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Berlekamp E.R., Conway J.H., Guy R.K. — Winning Ways for Your Mathematical Plays, Vol. 1
Berlekamp E.R., Conway J.H., Guy R.K. — Winning Ways for Your Mathematical Plays, Vol. 1



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Название: Winning Ways for Your Mathematical Plays, Vol. 1

Авторы: Berlekamp E.R., Conway J.H., Guy R.K.

Аннотация:

The second edition of this recreational mathematics text, which was originally published in 1982, has been corrected and split into four volumes. This second volume explores strategies for playing combinatorial theory- based games that may continue indefinitely due to infinitely many positions or several consecutive moves, and games in which the last player is declared the loser


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2nd edition

Год издания: 2001

Количество страниц: 296

Добавлена в каталог: 11.06.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Moves, good      16
Moves, half      4 19 20
Moves, hotter      173
Moves, quarter      6 20
Moves, reversible      55 56 60 62—64 66 70 71 75 77 126 212 213
Moves, temperature-selected      132
Moves, three-quarters      17
Moves, worthwhile      213 216
Mueller, Martin      18 188
Multiples of positive games      256
Multiples of up      71 242 247 256 258
Multiples, fractional & non-integer      236
Multiples, fractional and non-integer      256
Munro, Ian      226
Musical series      96 117
Negative      28
Negative charge      254
negative numbers      19 147 148
Negative of a game      33 35
Negative position      28
Negative positions      29
Neyman, A.      117
NIM      15 40 42 53 55 56 114 173 191 240
Nim in hot games      173
Nim, Double Duplicate      111
Nim, Duplicate      114 116
Nim, Lasker's      99 113 114
Nim, Poker      55
Nim, Poker-      53
Nim, Triplicate      114 116
Nim-addition      58 59 73 74 90 109 110 116 191 199 246
Nim-Addition Ride      60
Nim-Addtion Ride      59
Nim-heaps      41 42 56
Nim-heaps, bogus      56
Nim-position      41
Nim-sequence      82 84 86 87 94 98 99 101 103—105 107—109 113 114 116
Nim-sum      59 73 74 82 90 91 109—112
Nim-values      82 84 86 87 90—96 98 99 110—117 191—196
Nim-values, duplication      94 98 99 114 116
Nim-values, periodic      84 86 91 92 94 98 99 101 107—110 112—117
Nim-values, reflected      109
Nim-values, replication      98
Nim-values. doubling      91
Nim-values. halving      195
Nimber      231 258
Nimber arithmetic      42
Nimbers      40—42 56 57 65 74 84 110 119 199 200 262
Nimbers, adding      42 58
Node, tinted      48
Nodes, Col      47—51
Nodes, explosive      49 50
Nodes, game positions      40
Nodes, Hackenbush      191—194 201 202 204 222
Nodes, Snort      147 180
Nodes, tinted      204 206 208 222
Nodes, untinted      204
Non-number      147 148 159 160
Normal play      12 14
Northcott's Game      55
Norton's Lemma      220 243 244
Norton's product      247 256
Norton, Simon      145 168 188 247 256
Norton, Simon P.      220 243 244
Noughts-and-Crosses = Tic-Tac-Toe      14
Nowakowski, Richard Joseph      18 117 118 144 188 225 226
NP-complete      217 224 226
NP-hard      224 225
Number Avoidance Theorem      147—149 183
Number system, Hackenbush      78
Number tree and line      24
Numbers      22 119
Numbers, canonical form      22
Numbers, evil      110
numbers, negative      19
Numbers, odious      1 10
Numbers, overheated      176
Numbers, simplest      19 21 22
Numbers, Surreal      18
Numbers, thermographic thicket of      176
Numbers, triangular      254
Numbers, whole      19
O'Beirne, Thomas H.      79 118
Obtuse triangles      254
Octal games      101 103—105 107—116 262
Odious numbers      110
Officers = -6      95
Omar      42 72 109 138 188 262
ONAG = On Numbers and Games      18 22 48 52 117 139 144 188 193 225 234 236 262
One-upmanship Rule      242
Opposite sex      179
Option      11 154
Option, dominated      62 63 75 77 149
Option, Left      31 32
Option, reversible      60 62—64 70 71 75 77
Option, Right      31 32
Optional extras      84
Options, worthwhile      213—215
Ordinal addition      220
Ordinal sum      220
Ordinary sum      220 221
Outcome      28 35
Outcome classes      28 84
Outcome of sum      31 32
Overheating      174 176 187
Overheating operator      188
Ozery, M.      79
Pairing Property, Ferguson's      86
Parcels      187
Paricles      167
Parity      73 234
Parity Principle      191 194
Parted jungle      201 202
Particle      168—170
Partizan      15 65 187
Paths = tracks      193 202 204 222
Patience = Solitaire      15
Paul, Wolfgang J.      226
Pawns      89
Peek      224
Peg Solitaire      15
Pencil-and-paper game      1
periodicity      90—94 99 101 109 113—115 117 236
Periodicity, arithmetic      99 113—117 144 187
Periodicity, Blockbusting      187
Periodicity, Dawson's Chess      90 91
Periodicity, Domineering      144 187
Periodicity, Guiles      94
Periodicity, Kayles      91 92
Periodicity, non-arithmetic      115
Periodicity, octal games      101 103—105 107- 113—115
Periodicity, subtraction games      84 86
Periodicity, ultimate      99 101 112
Perpetual check = draw      14
Petal      33 47 66 67 199 201 240 245
Petals      29 30
Phase change      167 168
Phase change, latent      168
Picture      1 2 192
Picture of farm life      145 146
Picture, childish      43
Picture, grown-up      43
Piebald node      47 48
Piebald spot      145—147
Pink, Norbert      117
Plambeck, Thane      109 112 117
Play, infinite      14
Play, misere      15
Play, normal      12 14
Player, first      28—30
Player, second      28—30
Playing the averages      167 173
Ploy, Blue Flower      199 201 240 242
Ploy, Blue Jungle      201 210
Ploy, Red Jungle      210
Poker      15
Poker-Nim      53
Policy, Temperature      124 125 131 132
Polyominoes      139 142
Poroof      213
POSITION      14
Position, $\mathcal{N}-$      84
Position, $\mathcal{P}-$      84
Position, active      149 150
Position, Domineering      120 121 139 142 144 153 177
Position, fuzzy      28 32 33
Position, hot      149
Position, loopy      16 188
Position, negative      28—30 68
Position, positive      28 68
Position, starting      14
Position, terminal      2 7 28 41
Position, zero      3
Positive      28
Positive charge      254
Positive house      38
Positive house and garden      33
Positive position      28
Positive positions      68
Positive posy      29 30 33
Prim      98
Prince of Mathematicians      254
Principle, Bogus Nim-heap      56
Principle, Colon      191 193 194 220
Principle, Death Leap      127—130 135
Principle, Enough Rope      16
Principle, Exchange      246
Principle, Fusion      192—195
Principle, Gift Horse      72 77
Principle, Parity      191 194
Principle, Star Shifting      250 258
Principle, Translation      149 153 158
Principle, Uppitiness Exchange      246
Problems, hard      223 224
Profit      161
Profit-consciousness      171
proof      115 147 148 165 166 183 188 201 212 214 216 217 220 221 224 236 240 248—250 256—259
Propp, James      118
PSPACE-complete      224 226
PSPACE-hard      224
Purchasing contract      127
Purple mountain      198 199
Pursuit      15
Quadruple Kayles      99
Quantity beats quality      201
Quarter-move      6 19 20
Quotation marks = eccentric cases      231 232
Rare values      110—112
Reader, assiduous      42
Reader, persevering      90
Reader, skeptical      130
Real number line      24
Rectangles      25—27 142 234 236
Red edges      2 198 230 237
Red Jungle Ploy      210
Red tinted nodes      48 204
Red twig      213
Redwood bed      211 213—217 222
Redwood furniture      211—217 222
Redwood tree      214—217
Redwood twig      213 216
references      18 52 78 117 144 188 225 262
Reflexion of nim-values      109
Reisch, Stefan      226
Remote star      230—232 236 237 239 240 243- 258 259
Remote Star Test      246 248 249
Remoteness      173
Replication of nim-values      98
Resetting the thermostat      185
Restricted Translation Rule      261
Reversible moves      55 56 60 62—64 66 70 71 75 77 126 212
Reversible option      75 77
Right      2
Right boundary      154—156 164 169 170
Right excitable      158 159
Right slant      158 159
Right stop      149 150 152 163
Right-excitable      169 170
Rip Van Winkle's Game = Kayles      82
Rita      25 51 234
Robertson, Edward      226
Robson, J.M.      226
Rule, Atomic Weight      242
Rule, Berlekamp's      77 78
Rule, Difference      74
Rule, Flow      201 202 204 210
Rule, Go "dialects"      16
Rule, Mex      56
Rule, Misere Play      15
Rule, Nim-Addition      59 60 73 74
Rule, Normal Play      12 14
Rule, One-upmanship      242
Rule, Restricted Translation      261
Rule, Simplicity      22 24 25 27 39 45 48
Rule, Two-Ahead      199 200 242 246 249
Rule, With      256 257
Rule, Without      256 257
Rule, Wythoff's Difference      74
Ruler function      98
Rules      14
Saltus      99 114 117 144 187
Sarsfield, Richard      79
Saskatchewan landscape      157
Scale, Grundy      87 90 91 94 96 101
Schaefer, Thomas J.      109 118 224 226 227
Schaeffer, Jonathan      18
Schaer, Jonathan      43
Schuh, Fred.      118
Scissors-Paper-Stone      15
Scorer, R.S.      117
Seasoned campaigner      164
Seating Boys and Girls      132 133 179 261
Seating Couples      44 45 95 132 133 261
Seating Families      95 261
Second cousin      101 103—105 107 109 114 116
Second player wins      28—30
Sente      161 188
Sentestrat      188
Set, empty      82
Set, subtraction      84 86
Set, variation      220 221
Seven-up      218 225
Severed head      205 220 221
Sex, opposite      132 261
Shakespeare. William      145
She-Loves-Me, She-Loves-Me-Not      67 262
She-Loves-Me-Constantly, e.g. -.51      101 103
She-Loves-Me; She-Loves-Me-Not, e.g. -05      109 114 116
Shifting by stars      250 258
Shifting infinitesimally      177 198
Short hot games      225
Short-sighted view      159 160
Silber, Robert      79
Simplest form      19 22 71
Simplest number      19 21 22
simplicity      19 21 22
Simplicity Rule      22 24 25 27 39 45 48
Simplifying games      60 62 63 75 77
Singapore      16
Sipser, Michael      224 226
1 2 3 4
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