Art of Puzzle Solving


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A framework to solve puzzles and 10 popular puzzles from CSE Blog (

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Art of Puzzle Solving

  1. 1. ART OF PUZZLE SOLVINGA framework to solve puzzles and 10 popular puzzles from CSEBlog (
  2. 2. What is Puzzle Solving? "Solving math Puzzles" really reflects "Training of the Mind". Its not about smartness or intelligence or IQ. Its really about howwell you have trained your mind to solve problems.CSE Blog - May 16, 20132
  3. 3. How to train your mind? When you see a puzzle, questions you need to ask yourself:o Of course you begin with: How to solve the problem?o Once you have solved the problem or seen the solution, you needto ask What are the ways I could have solved this problem?.o Sanity check and intuitive thinking helps more than you wouldimagine. You need to ask Is there a way to check that my solutionis correct intuitively?o If you are not able to solve the problem, its fine! Read thesolution carefully. Then ask, What concept did I learn?o and Which are the other situations in which this concept can beapplied?CSE Blog - May 16, 20133
  4. 4. Types of Math Puzzles Most math puzzles are from the following topics:1) Casual Puzzles2) Combinatorics / Probability3) Algorithms4) Engineering Mathematics5) Coding (C/C++)CSE Blog - May 16, 20134
  5. 5. How to prepare? – books by topic(1/3)How to prepare:1) Casual PuzzlesMathematical Puzzles: A Connoisseurs Collection - by Peter WinklerEntertaining Mathematical Puzzles - by Martin GardnerMathematical Puzzles of Sam Loyd2) Combinatorics / ProbabilityProbability, Random Variables And Stochastic Processes - byPapoulisFifty Challenging Problems in Probability with SolutionsCSE Blog - May 16, 20135
  6. 6. How to prepare? – books by topic(2/3)How to prepare:3) AlgorithmsIntroduction To Algorithms - by Cormen, Lieserson, RivestAlgorithms - by Robert Sedgewick4) Engineering MathematicsAdvanced Engineering Mathematics - by KreyszigLinear Algebra And Its Applications - by Gilbert StrangWhat Is Mathematics? - by Richard CourantCSE Blog - May 16, 20136
  7. 7. How to prepare? – books by topic(3/3)How to prepare:5) Coding (C/C++)C++: The Complete ReferenceThe C++ Programming Language - by StroustrupProgramming in C++ - by Cohoon and DavidsonCSE Blog - May 16, 20137
  8. 8. How to prepare? – some puzzle blogs(1/2)CSE BlogGurmeet Singh Mankus BlogCMU - The Puzzle ToadIBM Ponder ThisWilliam Wus CollectionC Puzzles by Gowri KumarRustan Lieno CollectionCotpiA Puzzle BlogMe, Myself and MathematicsCSE Blog - May 16, 20138
  9. 9. How to prepare? – some puzzle blogs(2/2)A WandererNickss Mathematical PuzzlesGowerss BlogTanya Khovanova’s Math Blogin theoryThe Math Less TravelledWild About Math!Terry TaoA Computer Scientist in a Business SchoolCombinatorics and moreA Neighbourhood of InfinityCSE Blog - May 16, 20139
  10. 10. 10 Puzzle Collection – Puzzle 1Problem 1: Conway’s Soldiers (CheckerBoard Unreachable Line)Original Link: to me by Amol Sahasrabudhe (Morgan Stanley)Problem:An infinite checkerboard is divided by a horizontal line that extends indefinitely. Abovethe line are empty cells and below the line are an arbitrary number of game pieces, or"soldiers". A move consists of one soldier jumping over an adjacent soldier into an emptycell, vertically or horizontally (but not diagonally), and removing the soldier which wasjumped over. The goal of the puzzle is to place a soldier as far above the horizontal lineas possible.Prove that there is no finite series of moves that will allow a soldier to advance more thanfour rows above the horizontal line.CSE Blog - May 16, 201310
  11. 11. 10 Puzzle Collection – Puzzle 2Problem 2: Determinant of Binary MatrixOriginal Link: to me by Sudeep Kamath (PhD Student, UC at Berkeley, EE IITB Alumnus 2008)Problem:An N by N matrix M has entries in {0,1} such that all the 1s in a row appear consecutively.Show that determinant of M is -1 or 0 or 1.CSE Blog - May 16, 201311
  12. 12. 10 Puzzle Collection – Puzzle 3Problem 3: Hats in a CircleOriginal Link: Toad, CMUProblem:Each hat is black or white. The people are standing in a circle. Now our n hat wearingfriends are standing in a circle and so everyone can see everybody elses hat. The hatshave been assigned randomly and each allocation of hat colors is equally likely. At acertain moment in time each person must simultaneously shout "my hat is black or "my hatis white or "I havent a clue. The team wins a big prize if at least one person gets thecolor of his hat right and no one gets it wrong (saying "I havent a clue is not getting itwrong). Of course, if anyone gets it wrong, the whole team is eliminated and this is painful.The prize is big enough to risk the pain and so devise a strategy which gives a goodchance of success.CSE Blog - May 16, 201312
  13. 13. 10 Puzzle Collection – Puzzle 4Problem 4: Correct LettersOriginal Link: of Prof. Sundars course "Approximation Algorithms"Problem:There are n letters and n envelopes. Your servant puts the letters randomly in theenvelopes so that each letter is in one envelope and all envelopes have exactly one letter.(Effectively a random permutation of n numbers chosen uniformly). Calculate the expectednumber of envelopes with correct letter inside them.CSE Blog - May 16, 201313
  14. 14. 10 Puzzle Collection – Puzzle 5Problem 5: Don’t roll moreOriginal Link: from the book "Heard on The Street" (Problem 4.2 in Revised 9th Edition) by TimothyFalcon CrackProblem:I will roll a single die not more than three times. You can stop me immediately after thefirst roll, or immediately after the second, or you can wait for the third. I will pay you thesame number of dollars as there are dots on the single upturned face on my last roll (rollnumber three unless you stop me sooner). What is your playing strategy?CSE Blog - May 16, 201314
  15. 15. 10 Puzzle Collection – Puzzle 6Problem 6: Lion in a Circular Cage PuzzleOriginal Link: to me by Pramod Ganapathi (PhD Student at Stony Brook University)Problem:A lion and a lion tamer are enclosed within a circular cage. If they move at the samespeed but are both restricted by the cage, can the lion catch the lion tamer? (Represent thecage by a circle, and the lion and lion tamer as two point masses within it.)CSE Blog - May 16, 201315
  16. 16. 10 Puzzle Collection – Puzzle 7Problem 7: Consecutive HeadsOriginal Link: say A keep tossing a fair coin, until he get 2 consecutive heads, define X to be thenumber of tosses for this process; B keep tossing another fair coin, until he get 3consecutive heads, define Y to be the number of the tosses for this process.1) Calculate P{X>Y}2) Whats the expected value of X3) Whats the expected value of YCSE Blog - May 16, 201316
  17. 17. 10 Puzzle Collection – Puzzle 8Problem 8: Coins PuzzleOriginal Link: are 100 coins on the table out of which 50 are tail-face up and 50 are head faceup. You are blind folded and there is no way to determine which side is up by rubbing,etc. You have to divide the 100 coins in two equal halves such that both have equalnumber of coins with tails face up. (This obviously implies that the two have equal numberof coins with heads face up)Second part: There are 100 coins on the table out of which 10 are tail-face up and 90are head face up. You are blind folded and there is no way to determine which side is upby rubbing, etc. You have to divide the 100 coins in two halves (not necessarily equal) suchthat both have equal number of coins with tails face up.CSE Blog - May 16, 201317
  18. 18. 10 Puzzle Collection – Puzzle 9Problem 9: Arithmetic Puzzle: Broken CalculatorOriginal Link: ForumProblem:There is a calculator in which all digits(0-9) and the basic arithmetic operators(+,-,*,/) aredisabled. However other scientific functions are operational like exp, log, sin, cos, arctan,etc. The calculator currently displays a 0. Convert this first to 2 and then to 3.CSE Blog - May 16, 201318
  19. 19. 10 Puzzle Collection – Puzzle 10Problem 10: Number of Locks and KeysOriginal Link: paper on Secret Sharing Scheme states this problem and gives the answer withthe explanation that its written in standard Combinatorics booksProblem:7 thieves wanted to lock the treasure looted from a ship. They wanted to put locks to thetreasure where each lock had multiple keys. Find the minimum number of locks N andminimum no. of keys K with every thief subject to the following conditions:-All the locks should open each time a majority of thieves(4 or more) try to open the locks.At least one lock remains unopened if less than 4 thieves try opening them.All locks should have same no. of keys.All thieves must have same no. of keys with them.CSE Blog - May 16, 201319
  20. 20. Thanks Please visit CSE Blog( ) for more puzzles Author: Pratik PoddarEmail: pratikpoddar05051989@gmail.comLinkedin Profile: http://www.pratikpoddar.wordpress.comCSE Blog - May 16, 201320