Winning ways for your mathematical plays: 2
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London [u.a.]
CRC Press
2018
|
| Edition: | Second edition, first issued in hardback |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xvii, S. 277 - 473 Illustrationen, Diagramme |
| ISBN: | 9781138427570 |
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MARC
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| 245 | 1 | 0 | |a Winning ways for your mathematical plays |n 2 |c Elwyn R. Berlekamp ; John H. Conway ; Richard K. Guy |
| 250 | |a Second edition, first issued in hardback | ||
| 264 | 1 | |a London [u.a.] |b CRC Press |c 2018 | |
| 300 | |a xvii, S. 277 - 473 |b Illustrationen, Diagramme | ||
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Record in the Search Index
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| adam_text | Contents 9 Preface to Second Edition xiii Preface xiv Change of Heart xvii If You Can’t Beat ’Em, Join ’Em! 277 All the King’s Horses................................................................................................................. 277 We Can Join Any Games........................................................................................................ 278 How Remote Is a Horse?........................................................................................................... 278 What If the First Horse to Get Stuck Wins?......................................................................... 281 A Slightly Slower Join.............................................................................................................. 283 Moving Horses Impartially........................................................................................................ 283 Cutting Every Cake ................................................................................................................. 284 Eatcakes...................................................................................................................................... 286 When to Put Your Money on the Last Horse ...................................................................... 286 Slow Horses Join the Also-Rans...............................................................................................286 Let Them Eat Cake ................................................................................................................. 289 All the King’s Horses on a
Quarter-Infinite Board................................................................ 292 Cutting Yom Cakes and Eating Them.................................................................................. 292 References and Further Reading.............................................................................................. 298 10 Hot Battles Followed by Cold Wars 299 Cold Games - Numbers Are Still Numbers............................................................................ 300 Hot Games - The Battle Is Joined !........................................................................................ 300 Tolls, Timers and Tallies........................................................................................................... 301 Which Is the Best Option? .....................................................................................................303 Hot Positions............................................................................................................................. 304 Cold Positions .......................................................................................................................... 304 Tepid Positions.......................................................................................................................... 306 A Tepid Game .......................................................................................................................... 308 Select Boys and Girls................................................................................................................. 310
Mrs. Grundy............................................................................................................................. 310 How to Play Misère Unions of Partizan Games................................................................... 312 Urgent Unions (Shotgun Weddings?)......................................................................................312 Predeciders - Overriders and Suiciders.................................................................................. 312 ix
x Contents Հ2 Falada............................................................................................................................................... 312 Two More Falada Games ............................................................................................................. 320 Baked Alaska................................................................................................................................... 321 A Felicitous Falada Field .............................................................................................................324 The Rules for Tallies on Infinite Tolls ...................................................................................... 325 Time May Be Shorther than You Think!................................................................................... 326 11 Games Infinite and Indefinite 327 Infinite Enders................................................................................................................................329 The Infinite Ordinal Numbers...................................................................................................... 329 Other Numbers................................................................................................................................330 Infinite Nim...................................................................................................................................... 330 The Infinite Sprague-Grundy and Smith Theories................................................................ 333 Some Superheavy
Atoms............................................................................................................ 334 Fixed, Mixed and Free................................................................................................................... 335 Onsides and Offsides, Upsums and Downsums.......................................................................... 336 Stoppers............................................................................................................................................ 337 on, off and dud................................................................................................................................. 337 How Big Is on?......................................................................................................................................... 338 It’s Bigger than All of Them!...................................................................................................... 338 Sidling Towards a Game................................................................................................................ 338 Sidling Picks Sides......................................................................................................................... 340 Stoppers Have Only One Side...................................................................................................... 340 ’Tis!-’Tis n!-’Tis!-’Tis n!-............................................................................................................. 342 Loopy
Hackenbush......................................................................................................................... 343 Disentangling Loopy Hackenbush................................................................................................ 343 Loopily Infinite Hackenbush......................................................................................................... 344 Sisyphus............................................................................................................................................ 346 Living with Loops ......................................................................................................................... 348 Comparing Loopy Games............................................................................................................. 348 The Swivel Chair Strategy............................................................................................................. 349 Stoppers Are Nice ......................................................................................................................... 350 Plumtrees Are Nicer!...................................................................................................................... 353 Taking Care of Plumtrees............................................................................................................. 354 Working With Upsums and Downsums.......................................................................................355 on, off and
hot......................................................................................................................................... 356 A Summary of Some Sum Properties.......................................................................................... 357 The House of Cards ...................................................................................................................... 357 The Degree of Loopiness................................................................................................................ 361 Classes and Varieties...................................................................................................................... 362 No Highway...................................................................................................................................... 364 Backsliding Toads-and-Frogs ...................................................................................................... 367 Bach’s Carousel............................................................................................................................... 369 Getting on in Checkers ................................................................................................................ 370 Proof of the Sidling Theorem...................................................................................................... 371 Answer to Exercise One............................................................................................................ 374 tis and
tisn................................................................................................................................................374 upon ..........................................................................................................................................................375
V Content։ xi Backsliding Toads-and-Frogs .................................................................................................. 375 KOsin Go................................................................................................................................... 377 References and Further Reading...............................................................................................377 12 Games Eternal - Games Entailed 379 Fair Shares and Varied Pairs .................................................................................................. 379 How Soon Can You Win?........................................................................................................381 There May Be Open Positions (O-Positions)......................................................................... 382 Adders-and-Ladders................................................................................................................. 386 Just How Loopy Can You Get?.............................................................................................. 391 Corrali Automotive Betterment Scheme............................................................................... 391 Sharing Out Other Kinds of Nut........................................................................................... 393 Fair Shares and Unequal Partners............................................................................................394 Sweets and Nuts, and Maybe a Date? .................................................................................. 395 The
Additional Subtraction Games........................................................................................ 395 Horsefly...................................................................................................................................... 395 Selective and Subselective Compounds of Impartial Games ..................................................396 Entailing Moves.......................................................................................................................... 396 Sunny and Loony Positions.....................................................................................................397 Calculating with Entailed Values............................................................................................398 Nim with Entailing Moves....................................................................................................... 400 Goldbach’s Nim.......................................................................................................................... 401 Wyt Queens with Trains...........................................................................................................402 Adding Tails to Prim and Dim.............................................................................................. 404 Complimenting Moves.............................................................................................................. 405 On-the-Rails ............................................................................................................................. 407 De Bono’s
L-G ames ................................................................................................................. 408 Proving the Outcome Rules for Loopy Positions................................................................... 408 Fair Shares and Unequal Partners........................................................................................... 410 Were Your Ways Winning Enough?........................................................................................ 410 Did You Move First in Horsefly?........................................................................................... 411 References and Further Reading.............................................................................................. 412 13 Survival in the Lost World 413 Misere Nim................................................................................................................................ 413 Reversible Moves....................................................................................................................... 415 The Endgame Proviso..............................................................................................................416 The Awful Truth....................................................................................................................... 416 What’s Left of the Old Rules?..................................................................................................417 As Easy as Two and
Two?........................................................................................................418 The Misère Form of Grundy’s Game..................................................................................... 419 Animals and Their Genus........................................................................................................421 What Can We With the Genus? ........................................................................................... 423 Firm, Fickle and Tame..............................................................................................................423 Which Animals are Tame........................................................................................................... 424 ... and Which are Restive?........................................................................................................425 Some Tame Animals in the Good Child’s Zoo...................................................................... 426 Misère Wyt Queens ................................................................................................................. 426
xii Contents Փ Jelly Beans and Lemon Drops.................................................................................................. 427 Stalking Adders and Taking Squares......................................................................................429 “But What if They’re Wild?” Asks the Bad Child............................................................. 430 Misère Kayles............................................................................................................................. 431 The Noah’s Ark Theorem........................................................................................................ 432 The Half-Tame Theorem........................................................................................................... 435 Guiles......................................................................................................................................... 435 Dividing Rulers.......................................................................................................................... 436 Dawson, Officers, Grundy........................................................................................................ 438 All Subtraction Games Reduce to Nim.................................................................................. 442 Prim and Dim .......................................................................................................................... 442 Proof of the Noah’s Ark Theorem............................................................................................443
Misère Octal Games............................................................................................................. 444 Notes ......................................................................................................................................... 444 Stop Press: Even More Games are Tameable!...................................................................... 446 Glossary 453 Index 455
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| adam_txt |
Contents 9 Preface to Second Edition xiii Preface xiv Change of Heart xvii If You Can’t Beat ’Em, Join ’Em! 277 All the King’s Horses. 277 We Can Join Any Games. 278 How Remote Is a Horse?. 278 What If the First Horse to Get Stuck Wins?. 281 A Slightly Slower Join. 283 Moving Horses Impartially. 283 Cutting Every Cake . 284 Eatcakes. 286 When to Put Your Money on the Last Horse . 286 Slow Horses Join the Also-Rans.286 Let Them Eat Cake . 289 All the King’s Horses on a
Quarter-Infinite Board. 292 Cutting Yom Cakes and Eating Them. 292 References and Further Reading. 298 10 Hot Battles Followed by Cold Wars 299 Cold Games - Numbers Are Still Numbers. 300 Hot Games - The Battle Is Joined !. 300 Tolls, Timers and Tallies. 301 Which Is the Best Option? .303 Hot Positions. 304 Cold Positions . 304 Tepid Positions. 306 A Tepid Game . 308 Select Boys and Girls. 310
Mrs. Grundy. 310 How to Play Misère Unions of Partizan Games. 312 Urgent Unions (Shotgun Weddings?).312 Predeciders - Overriders and Suiciders. 312 ix
x Contents Հ2 Falada. 312 Two More Falada Games . 320 Baked Alaska. 321 A Felicitous Falada Field .324 The Rules for Tallies on Infinite Tolls . 325 Time May Be Shorther than You Think!. 326 11 Games Infinite and Indefinite 327 Infinite Enders.329 The Infinite Ordinal Numbers. 329 Other Numbers.330 Infinite Nim. 330 The Infinite Sprague-Grundy and Smith Theories. 333 Some Superheavy
Atoms. 334 Fixed, Mixed and Free. 335 Onsides and Offsides, Upsums and Downsums. 336 Stoppers. 337 on, off and dud. 337 How Big Is on?. 338 It’s Bigger than All of Them!. 338 Sidling Towards a Game. 338 Sidling Picks Sides. 340 Stoppers Have Only One Side. 340 ’Tis!-’Tis n!-’Tis!-’Tis n!-. 342 Loopy
Hackenbush. 343 Disentangling Loopy Hackenbush. 343 Loopily Infinite Hackenbush. 344 Sisyphus. 346 Living with Loops . 348 Comparing Loopy Games. 348 The Swivel Chair Strategy. 349 Stoppers Are Nice . 350 Plumtrees Are Nicer!. 353 Taking Care of Plumtrees. 354 Working With Upsums and Downsums.355 on, off and
hot. 356 A Summary of Some Sum Properties. 357 The House of Cards . 357 The Degree of Loopiness. 361 Classes and Varieties. 362 No Highway. 364 Backsliding Toads-and-Frogs . 367 Bach’s Carousel. 369 Getting on in Checkers . 370 Proof of the Sidling Theorem. 371 Answer to Exercise One. 374 tis and
tisn.374 upon .375
V Content։ xi Backsliding Toads-and-Frogs . 375 KOsin Go. 377 References and Further Reading.377 12 Games Eternal - Games Entailed 379 Fair Shares and Varied Pairs . 379 How Soon Can You Win?.381 There May Be Open Positions (O-Positions). 382 Adders-and-Ladders. 386 Just How Loopy Can You Get?. 391 Corrali Automotive Betterment Scheme. 391 Sharing Out Other Kinds of Nut. 393 Fair Shares and Unequal Partners.394 Sweets and Nuts, and Maybe a Date? . 395 The
Additional Subtraction Games. 395 Horsefly. 395 Selective and Subselective Compounds of Impartial Games .396 Entailing Moves. 396 Sunny and Loony Positions.397 Calculating with Entailed Values.398 Nim with Entailing Moves. 400 Goldbach’s Nim. 401 Wyt Queens with Trains.402 Adding Tails to Prim and Dim. 404 Complimenting Moves. 405 On-the-Rails . 407 De Bono’s
L-G ames . 408 Proving the Outcome Rules for Loopy Positions. 408 Fair Shares and Unequal Partners. 410 Were Your Ways Winning Enough?. 410 Did You Move First in Horsefly?. 411 References and Further Reading. 412 13 Survival in the Lost World 413 Misere Nim. 413 Reversible Moves. 415 The Endgame Proviso.416 The Awful Truth. 416 What’s Left of the Old Rules?.417 As Easy as Two and
Two?.418 The Misère Form of Grundy’s Game. 419 Animals and Their Genus.421 What Can We With the Genus? . 423 Firm, Fickle and Tame.423 Which Animals are Tame. 424 . and Which are Restive?.425 Some Tame Animals in the Good Child’s Zoo. 426 Misère Wyt Queens . 426
xii Contents Փ Jelly Beans and Lemon Drops. 427 Stalking Adders and Taking Squares.429 “But What if They’re Wild?” Asks the Bad Child. 430 Misère Kayles. 431 The Noah’s Ark Theorem. 432 The Half-Tame Theorem. 435 Guiles. 435 Dividing Rulers. 436 Dawson, Officers, Grundy. 438 All Subtraction Games Reduce to Nim. 442 Prim and Dim . 442 Proof of the Noah’s Ark Theorem.443
Misère Octal Games. 444 Notes . 444 Stop Press: Even More Games are Tameable!. 446 Glossary 453 Index 455 |
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| author | Berlekamp, Elwyn R. 1940-2019 Conway, John Horton 1937-2020 Guy, Richard K. 1916-2020 |
| author_GND | (DE-588)123359732 (DE-588)119529289 (DE-588)124655254 |
| author_facet | Berlekamp, Elwyn R. 1940-2019 Conway, John Horton 1937-2020 Guy, Richard K. 1916-2020 |
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| author_sort | Berlekamp, Elwyn R. 1940-2019 |
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| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | Second edition, first issued in hardback |
| format | Book |
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| index_date | 2024-07-03T21:18:02Z |
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| isbn | 9781138427570 |
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| spelling | Berlekamp, Elwyn R. 1940-2019 Verfasser (DE-588)123359732 aut Winning ways for your mathematical plays 2 Elwyn R. Berlekamp ; John H. Conway ; Richard K. Guy Second edition, first issued in hardback London [u.a.] CRC Press 2018 xvii, S. 277 - 473 Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Conway, John Horton 1937-2020 Verfasser (DE-588)119529289 aut Guy, Richard K. 1916-2020 Verfasser (DE-588)124655254 aut (DE-604)BV048642414 2 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034017345&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Berlekamp, Elwyn R. 1940-2019 Conway, John Horton 1937-2020 Guy, Richard K. 1916-2020 Winning ways for your mathematical plays |
| title | Winning ways for your mathematical plays |
| title_auth | Winning ways for your mathematical plays |
| title_exact_search | Winning ways for your mathematical plays |
| title_exact_search_txtP | Winning ways for your mathematical plays |
| title_full | Winning ways for your mathematical plays 2 Elwyn R. Berlekamp ; John H. Conway ; Richard K. Guy |
| title_fullStr | Winning ways for your mathematical plays 2 Elwyn R. Berlekamp ; John H. Conway ; Richard K. Guy |
| title_full_unstemmed | Winning ways for your mathematical plays 2 Elwyn R. Berlekamp ; John H. Conway ; Richard K. Guy |
| title_short | Winning ways for your mathematical plays |
| title_sort | winning ways for your mathematical plays |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034017345&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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