’s B: Which director’s favoriteare talking about their favorite animals. Study the favorite animal? animal is the giraffe?diagram for 1 minute and then cover it up and answerthe following questions: C: Which 2 animals are mentioned that belong to the cat family? Mr. Robert Ms. Black Mr. Shah Ms. Gold Camel Grizzly Bear Panda Lion Mr. Novak Mr. Taylor D: Who is sitting to the Elephant Giraffe left of the person whose favorite animal is a panda? Mrs. Rhodes Mr. Taibu Kangaroo Leopard Mr. Mukherjee Ms. Allen Mr. Alves Mrs. Jiaying E: What is Mr. Alves’ Chimpanzee Zebra Snake Crocodile favorite animal? correct answer20. Complete the cube 21. Colored squaresWhich 2 shapes will pair up to create the top shape? Are the red squares the same color throughout the “X”? same differentA B CD E F
Exercises: ﬁnal workout 16922. Shopping taskYou’re in a clothes shop buying items of clothing to goon vacation. You bought 11 items, paid $150 and got $48.50$3.10 change. How many of each item did you buy? $22.50Tops:Skirts: $4.30Socks:Belts: $4.5023. Locate the lootIn jail, Tony’s cellmate told him that he had buried the loot from a heist ina secret location, and showed him a map he’d drawn to keep a note of thelocation. Later on, Tony stole the map from under his cellmate’s pillow andhad only 1 minute to memorize the route before his cellmate returned.Assuming that you are Tony, study the footsteps on the map below for1 minute and then cover it up and draw it on the empty grid. correct route $ Solutions on p.185
170 Test your new brainpower24. Build the birdAll of these pieces can be put together to form thepicture of the bird below. Draw the individual piecesin the grid provided.25. Suitor challengeFour suitors approached a hotel magnate asking for hisdaughter’s hand in marriage. The hotelier thought of away to test his suitors. The suitor to pass the test wouldreceive his daughter’s hand in marriage.The daughter was put in the center of a large banquetroom. The four suitors were put in each corner of theroom on top of a podium. The ﬁrst one to touchthe daughter’s hand would be the winner andbecome his son-in-law.The rules of the test were that the suitorscould not walk over the carpet, cross theplane of the carpet, or hang from anything; norcould they use anything but their body and wits(no magic or telepathy, nor any items such as ladders,block and tackles, and so on).One suitor ﬁgured out a way and married the hotelier’sdaughter. What did he do?
172 SolutionsSolutions 8. Dog and bone 12. Numerical jigsaw1: Brain potential2. Number sequencesA: 768 (x 4 each time)B: 13 (add the preceding two numbersin the sequence)C: 37 (a sub-sequence of ascendingodd numbers drives this sequence, 13. Visual logic testwhich is added each time) C: The other shapes have 42 5 10 17 26 37 straight lines 3 5 7 9 11 C: The other shapes consist of aD: 253 (x 2 + 3 each time) 9. Light switches square, a circle and a triangle Turn the left switch on for 10 minutes D: This has 6 arrowhead shapes, then turn it off again. Turn the middle3. Building fences switch on and go upstairs. The light while the others have only 5B turned on matches the middle switch. Carefully touch the other two bulbs. 14. Manhole covers4. Goat, cabbage, and The one that’s hot matches the left 1. A square manhole cover can bewolf turned and dropped down the switch, the cool one matches the right.The farmer ferries the goat over ﬁrst. diagonal of the manhole. This willHe returns and takes the cabbage. He not happen with a round manhole 11. Spot the differences cover. So, for safety and practicality,deposits the cabbage on the other sideand takes the goat back. He then leaves all manhole covers should be round.the goat and picks up the wolf. He 2. Another answer is that a roundferries the wolf to the other side. Finally, manhole cover can be rolled aroundhe returns to pick up the goat again. to save having to lift it.5. Mental arithmetic 15. Moving by degreesA: 9 F: 32 K: 9 1 degreeB: 17 G: 5 L: 9C: 20 H: 72 M: 40 16. Motorcycle partsD: 12 I: 42 N: 12 CE: 49 J: 16 O: 24 17. Straight lines6. A perfect circle? Both horizontal lines are straight. SimilarThe inner circle is perfect. to exercise 6, your view is distortedSometimes it’s difﬁcult to see the wood by the circle of lines receding to thefor the trees, and the “information” vanishing point. Your eyes focus onaround the object you are interested in the vanishing point, and this causes thecan distort your view. Try covering the two straight lines to appear warped.lines with a card, and you will see thatthe circle is perfect.
Brain potential/memory 17319. Magic square 21. A perfectly boiled egg 4. Spot the changes Turn both timers upside down and put the egg into the boiling water. After 7 6 7 2 minutes, turn the 7-minute timer. Then when 11 minutes have passed, turn the 7-minute timer again. Then it will 1 5 9 take another 4 minutes until the 7-minute timer stops. At that time, exactly 15 minutes have passed. 8 3 4 22. Spot the odd picture A: Feet (the rest are parts of the face) B: Bread slice (the rest are whole) C: Plank of wood (the rest can be melted)20. Color mazes D: Gold (the rest are precious stones)A: E: Pen (the rest convey information) 23. Odd word out A: Fish (the rest are land animals) B: Stream (the rest are still waters) C: Stool (the rest are raw materials) D: Lawn (the rest are naturally occurring landscapes) E: Corfu (the rest are names for the country of Cyprus in French, English and GermanB: 11. Where was that? B 13. Sewing patterns Most people should be able to remember more strokes in the second grid, simply because the brain identiﬁes the representation of sea creatures and can, therefore, form a memory of them more easily. 14. Memory math A: 8C: B: 7 C: 56 2: Memory 15. Olympic colors A: Blue D: Green 2. Attention to detail E: Red A: The painting of the Mona Lisa has no eyebrows B: The right hand rests on the left
174 Solutions 6. Reversed digits 14. Solitary snowﬂake3: Visual reasoningand spatialawareness1. Overlapped objectsA: Apple; wrench; staplerB: Guitar; bicycle; carC: Calculator; saw; yachtD: Fish; pen; toothbrush 15. Find the treasure2. Guess the picture 7. Quick-speed D accounting A: 33 16. Origami enigma B: 23 “3”s and 36 “7”s C 8. Largest circle 17. Shape shifting A, B, and C, would have the same C diameter. 18. Stacking mosaic tiles 9. Straight or crooked? A Straight 19. Squaring up 10. Phony image C D and F3. Triangle test 11. Largest parcel?24 They all have the same surface area.4. Spot the ﬂipper 12. Sharp foxA: 2 C: 3 28 trianglesB: 3 D: 1 13. Counting stars5. Cake for eight A: 5All you need is 2 vertical and 1 B: 4horizontal cut C: 3 20. The correct cube C 21. False pattern C
Visual reasoning and spatial awareness/Think creatively 17522. Perfect ﬁt 9. The elder twinB At the time she went into labor, the mother of the twins was traveling by23. On a roll boat. The older twin, Terry, was bornD 4: Think creatively ﬁrst, in the early hours on March 1st. The boat then crossed the International Date Line (or any time zone line) and24. The vanishing area Kerry, the younger twin, was born onMartin Gardner ﬁrst described the February the 28th. In a leap year thevanishing area paradox in 1961. 5. Horsing around younger twin celebrates her birthdayThe paradox concerns a triangle 1. Only 3 of the 4 horses are his, so two days before her older brother.constructed with 4 colored pieces. he only needs to lasso 3 to make sureWhen the pieces are rearranged to that none of his horses remain 10. The swimmer in theform a second triangle, a tiny empty untethered.area appears. 2. One of his horses is already forest tethered, so he only needs to throw During a forest ﬁre a ﬁre-ﬁghting The answer to this problem is the lasso over the 3 other horses. plane had scooped up some waterfairly simple. The 2 “triangles” are 3. The white horse is an inanimate from the lake to drop on the ﬁre. Theactually optical illusions, because the carousel ﬁgure and therefore cannot plane had accidentally picked up theorange triangle and the green one escape. If you are prepared to open swimmer as well.are not in equal proportions. Thegreen one is 8 x 3 squares, and the your mind, you’ll ﬁnd that there areorange one is 5 x 2 squares. Therefore, other possibilities too. 11. Crossing the bridgein the 2 complex “triangles” the One solution:hypotenuse is not a straight line. In 6. Doubling the window The singer and the guitarist cross =the ﬁrst example it bends downward size 2 mins (total = 2)slightly, and in the second one it 1. Open the window. The singer goes back = 1 min (total = 3)bends upward slightly. The difference 2. Providing it’s a double pane The drummer and the keyboardistbetween these two lines is the “extra” window, if you were to separate the cross = 10 mins (total = 13)square in the lower drawing. panes, the window would become The guitarist goes back = 2 mins (total twice as large. = 15) 3. Put a giant magnifying glass in The singer and the guitarist cross = front of it. 2 mins (total = 17) 4. Place a giant mirror at an angle An alternative solution is to swap the beside it. singer with the guitarist. 7. Enough ﬁsh There was the father, his son, and his son’s son. This equals 2 fathers and 2 sons! 8. Drinking glasses You can solve the problem by moving a single glass. Simply pick up the middle one of the full glasses, pour the water into the middle one of the empty glasses, and return the glass to25. Spinning blossom its original position.C
176 Solutions12. The third square 16. Try for ﬁve 20. Equal divide 21. Find the extra triangle13. Three for two 17. Even out 22. Break the wheel14. Remove a square 18. All the threes 23. More for less15. Swimming ﬁsh 19. Total wipeout 24. Ice in the glass
Think creatively 17725. Doubling up 30. Deadly shell 37. Bottled money Aeschylus died when the tortoise was Push the cork into the bottle, and dropped on him from a height by shake out the coin. an eagle that might have mistaken Aeschylus’ bald head for a rock on 38. Separated at birth? which to break the tortoise’s shell. They were two of a set of triplets (or quadruplets, and so on). 31. Foiled robbery26. The elusive square Panic stricken, the bank robber dashed 39. Push that car to the revolving door and tried to The man pushing the car was a player barge in the direction the door would in a Monopoly game and his not turn. The force of his own push gamepiece was a car. knocked him to the ground, the weapon fell out of his hand, and a 40. Newspaper divider brave customer grabbed the gun. Tom’s mother slid the newspaper under a closed door, and made each 32. Futile car chase sibling stand on either side of it. The getaway vehicle was a double-decker27. Two’s company bus that went under a low bridge. The 41. Nail on the tree top deck of the bus was ripped off The nail would remain at the same and fell over the pursuing police car. height since trees grow at their tops. 33. Clever dunce 42. The café wall William’s name was William Abbot The “Café Wall” illusion was ﬁrst and the results were given in reported by Richard L. Gregory and alphabetical order. Priscilla Heard in 1979, after they noticed it in the pattern of tiles on a 34. The fatal ﬂash café wall in Bristol. The illusion gives The man is a lion-tamer, posing for a the impression that the tiles are28. Polar explorer photo with his lion. The lion reacts badly wedge-shaped because the grout lines1. Scott Amundsen Peary drove his car to the ﬂash of the camera, and the man appear to slope alternately upward andfor 1 mile in reverse. can’t see properly, so he gets mauled. downward. However, if you were to2. If the road is icy enough, he could align the tiles, you will see that the linesspin his wheels, measure the distance 35. Lax borders are actually parallel, and all the tiles areon the odometer, and wind up in the He is a mailman who delivers packages perfectly square and of the same size.same place he started. to the different foreign embassies in3. The road curves around. the United States. The land of an 43. Big-headed ﬂower embassy belongs to the country of the This is called the Ebbinghaus illusion29. A son’s gratitude embassy, not to the United States. (also known as the “TitchenerThe son, in his late teens, was spoiled illusion”)—it’s an optical illusion ofand idle. The father believed that 36. Strange detour relative size perception. The 2 circles ofevicting him and forcing him to ﬁnd his The elevator only runs to the 7th ﬂoor. identical size are placed near eachown way through life would beneﬁt The riddle did not state that he takes other; larger circles surround one whilehim, however unpleasant it would be at the elevator from the 10th ﬂoor in the smaller circles surround the other. Theﬁrst, and so threw him out. When the morning, just that he takes it to the ﬁrst central circle then appears smallerson found a job and worked his way up ﬁrst ﬂoor. He walks down to the 7th than the second central circle. Thethe career ladder, he understood how ﬂoor each morning to take the Ebbinghaus illusion provides a valuablehis father’s action had made his life elevator to the ﬁrst ﬂoor also. way to investigate how the eye andconstructive and successful. Therefore, brain process visual information.he returned to thank his father.
178 Solutions44. Confused creature 1. Under the bridgeThis illusion offers up an ambiguous 54 ftillustration in which the brain switchesbetween seeing a rabbit and a duck. 5: Numerical 2. Casting shadowsThe duck-rabbit was originally noted A: 90 ftby American psychologist Joseph reasoning B: 202½ ftJastrow in 1899. Jastrow used thedrawing to point out that perception 3. Wedding ﬁtis not just a product of the stimulus, A: Januarybut also of mental activity. Quick-ﬁre arithmetic test 1. c B: Tara 2. a C: Tara45. Dotty or what? 3. aThis is called the Hermann grid 4. Chance amour 4. billusion. It is characterized 10 seconds 5. aby “ghostlike” gray blobs perceived The man would have progressed 6. aat the intersections of a white (or 90 ft and the woman, 30 ft. 7. blight-colored) grid on a black 8. abackground. The gray blobsdisappear when you look directly 9. b 5. Keen student 10. c A: 2 milesat an intersection. 11. b B: 3 miles 12. a C: 24 mph46. Look into my tie ... 13. bThis is one of many versions of the 14. b 6. Carrying cupcakesrolling wave illusion. Because our eyes 15. c Small tray 24 cakesand minds have been hardwired by 16. a Medium tray 40 cakesevolution to identify patterns and 17. c Large tray 48 cakesrelationships to help recognize the 18. bworld around us, they can be fooled 19. cby images that seemingly replicate 20. b 7. Land up for grabsthose patterns and relationships. A: 5,184 ft2 21. cWhen you stare at this illusion, the B: 2,592 ft2 22. bbrain is being fooled and is failing C: 3,456 ft2 23. cto re-create the physical world. D: $3,840 24. a E: $11,520 25. c47. Poles apart 26. bThis is a version of the twisted cord 27. a 8. Bathroom makeoverillusion. The horizontal lines seen 28. a A: 1⁄7contain obvious sloping elements. 29. b B: 7 packsThis information takes precedence, 30. a C: $16.80which the eyes transfer to the brain, 31. cso despite the poles being parallel to 32. b 9. Computer saleseach other, the brain only recognizes 33. a A: Maythe sloping elements and deduces that 34. c B: 27 percentthe poles must be slanted. 35. c C: 1,050 units
Think creatively/numerical reasoning 17910. The shortest route 14. Cross math Intermediate Sudoku39 yards Grid C Easy Sudoku11. The broken calculator Grid A Grid D2 = 0.5 x 4 9=4+53 = 0.5 x 5 + 0.5 10 = 5 x 24=2x2 11 = 2 + 4 + 55 = 2.5 x 2 12 = 3 x 46=2x3 13 = 5 x 2 + 37=4+3 14 = 5 x 2 + 48=4x2 15 = 5 x 312. Unfold the folds32 x 28 inEach stage of unfolding:1=8x72 = 8 x 143 = 16 x 144 = 16 x 285 = 32 x 28 Hard Sudoku13. Triangle ratio Grid B Grid EYou don’t need to do any complicatedmathematics. If you rotate the innertriangle by 180 degrees it shouldbecome obvious quickly that theratio is 1:4.
180 SolutionsSamurai Sudoku Kakuro gamesGrid A Grid A Grid B Grid C Grid DGrid B Grid E 15. Lottery numbers This is known as the neglect of probability bias. It is a type of cognitive bias when one has a tendency to completely disregard probability when making a decision under uncertainty. Mathematically speaking, the numbers 1, 2, 3 ,4, 5, 6 are just as likely to come up as any other combination of numbers. Yet, people apply emotion and tend to pick numbers they feel Grid F they have a special connection with, such as birthdays, anniversary dates and “lucky” numbers. 16. Beer money In psychology, this is called effort heuristic. It is a bias in which the value given to an object is based on the amount of perceived effort that went into producing the object. In our example, the $50 found in the street is considered less valuable because no effort has been made to earn the
Numerical reasoning 181money, although that money has For instance, if “heads” lands for 23. The famous 3 doorsexactly the same monetary value the ﬁrst 10 tosses, intuition will suggest conundrumas $50 earned by working at the coal that, because tails has not come up in the If you don’t change your mind, youmine, for example. last 10 tosses of the coin, it must have a 1 in 3 chance of winning the therefore have a high probability of car. If you do change your mind, you17. Bidding war coming up next. This is false. In reality, have a 2 in 3 chance of winning.This is a case that demonstrates the it has the same probability as at any Many people ﬁnd this answer veryconcept of scarcity heuristics. In human other throw. There is no causal link hard to believe, but it’s true. For morepsychology, this is a mental heuristic between previous throws and the explanation, see this website:in which the mind values something next. History does not come into it. www.jimloy.com/puzz/monty.htmbased on how easily it may lose it,especially to competitors. Auctions 21. Number sequences 24. Weighing marblesoperate on this concept. The auctioneer A: 13112221—Each line describes the Number the bags from 1 to 10.assigns a relatively low value to an previous sequence. Take 1 marble from bag 1,object and hopes that several bidders 1 Take 2 marbles from bag 2,will be interested enough to begin 11—one number one Take 3 marbles from bag 3, ...outbidding each other, thereby raising 21—two number ones Take 9 marbles from bag 9 andthe value of the object. 1211—one number two and one Take 10 marbles from bag 10. number one18. Expensive tastes 111221—one number one, one Now put them on the scale. There arePsychologists have identiﬁed a penchant number two, two number ones 10 possible measurements. If allfor people to perceive more expensive 312211—one number three, three marbles weighed 1 ounce, the totalgoods as being better than inexpensive number ones, two number twos, one would be 55 oz. But one or moreones (providing they are of similar number one. marbles weigh 0.9 oz. So if you tookquality and style). They found this even B: 30—The sequence follows the one 0.9 oz marble, the total would beholds true when prices and brands are number of days in the months of the 54.9 oz, if you took two 0.9 ozswitched—putting the high price on the year, Jan = 31, Feb = 28, March = 31, marbles, 54.8 oz, and so on.normally relatively inexpensive brand is and so on. You know the total weight, so youenough to lead people to perceive it as C: 5—The sequence follows the digits know the number of 0.9 oz marblesbeing better than the other product that of Pi. you took. That is, if the total was 54.9is normally more expensive. D: 1—This is an exception because it oz, you took one 0.9 oz marble. If the does follow mathematical logic. total was 54.8 oz, you took two 0.9 oz19. Bad luck? marbles. And so on. Now that youYou both have exactly the same Do you see what comes next? First we know how many 0.9 oz marbles youchance, irrespective of how many took SIX to a power of ONE, then FIVE took, you know which bag they’re intimes red has already come up. to the power of TWO, then FOUR to because you took 1 marble from bag the power of THREE, and so on. Thus, 1, 2 marbles from bag 2, and so on.20. Heads or tails? the next number in the sequenceThe odds of it remain unchanged, equates to: 1x1x1x1x1x1x1 = 1 So if the weight is:at 50-50. 54.9 oz— the bag with the 0.9 oz The misconception is that, given a 22. Chasing cars marbles is bag 1.set of possible alternative outcomes, If you have written down a whole 54.8 oz—the bag with the 0.9 oznamely, heads or tails, the distribution page full of mathematical formulas, marbles is bag 2.of said outcomes will tend to be even, or then you have probably been thinking 54.1 oz— the bag with the 0.9 oz“average out,” with repetition over time. in the wrong direction for this puzzle. marbles is bag 9. Belief in The Law of Averages is The 2 cars will meet each other after 54. oz—the bag with the 0.9 ozparticularly prevalent in games of 1 hour, hence the bird has been ﬂying marbles is bag 10.chance, in all of which cases it is for 1 hour. The bird has ﬂown 80 milesentirely false, owing to the fact that when the cars meet.the outcome of previous games hasno bearing on the next game.
182 Solutions25. The condemnedprisoner conundrum 7: The word ladderWhite. If you had a black disk, the There can be any number of answers.other 2 prisoners would be able to see Here’s an example of how you could1 black and 1 white. They would know climb each ladder:neither of theirs was black, because 6: Verbal reasoning A: umbrella —rain—sun—ﬁre—otherwise someone would have been candles—cakeable to see 2 blacks. Since no one has B: bicycle—sport—race—time—yet said a word, yours must be white. stopwatch—clock(Naturally, they can use the same C: glasses—book—paper—tree—reasoning; the trick is to be quickest.) 1. Dictionary corner nest—bird 1: A D: chair—desk—pen—letter— 2: B photograph—camera26. Break up time 3: A 4: B 5: A 8. Word-play analogies A: departure 6: C B: foot C: above 2. Like for like D: animal 1: D 8: B E: cold 2: B 9: B 3: B 10: C 4: C 11: D 9. Student lodgings A: 5: A 12: B 1: David 6: B 13: C 2: George 7: C 3: Harriet and Fiona 4: Emma 3. Find the opposite 1: B 6: B B: 2: A 7: B 5: Andrew and Fiona 3: B 8: C 6: George 4: C 9: D 7: George 5: A 10: D 8: House 2 (blue) 6. Scrambled sentences C: A: Margaret is a strict schoolteacher 9: David B: Physical exercise improves blood 10: Emma circulation to the brain 11: David C: Your brain consists of about 100 12: Bruce billion neurons D: Sudoku is a good brain-training 10. Odd one out exercise A: Train E: The average reading speed is A train travels on tracks. The rest travel 200–250 words a minute on roads. F: You are what you read B: Stocking G: By reading you experience life A stocking is worn over the foot and vicariously through the eyes of another leg. The rest are worn on the head. H: Interviewers use verbal reasoning C: Tiger tests to ﬁnd out how well a candidate A tiger has stripes. The rest have spots. can assess verbal logic D: Log A log is a portion of a tree. The rest are rocks.
Numerical reasoning/verbal reasoning 183 E: Tomato assess what they read correctly. I think 13. Wordy riddles A tomato is classiﬁed as a fruit. The it’s wrong for any teacher to ignore a A: Voice rest are vegetables. student’s bad spelling, and not prepare B: One—you have taken one cup of F: Clarion them adequately to go out into the sugar A clarion is a wind instrument. The wider world. We should, however, C: He said: “You’ll sentence me to rest have a keyboard. remember that bad spelling and bad 6 years in prison.” thinking are completely separate If it were true then the judge would 11. Spot the errors issues. Just because you’re a bad have to make it false by sentencing Only last night, I argued with my speller doesn’t make you dumb. All it him to 4 years. If it were false, then he friend about the correct spelling of a means is that you need to work harder would have to give him 6 years, which word: I said the correct spelling was to improve your spelling. It will really would make it true. Rather than “committed” while my friend insisted make a big difference when you start contradict his own word the judge set that it’s “committed.” Actually I am sending your CV to employers as to the man free. surprised that people can make so whether or not you get an interview. D: Time many spelling errors. Often when you point out people’s mistakes they feel 12. Fill in the blanks 14. Summer job criticized. Of course, the last thing I A: Fireman Statement A—True want to do is offend anybody; I just B: Mesmerizing Statement B— False think it is good for one’s personal C: Bombarding Statement C—Cannot say development to improve their D: Extend spelling. I’ve also found that if you E: Expand 15. The sounds in my life point out people’s spelling errors some F: Trouncing 1: C people just get embarrassed, or G: Scientist 2: B become really defensive. I am really 3: B happy to report that the college I go to 4: A is implementing measures to tackle 5: C bad spelling; they are drawing up 6: B classes to teach students how to 7: C 16. Dog’s day outONE MORNING... About time too... I’ll try... but I have I’m off to school... Behave yourself Orca Here we go... be a good dog a short memory As if I’d be anything else SOON... LATER... LATER STILL... It’s good to have Did you have Mad mutt! a city break! a good day? Crazy dog! Woof! Oh, the usual. Woof! Mineral water please, no ice.
184 Solutions 6. Memory math 9. Samurai Sudoku A: 13 B: 4.5 8 9 5 1 7 2 6 4 3 6 3 2 1 7 9 4 8 5 2 1 3 4 5 6 7 9 8 8 5 7 4 2 6 1 3 9 C: 12 6 4 3 1 5 28: Test your new D: 156 1 7 4 9 8 7 9 6 8 2 5 3 2 5 9 7 1 2 4 5 3 8 9 8 4 6 6 1 7 3 2 3brainpower 3 5 8 2 7 6 9 1 3 5 4 4 8 6 7 9 1 1 3 8 4 6 9 7 2 6 5 1 9 7 2 5 4 8 7. Squaring up: part two 9 3 2 6 8 7 5 1 4 8 7 9 2 6 3 5 4 7 8 9 1 4 6 1 5 2 9 3 8 7 2 6 5 4 9 1 6 8 3 5 7 2 C and D 7 5 8 3 4 1 9 2 6 1 3 4 5 7 8 9 1 2 3 4 6 8 4 3 6 2 7 9 1 51. Number recall 6 9 1 5 4 8 7 3 2A: 22 7 5 2 9 1 3 8 4 6 9 4 8 1 3 6 2 7 5 3 9 1 6 8 4 1 7 2 9 3 5B: 16 6 5 1 7 2 9 4 3 8 7 5 6 1 2 9 5 3 6 4 8 7C: Yellow 3 7 2 8 4 5 1 6 9 4 8 2 3 5 7 8 4 9 2 1 6 7 8 3 9 5 1 6 2 4 8 7 1 3 6 4 5 9 2D: 8 2 1 4 6 8 3 9 5 7 4 9 6 2 5 1 8 7 3E: 38 5 9 6 2 7 4 3 8 1 5 3 2 7 9 8 6 4 1 4 6 7 5 1 2 8 9 3 9 1 5 6 8 7 3 2 4 1 2 5 3 9 8 7 4 6 7 6 8 4 2 3 1 5 92. The correct cube 8 3 9 4 6 7 5 1 2 2 4 3 9 1 5 7 6 8D3. Old friendsMr. Smith’s old classmate is called 10. The word ladderLucy. In other words, he went to These are just examples:school with the mother. A: hear—sound—music—emotion— anger—ﬁght B: storm—lightning—electricity— energy—food—rice4. Number grid C: ﬂask—drink—water—river—ﬁsh— net D: child—school—book—paper— tree—forest 3 × 1 + 5 = 8 8. Matchstick mayhem 11. Hungry lion 1. Take off your shirt and try to throw × + – it over the candle to douse it. 4 × 8 – 3 = 29 2. Stop imagining being in that situation. – – × 3. It is a trained circus lion, and when 9 × 6 ÷ 2 = 27 you sing “happy birthday” it will walk over to the candle and blow it out. × × × 5 + 3 – 7 = 1 12. Shooting arrows + ÷ A: 14 – B: 43 4 × 9 ÷ 6 = 6 C: 11 = = = D: Carla 23 19 1 22
Test you new brainpower 18513. Scrambled sentences 18. Spot the errors 25. Suitor challengeA: Daily exercises can boost memory A: The baby wailed throughout the The successful suitor simply asked theand concentration skills church service daughter to walk over to where heB: Your brain uses about as much B: He was an accessory to the crime stood and to touch his hand!energy as a refrigerator light C: They accommodated us really wellC: No matter how ticklish you might during our holidaysbe you can’t tickle yourself D: Philip was deﬁnitely unaccustomed 26. Fitting jigsaw piecesD: Learning to play a musical to public speakinginstrument improves spatial reasoning E: The weather looks very changeableE: Physical exercise and a good diet F: The teacher was very disappointedmaintains brain health G: The television was cheap but cameF: Emotionally intense events produce without a guaranteevivid memoriesG: Social skills depend on the 20. Complete the cubeawareness of what others are feeling C and E15. Stacking mosaic tiles 21. Colored squaresB Same. It may look as if the 2 arms of the “X” use different shades of pink,16. Quick-ﬁre riddles but in fact the whole “X” only uses aA: Only once. After that you would be single color.subtracting from 20. Painters have long known that theB: Chalkboard/blackboard way a color looks in a painting isC: Your name affected not only by the actual shade of the color itself, but also by the colors that surround it. 27. The shortest route17. Krazy Kakuro 22. Shopping task 7 5 1 2 5 7 2 2 2 4 7 5 9 5 1 3 1 Tops: x 1 ( = $48.50) 6 5 2 8 3 5 6 6 Skirts: x 3 ( = $67.50) 1 5 1 7 8 5 7 8 8 1 2 2 9 5 1 4 5 Socks: x 4 ( = $18) 3 8 5 3 4 1 4 5 5 Belt: x 3 ( = $12.90) 8 2 3 4 2 9 5 8 8 7 6 7 9 (Total = $146.90) 3 1 7 6 8 6 9 1 1 9 4 2 1 7 5 8 6 2 6 9 9 9 7 4 2 1 8 8 2 9 4 5 5 1 5 3 1 3 2 8 4 7 9 1 9 9 9 8 9 4 2 6 8 8 3 8 9 2 24. Build the bird 6 8 8 6 3 7 2 3 1 8 8 5 5 7 7 9 4 3 8 9 1 4 9 3 4 4 2 8 3 1 2 9 7 1 3 5 8 4 3 8 1 1 5 3 9 5 8 9 9 8 5 8 9 7 4 2 6 1 2 8 6 1
186 Useful websitesUseful websitesGeneral More puzzles Mind-bodyNewScientist and exercises Acupuncturewww.newscientist.com/topic/brain www.stetson.edu/~efriedma/puzzle American Academy of MedicalFor more information and the latest For a huge range of puzzles Acupunctureresearch into how the brain works www.medicalacupuncture.org Learn about acupuncture and howMemory techniques Visual reasoning and to ﬁnd an acupuncturist spatial awarenesswww.youramazingbrain.org/yourmemory www.geocities.com/CapeCanaveral/ Meditationwww.mindtools.com Lab/8972/ International Meditation Center–USAwww.buildyourmemory.com www.sharpbrains.com internationalmeditationcentre.org/usawww.changingminds.org/techniques/ For more information on meditationmemory/peg Think creativelyMind maps and Tony Buzan www.cul.co.uk/creative/puzzles.htm Stresswww.buzanworld.com www.learning-tree.org.uk American Institute of StressThe World Memory Championships www.stress.org Creative Problem Solving Institutewww.worldmemorychampionships.com Advice on symptoms, treatment, and Creative Education Foundation prevention www.mycoted.com T’ai Chi Numerical reasoning Taoist T’ai Chi Society of the www.cut-the-knot.com United States of America www.jimloy.com www.usa.taoist.org For more numerical riddles Part of the International Taoist T’ai Chi Society; for more information on T’ai www.krazydad.com Chi, including where to ﬁnd a teacher in For more Sudoku puzzles the US www.riddles.com For further creative conundrums Yoga www.visualmathlearning.com Yoga Alliance www.yogaalliance.org Verbal reasoning Find a certiﬁed yoga teacher in the US www.puzzlechoice.com For crosswords, word searches, and word play games www.wordplays.com For more verbal games
Further reading 187Further readingIntroduction to the brain Verbal reasoningThe Rough Guide to the Brain by Barry Gibb (Rough The Power of Verbal Intelligence: 10 Ways to Tap into YourGuides), 2007 Verbal Genius by Tony Buzan (Thorsons), 2002The Private Life of the Brain by Susan Greenﬁeld (Wiley), Practice Tests for Critical Verbal Reasoning by Peter Rhodes2000 (Hodder Arnold), 2006The Human Brain: A Guided Tour by Susan Greenﬁeld (Basic Verbal Reasoning: Challenge Tests by Stephen McConkeyBooks), 1998 (Learning Together), 2007Memory Mind-body connectionUse Your Memory: Understand Your Mind to Improve Your How the Body Shapes the Mind by Shaun Gallagher (OxfordMemory and Mental Power by Tony Buzan (BBC Active), 2006 University Press), 2006How to Develop a Brilliant Memory Week by Week: 52 Proven The Feeling of What Happens: Body, Emotion and the MakingWays to Enhance Your Memory Skills by Dominic O’Brien of Consciousness by Antonio R. Damasio (Harvest), 2000(Duncan Baird Publishers), 2005 The Yoga Bible: The Deﬁnitive Guide to Yoga Postures byYour Memory: How It Works and How to Improve It by Kenneth Christina Brown (Walking Stick Press), 2003L. Higbee (Da Capo Press), 2001 Finding the Still Point: A Beginner’s Guide to Zen Meditation by John Daido Loori (Shambhala Publications Inc), 2007Visual reasoning and spatial awareness 1001 Ways to Relax by Susannah Marriott (DK Publishing), 2008Visual and Spatial Analysis: Advances in Data Mining,Reasoning, and Problem Solving by Boris Kovale-chuk & James Final workout (puzzles)Schwing (Springer), 2005 The Buzan Study Skills Handbook: The Shortcut to Success inMensa Mighty Visual Puzzles: Over 300 Puzzles To Test Your Your Studies with Mind Mapping, Speed Reading and WinningPowers Of Reasoning by John Bremner (Carlton Books Ltd), 1997 Memory Techniques by Tony Buzan (BBC Active), 2006Near and Far at the Beach: Learning Spatial Awareness Concepts The Big Book of Mind-bending Puzzles (Ofﬁcial Mensa Puzzle(Math for the Real World: Early Emergent) by Amanda Boyd Book) by Terry H. Stickels (Sterling), 2006(Rosen Publishing Group), 2008 The 10-Minute Brain Workout by Gareth Moore (Michael O’Mara Books Ltd), 2006Creativity Will Shorts Presents KenKen Easy to Hard: 100 Logic PuzzlesThis is Your Brain on Music: Understanding a Human Obsession That Make You Smarter by Tetsuya Miyamoto (St. Martin’sby Daniel J. Levitin (Atlantic Books), 2008 Grifﬁn), 2008Mind Mapping: Kickstart Your Creativity and Transform YourLife (Buzan Bites) by Tony Buzan (BBC Active), 2006 Other interesting readingThe Power of Creative Intelligence by Tony Buzan (Thorsons), 2001 The Man Who Mistook His Wife for a Hat by Oliver SacksHow to Have Creative Ideas: 62 Exercises to Develop the Mind (Simon & Schuster), 1986by Edward De Bono (Vermilion), 2007 Six Thinking Hats by Edward de Bono (Back Bay Books), 2000Thinkertoys: A Handbook of Creative-Thinking Techniques by Emotional Intelligence: Why it Can Matter More Than IQ byMichael Michalko (Ten Speed Press), 2006 Daniel Goleman (Bantam Books), 1996 The Lost Cause: An Analysis of Causation and the Mind-bodyNumerical reasoning Problem by Celia Green (Oxford Forum), 2003Mensa Challenge Your Brain Math and Logic Puzzles Teach Yourself Training Your Brain by Simon Wootton & Terry(Ofﬁcial Mensa Puzzle Book) by Dave Tuller & Michael Rios Horne (McGraw-Hill), 2007(Sterling), 2006 Phantoms in the Brain: Human Nature and the Architecture ofTrain Your Brain by Ryuta Kawashima (Kumon Publishing), 2008 the Mind by V.S. Ramachandran & Sandra Blakeslee (FourthTesting Series: How to Pass Numerical Reasoning Tests: A Estate Ltd.), 1999Step-by-step Guide to Learning the Basic Skills by Heidi Smith(Kogan Page), 2003
192 AcknowledgmentsAbout the AuthorsJames Harrison Mike HobbsHarrison is a writer and editor. He cowrote The Buzan Study Mike is an author, journalist, and copywriter. He has writtenSkills Handbook (BBC Active, 2006), and was editorial nine books, including The Big Challenge: Working Your Wayconsultant on How to Be Conﬁdent Using the Power of NLP To Health (BBC Books, 2005) and Easy PC (Right Way, 2008).(Prentice Hall Life, 2008) and How to Help Your Child Succeed In addition, he has ghostwritten six more on subjects as diverseAt School (Prentice Hall Life, 2007). Harrison edited Natural as soccer, pop music, and sex changes. His journalism has beenChoice (Orbis), which explored complementary therapies published in the Daily Telegraph, the Financial Times, thefor mind-body-spirit. He is currently working on a series of Guardian, the Independent, Time Out, and the Independent“Mind Set” books by Tony Buzan (BBC Active), which include on Sunday. Through his company, Westword, he has writtentitles on Mind Mapping, memory boosting and speed reading. marketing and public relations material for 20 years.AcknowledgmentsAuthors’ acknowledgments www.sharpbrains.com for “Cake for eight,” p.52,This was a team effort in which we were merely players, so ﬁrstly “Quick-speed counting,” p.53.we’d like to thank Peggy Vance for championing the project and www.geocities.com/CapeCanaveral/Lab/8972 forfor her enthusiastic support throughout. Our gratitude also “Largest circle,” p.53, “Straight or crooked?”, p.54,goes to Suhel Ahmed and Charlotte Seymour for the tough “Largest parcel,” p.54, “The vanishing area,” p.60.task of marrying the words and design, and to Helen Murray,Penny Warren, and Liz Sephton for their calm overseeing. Our www.mycoted.com for “A perfect circle?”, p.21, “Speedparticular thanks also to Keith Hagan, who has created extremely reading,” p.23, “Manhole covers,” p.25, “Drinkingeye-catching illustrations to make Brain Training really stand out. glasses,” p.73, “The elder twin,” p73, “The swimmer in theThanks also to Phil Chambers for his knowledgeable and helpful forest,” p.73, “Crossing the bridge,” p.73, “Lateraladvice. A heartfelt thanks to Tony Buzan for being an inspiration thinking,” p.78, “Original answers,” p.84, “Strangeand showing that there are no limits to the amazing brain and detour,” p.88, “Bottled money,” p.88, “Separated atthat it is possible to create a manual for it! birth?”, p.89, “Push that car,” p.89, “Triangle ratio,” p.105, Of course, ﬁnally a big thank you to our families (Joanna “Chasing cars,” p.120.Harrison, Katie, Hugo, and Louise; Maureen Hobbs, Anna, Oh Teik Bin for “Creative conundrums,” pp.86–87, “TheJack, and Elliott) for watching us both live in “puzzlesville,” fatal ﬂash,” p.88, “Lax borders,” p.88.putting up with endless quizzes—and inadvertently trainingtheir brains in the process. www.riddles.com for “Enough ﬁsh,” p.72, “Newspaper divider,” p.89, “Nail on the tree,” p.89. www.cul.co.uk/creative/puzzles.htm for “The hiddenPublisher’s acknowledgments story,” p.70, “Horsing around,” p.72.DK Publishing would like to thank Sue Bosanko for the indexand Angela Baynham for proofreading in such a short amount Brian Clegg (Instant Brainpower, Kogan Page Ltd, 1999)of time. Also, many thanks to Matilda Gollon, Felicity for “Summer job,” p.136.Blackshaw, and Clementine Beauvais for editorial assistance, www.learning-tree.org.uk for “Matchstick mayhem,”and Jennifer Murray and Ivy Fisher for checking the puzzles. pp.80–83 and p.164.We would like to thank the following people/websites www.eﬁnancialcareers.co.uk for “Keen student,” p.101,for providing access to their puzzles and exercises: “Computer sales,” p.103.www.umapalata.com for “Building fences,” p.21 and www.cut-the-knot.com for “The broken calculator,” p.104.“Build the bird,” p.170. www.krazydad.com for “Kakuro,” pp.112–113 and p.167.www.stetson.edu/~efriedma/color/ for “Numerical www.jimloy.com for “The famous 3 doors conundrum,” p.121.jigsaw,” p.24, “Color mazes,” p.26. www.visualmathslearning.com for “The shortest route,” p.104 and p.171.