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ix | |
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xiii | |
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1 What is Recreational Mathematics? |
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1 | (8) |
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7 | (2) |
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9 | (149) |
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2 Puzzles from The Greek Anthology |
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11 | (6) |
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12 | (3) |
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2.2 Solutions and Comments |
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15 | (1) |
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16 | (1) |
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3 Aryabhata and Other Early Indian Mathematicians |
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17 | (20) |
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3.1 Pythagorean Recreations |
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18 | (10) |
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3.2 Knowing What Each Pair Has |
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28 | (3) |
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3.3 The Snail in the Well |
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31 | (3) |
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34 | (3) |
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4 Alcuin and his Propositiones |
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37 | (48) |
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38 | (3) |
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41 | (2) |
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4.3 Managing the Text of Propositiones |
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43 | (2) |
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4.4 An Annotated Translation of Propositiones |
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45 | (30) |
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4.5 Summary and Discussions |
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75 | (7) |
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82 | (3) |
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5 The Problems of Abbot Albert |
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85 | (16) |
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100 | (1) |
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100 | (1) |
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6 Pacioli: The First Book of Mathematical Puzzles |
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101 | (30) |
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6.1 De Viribus Quantitatis |
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106 | (3) |
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6.2 Recreational Material in De Viribus Quantitatis |
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109 | (20) |
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129 | (2) |
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7 Pacioli's Magic and Card Tricks |
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131 | (8) |
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137 | (2) |
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8 Some Early Topological Puzzles |
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139 | (24) |
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8.1 The Chinese Wallet or Flick-Flack or Jacob's Ladder |
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140 | (3) |
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8.2 The Alliance and Victoria Puzzle |
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143 | (1) |
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8.3 Solomon's Seal or African Beads Puzzle |
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144 | (2) |
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146 | (3) |
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149 | (2) |
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151 | (2) |
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153 | (1) |
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154 | (2) |
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156 | (1) |
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156 | (2) |
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Interlude: Finding a Sardinian Maze |
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158 | (5) |
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Part II. New Ideas about Old Puzzles |
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163 | (118) |
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165 | (18) |
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166 | (4) |
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9.2 Analysis of the 17 Camels Problem |
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170 | (4) |
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9.3 Analysis of the 13 Camels Problem |
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174 | (5) |
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179 | (4) |
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183 | (6) |
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10.1 Determination of Pythagorean triples |
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184 | (1) |
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10.2 Determination of Heronian triples |
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185 | (2) |
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187 | (2) |
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11 The Ass and Mule Problem |
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189 | (8) |
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11.1 Analysis of the Original Problem |
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190 | (1) |
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191 | (2) |
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11.3 Another Simpler Variation |
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193 | (2) |
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195 | (2) |
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12 How to Count Your Chickens |
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197 | (14) |
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209 | (1) |
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210 | (1) |
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13 The Monkey and the Coconuts |
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211 | (24) |
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13.1 Determinate Versions |
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212 | (6) |
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13.2 Indeterminate Versions |
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218 | (6) |
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224 | (6) |
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230 | (2) |
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13.5 Solutions and Some Comments |
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232 | (1) |
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233 | (2) |
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14 Two River Crossing Problems |
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235 | (20) |
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14.1 De Fontenay's Generalization |
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237 | (3) |
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240 | (1) |
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241 | (3) |
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244 | (5) |
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14.5 Missionaries and Cannibals |
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249 | (2) |
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251 | (1) |
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252 | (3) |
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255 | (14) |
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256 | (1) |
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256 | (1) |
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15.3 Triangular Coordinates |
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257 | (1) |
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15.4 The Number of Integral Triangles |
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258 | (1) |
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15.5 The Number of Incongruent Integral Triangles |
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259 | (1) |
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15.6 Relation to Partitions |
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260 | (2) |
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262 | (3) |
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15.8 Fair Division of the First kn Integers into k Parts |
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265 | (2) |
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267 | (2) |
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16 Vanishing Area Paradoxes |
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269 | (12) |
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274 | (4) |
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278 | (3) |
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Appendix A: Ancient and Important Sources |
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281 | |
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A.1 Bibliography of Early Work |
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281 | (14) |
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295 | (2) |
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297 | |
| Volume 2 |
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xi | |
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xiii | |
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1 Why Recreational Mathematics? |
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1 | (28) |
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1.1 The Nature of Recreational Mathematics |
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1 | (2) |
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1.2 The Utility of Recreational Mathematics |
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3 | (1) |
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1.3 Some Examples of Useful Recreational Mathematics |
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4 | (8) |
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1.4 Recreational Mathematics with Objects |
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12 | (2) |
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1.5 Examples of Medieval Problems |
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14 | (3) |
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1.6 Examples of Modern Recreational Problems |
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17 | (3) |
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1.7 The Educational Value of Recreations |
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20 | (4) |
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1.8 Why Is Recreational Mathematics So Useful? |
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24 | (1) |
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25 | (4) |
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2 On Round Pegs in Square Holes and Vice Versa |
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29 | (12) |
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32 | (1) |
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33 | (3) |
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36 | (3) |
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39 | (1) |
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40 | (1) |
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41 | (6) |
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3.1 The Square Path Version |
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42 | (3) |
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45 | (2) |
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4 Sum = Product Sequences |
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47 | (4) |
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50 | (1) |
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51 | (8) |
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51 | (4) |
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55 | (2) |
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57 | (2) |
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6 Recurring Binomial Coefficients |
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59 | (10) |
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6.1 Recurring Binomial Coefficients and Fibonacci Numbers |
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60 | (5) |
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65 | (2) |
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67 | (2) |
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7 Sums of Squares and Pyramidal Numbers |
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69 | (6) |
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73 | (2) |
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8 The Bridges of Konigsberg |
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75 | (14) |
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80 | (2) |
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82 | (4) |
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86 | (1) |
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87 | (2) |
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9 Triangles with Doubled Angles |
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89 | (18) |
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89 | (6) |
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95 | (10) |
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105 | (2) |
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10 Quasicrystals and the University |
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107 | (6) |
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110 | (3) |
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113 | (12) |
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11.1 The Height of the Center of Gravity |
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113 | (4) |
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11.2 The Distance Between Contacts |
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117 | (1) |
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117 | (2) |
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119 | (2) |
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121 | (2) |
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123 | (2) |
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125 | (28) |
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12.1 The Chessboard Reward |
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125 | (4) |
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12.2 The Landowner's Earth and Air |
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129 | (3) |
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132 | (6) |
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12.4 "It's a Hard Rain a Gonna Fall!" |
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138 | (1) |
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12.5 Permutations and the Number of Crosswords |
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139 | (3) |
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12.6 Grains of Sand versus Stars in the Sky |
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142 | (1) |
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12.7 "A Lottery is a Tax on the Innumerate." |
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143 | (1) |
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12.8 Storing a Million Pounds |
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144 | (1) |
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144 | (3) |
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147 | (3) |
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150 | (3) |
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13 Three Rabbits or Twelve Horses |
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13.1 The Three Rabbits Puzzle |
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153 | (4) |
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13.2 Four Horses, Twelve Horses and Other Puzzles |
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157 | (7) |
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164 | |
