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# Maths starters

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Quick Brainteaser questions to start a maths class

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• Brainteaser answer100 chocolate bars have 100 wrappers, which can be traded for 10 free bars. The wrappers for the free bars can then be traded for one more free bar (and an extra wrapper). 100 + 10 + 1 = 111 chocolate bars.
• Brainteaser answerA line can only have one of each digit, so the biggest sum is:1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45
• Brainteaser answerThere are five different ways to make \$1.10 with seven coins. You can’t use a \$1 coin – it’s too big. You can’t use two 50c coins either. With one 50c coin, you can make:50c, 20c, 20c, 5c, 5c, 5c, 5c50c, 20c, 10c, 10c, 10c, 5c, 5c50c, 10c, 10c, 10c, 10c, 10c, 10cWith no 50c coins, you can make:20c, 20c, 20c, 20c, 20c, 5c, 5c20c, 20c, 20c, 20c, 10c, 10c, 10cAnd that’s all the combinations you can make.
• Brainteaser answerIt is possible if the date is 1 January, and George’s birthday is on 31 December. Then last year he turned 13, this year he’ll turn 14 and next year he’ll turn 15.
• Brainteaser answerThey are in alphabetical order!(Eight, five, four, nine, one, seven, six, ten, three, two, zero.)
• Brainteaser answerEach student sends one letter to each person in the class except themselves. If there were 6 people in the class, each would send 5 letters, which makes 6 x 5 = 30 letters in total.306 = 18 x 17, so 18 students each sent 17 letters to make the total.A good place to start with this puzzle would be calculating the square root of 306. Since the number of students and the number of letters that each student sends are very close, it will give you a good estimate of the number of people in the class.
• Brainteaser answerIf one player has all the clubs, then the other has none – you can’t have one without the other. So both outcomes are equally likely!
• Brainteaser answerThe first and third primes are 2 and 5. If you multiply anything by 2 and 5, it will be divisible by 10, and that means it ends in a 0!
• ### Maths starters

1. 1. Maths Starters In small groups attempt to answerthe following brainteaser questions.
2. 2. Brainteaser questionTo celebrate the New Year, a principal orders100 chocolate bars to give to her students.When the chocolate bars arrive, she realises thechocolate bars have a special offer. If you handin 10 wrappers, you receive a free chocolatebar!If everyone in the school saves their wrappers, how manychocolate bars can the school get?
3. 3. Brainteaser questionWhat is the largest numberthat can be a clue in Kakuro?(A Kakuro consists of a grid of boxes, someempty and some filled. Lines of emptyboxes run across and down. These lineseach have a clue – to the left of horizontallines and above vertical ones. The aim is towrite a digit from 1 to 9 in each empty boxfollowing two rules:1.No two boxes in a line contain the samedigit2.Adding up all the digits in the line willequal the clue )
4. 4. Brainteaser questionTasko the Sea Lion lives at Adelaide Zoo. Recently, he wasvery sick, and the zoo’s vets realised he’d been eatingsome coins. They removed seven coins, adding up to\$1.10, from Tasko’s belly. Since they removed the money,Tasko is feeling a lot better.Can you come up with a set of seven coins that add up to\$1.10? How many ways arethere to make \$1.10 with seven coins?
5. 5. Brainteaser questionThe day before yesterday, George was 12 yearsold. Next year, he’ll turn 15. How is thispossible?
6. 6. Brainteaser questionHere are four dots, arranged in a square:Without lifting your pen, draw three straightlines, pass through all four dots and finish upexactly where you started.
7. 7. Brainteaser questionCan you work out the pattern in these numbers?8, 5, 4, 9, 1, 7, 6, 10, 3, 2, 0
8. 8. Brainteaser question• One day in class, the students were writing letters. Each student wrote one letter to each other student in the class. In total, 306 letters were written. How many students were there in the class?
9. 9. Brainteaser question• In a card game, two players are each dealt 26 cards from a deck of 52. Thirteen of the cards have a club on them.Which event is more likely:getting dealt all of the clubs,or getting none of them?
10. 10. Brainteaser questionIf you multiplied thefirst 1000 primenumbers together,what digit would be inthe ones place (the lastdigit of the number)?
11. 11. Math puzzle• Five people order a square pizza. The first person dives in an eats a quarter of the pizza. The other four people have to divide the remaining three- fourths into four equal and identically shaped slices. The cuts must be straight. How must they cut the remaining pizza in order to produce four identical slices?