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| Averbach B., Chein O. — Problem solving through recreational mathematics |
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| Ïðåäìåòíûé óêàçàòåëü |
Multigraph 176n.
Multiple 105
Multiplication principle 19—20 42 113 234 290—300 345 356
Necessary condition 45
Negation 41 42 48
Network 176 176n.
NIM 214—215 246—249 268
Nim, even and odd positions 248—249
Nim, Moore’s 255
Nim, Northcott’s 258
Nim, Wythoff’s 255
Node 17 176
Northcott’s Nim 258
Noughts and Crosses see Tic Tac Toe
Odd vertex see Vertex odd
Odds 341 338 361 362 372—373
Outcomes 338
Oware 312
Pacioli 337
Pairing 404
Pairing strategy 250—251 370
Pairwise disjoint 344
Parity 248 287
Parity, in Fifteen Puzzle 293—294 295—296 298
Parity, in Peg Solitaire 287
Parity, of a permutation 292
Pascal 337
Paterson, M. S. 265
Path 17 178
Path, dipath 191
Path, edge-disjoint 187—189
Path, Eulerian 178 179 181—182 185 186 187 190 191—192 202—205
Path, Hamiltonian 193 195 196
Pawn move 264
Peg Solitaire 274 285—288 308—310
Peg Solitaire, French version 309
Peg Solitaire, Hi Q 274 286—288 308—309
Pentominoes 281 308 415
Perfect information 216 218
Perfect numbers 100
permutations 290—296 298—299 346 345-348
Permutations, even 291 293
Permutations, odd 291 293
Phillips, H. 38
Pigeolet, M. 147
Place value 147
Planar graph 177
Planar map 198
Point of view 4
Poker 370
Polycube 308
Polyominoes 281—282 284 308 415
Position (of a game) 225 224—227 228 404
Position (of a game), drawing 225—227
Position (of a game), equivalence of 235 238
Position (of a game), equivalence of, examples of 236 237 238—240 413
Position (of a game), even and odd see Nim
Position (of a game), initial 225 226—227
Position (of a game), losing 225—227 228
Position (of a game), penultimate 233
Position (of a game), starting see Position initial
Position (of a game), terminal 225 226
Position (of a game), winning 225—227 228
Position (of a game), winning, examples of 229 230—232 241—245 246-249
positional notation 147—148 154 156—157
Potential payoff 361
Premise 55—56
Presenting a solution 11
Prime factorization 109—110 111
Prime number 100 106—111 137 332—333
Prime number, infinitude of 106—107
Prime number, relatively 116
probability 338 337—365
Probability, of an event 339
Problems, age 72 74—75 77—78 87-88
Problems, ancient 72 95—96
Problems, counting 366—370 373—375
Problems, crossing 175 196—197 208—209
Problems, cryptarithmetic 147 157—162 169—172
Problems, decanting 101 117—118
Problems, decimation 313—315
Problems, dissection 279—282 306—307
Problems, inference 2—3 26—35 38—39 61-69
Problems, logic see Problems inference
Problems, matching 2—3 26—28 30 32—35 66-67
Problems, odds 341 372
Problems, shunting 3 22—25 35—36 316—317
Problems, tracing 174 202—205
Problems, truthful-liar 38—39 61—66
Problems, uniform motion 72 78—79 88—92
Problems, weighing 94—95 146 151—153 168 315-316
Problems, well-posed 12
Problems, work 72 81—84 92—93
Proof (nature of) 137 202
Proposition see Statement
Propositional variable 41
Pythagoras 100
Pythagorean Theorem 279 280 306—307 414
Quadratic equations 324—325 329—330
Quadratic formula 83 324—325
Queen’s move 211 258
Quotient 120 160
Reentrant knight’s tour 194 312
Relatively prime numbers 116
Remainder 120 123—124 125 127 351—352
| Remainder class 120—122
Repeated experiments 356—361
Repeated trials 356 371—372
retracing 189 204—205
Rook’s move 207 257
Roulette 340 360 362 363
Ruma 312
Shader, L. 373
Sheep and Wolves see Fox and Hounds
Shunting Problems see Problems shunting
Sieve of Eratosthenes 107—108
Silverman, D. L. 262
SIM 266 403 413
Simmons, G. J. 266
simplification 22 232—233
Simplification, examples of 22—25 241 246 289—291
Simultaneous equations 325—330
Sliding block puzzles see Fifteen Puzzle
Slither 262—263 269
Solving problems, point of view 4
Solving problems, presenting solutions 11
Solving problems, simplification 22—25
Solving problems, techniques 11—12
Solving problems, visual aids 10
Soma 284—285
Sprague — Grundy method 229
Sprouts 265 413
State diagram 228—229 230
State of a game 224—225
Statement 39—40 49
Statement, compound 49
Strategy 21—22 215 221 225 228
Strategy, drawing 215 218 221 227
Strategy, drawing, examples of 407—408 408—409
Strategy, pairing 250—251 410
Strategy, winning 215 218 221 222 224 226—227 409
Strategy, winning, examples of 227—228 230—232 245 250—251 366 368—369 406 408—409 410 412
Strategy, winning, how to find 218—221 228—229 230 232-234
Subscripts, use of 80
Substitution, method of 77—78 325—326
Sufficient condition 45
Summation 350
Summers, G. 38
Syllogism 38 317—318 417 18
Symmetry 237—238 234—240 252
Symmetry, as a game strategy 250—251 406 408
Symmetry, as a limiting factor 234—236 238—240 243 246 406 408 411 417
Symmetry, central 235 408
Symmetry, diagonal 236
Symmetry, horizontal 235
Symmetry, vertical 235
Tac Tix 260 268
Tangrams 280—281 307—308
Tetrominoes 281 282 308
Theorem 137 202
Tic Tac Toe 224
Tic Tac Toe, symmetries of 234—236
Tic Tac Toe, three-dimensional 260—261 270—271
Tic Tac Toe, variations 214 238 258—261 270—271
Tower of Brahma 274 276—279 305
Tower of Hanoi see Tower of Brahma
Traceable graph 178 (see also Path Eulerian)
Tree diagram 16—18 19—20 230
Tree diagram, examples of 17—18 20—22 42 112 218—222 355 357-359
Tricks 71 74 96—99 141—143 164—165 165—168 205 314
Tricks, card 96—99 141—142 314
Tricks, domino 205
Tricks, number guessing 71 74 96 142—143 164—165 165-168
Tricube 285 308
Trominoes 274 281 283—284
True odds 340
Truth table 42 43 44 45 54
Truth value 39—40
Truthful-liar problems see Problems truthful-liar
Unfavorable game 363
Unfavorable outcomes 338
Uniform motion problems see Problems uniform
Unique factorization theorem 109—110
Validity 56 55—57 59—60 418
Variables 72—73 80
Variables, propositional 41
Variations of a game 251—252
Vertex 176
Vertex, even 180 182 186 190
Vertex, odd 180 181 182 185 186 187
Vertex, of degree one 193
Vertex, of degree two 188 193 195
Vertices, set of, dominating 211 404
Vertices, set of, independent 212 404
visual aids 10
Weighing problems see Problems weighing
Weight 339
Well-posed problem 12
Winning strategy see Strategy winning
Work problems see Problems work
Wylie, C. R. 38
Wythoff’s nim 255
“And” see Conjunction
“Cubby Hole” Principle 402—403
“If and only if” see Biconditional statement
“If, then” see Conditional statement
“not” see Negation
“Or” see Disjunction
“Or”, exclusive sense 43
“Or”, inclusive sense 43
“Pigeon Hole” Principle 402—403
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