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The Master Book of Mathematical Recreations (Dover Recreational Math)by Frederik Schuh
Synopses & ReviewsPublisher Comments:Praised for its "exceptionally good value" by the Journal of Recreational Math, this book offers funfilled insights into many fields of mathematics. The brainteasers include original puzzles as well as new approaches to classic conundrums. A vast assortment of challenges features domino puzzles, the game of noughts and crosses, games of encirclement, sliding movement puzzles, subtraction games, puzzles in mechanics, games with piles of matches, a road puzzle with concentric circles, "Catch the Giant," and much more.
Detailed solutions show several methods by which a particular problem may be answered, why one method is preferable, and where the others fail. With numerous worked examples, the clear, stepbystep analyses cover how the problem should be approached, including hints and enumeration of possibilities and determination of probabilities, application of the theory of probability, and evaluation of contingencies and mean values. Readers are certain to improve their puzzlesolving strategies as well as their mathematical skills. Synopsis:A wealth of original challenges and new approaches to classic conundrums includes numerous worked examples and a focus on the mathematics behind the puzzles. "Exceptionally good value." — Journal of Recreational Math. Synopsis:Praised for its "exceptionally good value" by the Journal of Recreational Math, this volume offers original puzzles as well as new approaches to classic conundrums. Puzzle fans will enjoy mastering these domino puzzles, noughts and crosses, and other challenges. They'll also appreciate the numerous worked examples, which will improve their puzzlesolving strategies and mathematical skills. About the AuthorDutch mathematician Frederik Schuh (18751966) received his PhD in algebraic geometry from Amsterdam University and taught at the Delft University of Technology. Table of Contents[Asterisks indicate sections that involve algebraic formulae.]
Chapter I: Hints for Solving Puzzles I. Various Kinds of Puzzles 1. Literary puzzles 2. Pure puzzles 3. Remarks on pure puzzles 4. Puzzle games 5. Correspondences and differences between puzzles and games II. Solving by Trial 6. Trial and error 7. Systematic trial 8. Division into cases 9. Example of a puzzle tree III. Classification System 10. Choosing a classification system 11. Usefulness of a classification system 12. More about the classification system IV. Solving a Puzzle by Simplification 13. Simplifying a puzzle 14. Example of how to simplify a puzzle 15. Remarks on the seven coins puzzle 16. Reversing a puzzle 17. Example of reversing a puzzle V. Solving a Puzzle by Breaking It Up 18. Breaking a puzzle up into smaller puzzles 19. Application to the crossing puzzle 20. Number of solutions of the crossing puzzle 21. Restrictive condition in the crossing puzzle 22. Shunting puzzle VI. Some Puzzles with Multiples *23. Trebles puzzle *24. Breaking up the trebles puzzle *25. Trebles puzzle with larger numbers *26. Doubles puzzle with 7digit numbers *27. Remarks on the numbers of §26 *28. Quintuples puzzle Chapter II: Some Domino Puzzles I. "Symmetric Domino Puzzle, with Extensions" 29. Symmetric domino puzzle 30. Extended symmetric domino puzzle *31. Another extension of the symmetric domino puzzle II. Doubly Symmetric Domino Puzzle *32. First doubly symmetric domino puzzle *33. Doubly symmetric domino puzzle without restrictive condition *34. Connection with the puzzle of §32 35. Second doubly symmetric domino puzzle 36. Puzzle with dominos in a rectangle III. Smallest and Largest Numbers of Corners 37. Salient and reentrant angles 38. Puzzle with the smallest number of angles 39. Puzzle with the largest number of angles Chapter III: The Game of Noughts and Crosses I. Description of the Game 40. Rules of the game 41. Supplement to the game 42. Consequences of the rules II. Considerations Affecting Values of the Squares 43. Value of a square 44. Remarks on the value of a square III. Directions for Good Play 45. Semirow or threat 46. Double threat 47. Combined threat 48. Replying to a double threat 49. Further directions for good play IV. Some Remarks on Good Play 50. Remarks on the double threat 51. Connection with the value of a move V. General Remarks on the Analysis of the Game 52. Preliminary remarks 53. Diagrams 54. Tree derived from the diagrams VI. Partial Analysis of the Game 55. "John starts with the central square 5, Peter replies with the corner square 1" 56. "John starts with the corner square 1, Peter replies with the central square 5" 57. "John starts with the border square 2, Peter replies with the central square 5" 58. Equitable nature of the game VII. Complete Analysis of the Game 59. "John starts with the central square 5, Peter replies with the border square 2" 60. "John starts with the corner square 1, Peter replies with the border square 2" 61. "John starts with the corner square 1, Peter replies with the corner square 3" 62. "John starts with the corner square 1, Peter replies with the border square 6" 63. "John starts with the corner square 1, Peter replies with the corner square 9" 64. Results of John's first move 1 65. "John starts with the border square 2, Peter replies with the corner square 1" 66. "John starts with the border square 2, Peter replies with the border square 4" 67. "John starts with the border square 2, Peter replies with the corner square 7" 68. "John starts with the border square 2, Peter replies with the border square 8" 69. Results of John's first move 2 VIII. Modification of the Game of Noughts and Crosses 70. First modification of the game 71. Second modification of the game 72. Conclusions from the trees of §71 IX. Puzzles Derived from the game *73. Possible double threats by John *74. Possible double threats by Peter *75. Some more special puzzles *76. Possible cases of a treble threat 77. Remark on the treble threat Chapter IV: Number Systems I. Counting 78. Verbal counting 79. Numbers in written form 80. Concept of a digital system II. Arithmetic 81. Computing in a digital system *82. Changing to another number system III. Remarks on Number Systems 83. The only conceivabe base of a number system is 10 84. Comparison of the various digital systems 85. Arithmetical prodigies IV. More about Digital Systems 86. Origin of our digital system 97. Forerunners of a digital system 88. Grouping objects according to a number system Chapter V: Some Puzzles Related to Number Systems I. Weight Puzzles 89. Bachet's weights puzzle 90. Weights puzzles with weights on both pans 91. Relation to the ternary system II. Example of a Binary Puzzle 92. Disks puzzle 93. Origin of the disks puzzles III. Robuse and Related Binary Puzzle 94. Robuse 95. Transposition puzzles *96. Other transposition puzzles CHAPTER VI: Games with Piles of Matches I. General Observations 97. General remarks 98. Winning situations II. Games with One Pile of Matches 99. Simplest match game 100. Extension of the simplest match game 101. More difficult game with one pile of matches III. Games with Several Piles of Matches 102. Case of two piles 103. Case of more than two piles and a maximum of 2 104. Case of more than two piles and a maximum of 3 *105. Case of more than two piles and a maximum of 4 or 5 *106. "As before, but the last match loses" IV. Some Other Match Games 107. Game with two piles of matches 108. Game with three piles of matches *109. Extension of four or five piles *110. Modification of the game with three piles of matches 111. Match game with an arbitary number of piles *112. Case in which loss with the last match is a simpler game V. Game of Nim 113. General remarks 114. Game of nim with two piles 115. Some winning situations VI. Game of Nim and the Binary System 116. Relation to the binary system 117. Proof of the rule for the winning situations 118. Remarks on the correct way of playing 119. Case in which the last match loses 120. Simplest way to play VII. Extension or Modification of the Game of Nim 121. Extension of the game of nim to more than three piles *122. Further extension of the game of nim *123. Special case of the game of §122 *124. Modification of the game of nim Chapter VII: Enumeration of Possibilities and the Determination of Probabilities I. Number of Possibilities 125. Multiplication 126. Number of complete permutations 127. Number of restricted permutations 128. Number of combinations 129. "Number of permutations of objects, not all different " 130. Number of divisions into piles II. Determining Probabilities from Equally Likely Cases 131. Notion of probability 132. Origin of the theory of probability 133. Misleading example of an incorrect judgment of equal likelihood III. Rules of Calculating Probabilites 134. Probability of either this or that; the addition rule 135. Probability of both this and that; the product rule 136. Examples of dependent events 137. Maxima and minima of sequences of numbers 138. Extension to several events 139. Combination of the sum rule and product rule 140. More about maxima and minima in a sequence of numbers IV. Probabilities of Causes 141. A posteriori probability: the quotient rule 142. Application of the quotient rule 143. Another application Chapter VIII: Some Applications of the Theory of Probability I. Various Questions on Probabilities 144. Shrewd prisoner 145. Game of kasje *146. Simplification of the game kasje 147 Poker dice 148. Probabilities in poker dice II. Probabilities in Bridge 149. Probability of a given distribution of the cards 150. A posteriori probability of a certain distribution of the cards 151. Probabilities in finessing Chapter IX: Evaluation of Contingencies and Mean Values I. Mathematical Expectation and Its Applications 152. Mathematical Expectation 153. Examples of mathematical expectation 154. More complicated example 155. Modification of the example §154 156. Petersburg paradox II. Further Application of Mathematical Expectation 157. Appplication of mathematical expectation to the theory of probability 158. Law of large numbers 159. Probable error 160. Remarks on the law of large numbers 161. Further relevance of the law of large numbers III. Average Values 162. Averages 163. Other examples of averages 164. Incorrect conclusion from the law of large numbers Chapter X: Some Games of Encirclement I. Game of Wolf and Sheep 165. Rules of the game of wolf and sheep 166. Correct methods for playing wolf and sheep 167. Some wolf and sheep problems 168. Even and odd positions 169. Final remark on wolf and sheep II. "Game of Dwarfs or "Catch the Giant!" 170. Rules of the game 171. Comparison with wolf and sheep 172. Remarks on correct lines of play 173. Correct way of playing 174. Winning positions 175. Positions where the dwarfs are to move III. Further Considerations of the Game of Dwarfs 176. "Remarks on diagrams D, E, and G" 177. Critical positions 178. More about the correct way of playing 179. Trap moves by the giant 180. Comparison of the game of dwarfs with chess IV. Modified Game of Dwarfs 181. Rules of the game 182. Winning positons of the modified game 183. Case in which the dwarfs have to move 184. Dwarfs puzzle 185. Remark on diagrams AH 186. Other opening moves of the giant V. The Soldier's Game 187. Rules of the game 188. Winning positions 189. Course of the game 190. Other winning positions 191. Modified soldier's game Chapter XI: SlidingMovement Puzzles I. Game of Five 192. Rules of the game 193. Some general advice 194. Moving a single cube 195. Condition for solvability II. Extensions of the Game of Five 196. Some results summarized 197. Proof of the assertions of §196 III. Fatal Fifteen 198. Further extension of the game of five 199. Proof of corresponding results IV. Futher Considerations on Inversions 200. Property of inversions *201 Cyclic permutation *202. Parity determination in terms of cyclic permutations V. Least Number of Moves 203. Determination of the least number of moves 204. First example *205. Some more examples VI. Puzzles in Decanting Liquids 206. Simple decanting puzzle with three jugs 207. Another decanting puzzle with three jugs 208. Remarks on the puzzles of §§206 and 207 209 Changes of the three jugs 210. Further remarks on the threejug puzzle 211. Decanting puzzle with four jugs 212. Another puzzle with four jugs Chapter XII: Subtraction Games I. Subtraction Game with a Simple Obstacle 213. Subtraction games in general 214. Subtraction games with obstacles 215. Winning numbers when 0 wins 216. Winning numbers when 0 loses II. Subtraction Game with a More Complicated Obstacle 217. Rules of the game 218. Evensubtraction game 219. Oddsubtraction game III. "3,5,7 and 9Subtraction Games" 220. 3subtraction game 221. The other 3subtraction games 222. 5subtraction game 223. 7subtraction game 224. 9subtraction game IV. Subtraction Game where the Opener Loses 225. Modified subtraction game 226. "Modified 2,3, 4, and 5subtraction games" 227. "Modified 6, 7, 9, and 9subtraction games" *228 Modified subtraction game with larger deductions Chapter XIII: Puzzles with Some Mathematical Aspects I. Simple Puzzles with Squares 229. Puzzle with two square numbers of two or three digits 230. Puzzle with three 3digit squares 231. Puzzle of §230 with initial zeros II. Puzzle with 4Digit Squares 232. 4digit squares 233. Puzzle of the four4digit squares 234. Puzzle of §233 with zeros III. A Curious Multiplication 235. Multiplication puzzle with 20 digits 236. Connection with remainders for divisions by 9 237. Combination of the results of §§235 and 236 IV. Problem on Remainders and Quotients 238. Arithmetical puzzle 239. Variants of the puzzle of §238 *240. Mathematical discussion of the puzzle V. Commuter Puzzles 241. Simple commuter puzzle 242. More difficult commuter puzzle 243. Solution of the puzzle of §242 VI. Prime Number Puzzles 244. Prime number puzzle with 16 squares 245. Solution of the puzzle of §244 246. Examination of the five cases 247. Puzzle of §244 with a restriction 248. Prime number puzzle with 25 squares 249. Puzzle with larger prime numbers VII. Remarkable Divisibility 250. Divisibility of numbers in a rectange 251. Puzzle with multiples of 7 252. Multiples of 7 puzzle with the largest sum 253. Proof that the solutions found do in fact yield the largest sum 254. Multiples of 7 with the maximum product VIII. Multiplication and Division Puzzles 255. "Multiplication puzzle "Est modus in rebus" 256. Multiplication and division puzzle *257. Terminating division puzzle *258. Repeating division puzzle IX. Dice Puzzles 259 Symmetries of a cube *260. Group of symmetries *261. Symmetries of the regular octahedron 262. Eight dice joined to make a cube *263. More difficult puzzle with eight dice *264 Which are the invisible spot numbers? Chapter XIV: Puzzles of Assorted Types I. Network Puzzle 265. Networks 266. Puzzle on open and closed paths 267. Relation to the verti What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
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