# The Master Book of Mathematical Recreations.pdf

*类 别*进口原版*关键字*masterbookmathematicalrecreations*发 布**2015-12-28 07:18:00**试 读*在线试读

*书籍描述*

**内容简介**

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 puzzle-solving strategies and mathematical skills.

**作者简介**

Dutch mathematician Frederik Schuh (1875–1966) received his PhD in algebraic geometry from Amsterdam University and taught at the Delft University of Technology.

**目录**

[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 7-digit 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 re-entrant 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. Semi-row 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 A-H

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: Sliding-Movement 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 three-jug 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. Even-subtraction game

219. Odd-subtraction game

III. "3-,5-,7- and 9-Subtraction Games"

220. 3-subtraction game

221. The other 3-subtraction games

222. 5-subtraction game

223. 7-subtraction game

224. 9-subtraction game

IV. Subtraction Game where the Opener Loses

225. Modified subtraction game

226. "Modified 2-,3-, 4-, and 5-subtraction games"

227. "Modified 6-, 7-, 9-, and 9-subtraction 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 3-digit squares

231. Puzzle of §230 with initial zeros

II. Puzzle with 4-Digit Squares

232. 4-digit squares

233. Puzzle of the four-4digit 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