Winning ways for your mathematical plays: 3
Gespeichert in:
| Beteiligte Personen: | , , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
London [u.a.]
CRC Press
2019
|
| Ausgabe: | Second edition, first issued in hardback |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034017368&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | xxi, S. 461 -801 |
| ISBN: | 9781138427563 |
Internformat
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| 245 | 1 | 0 | |a Winning ways for your mathematical plays |n 3 |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 2019 | |
| 300 | |a xxi, S. 461 -801 | ||
| 336 | |b txt |2 rdacontent | ||
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| 700 | 1 | |a Conway, John Horton |d 1937-2020 |e Verfasser |0 (DE-588)119529289 |4 aut | |
| 700 | 1 | |a Guy, Richard K. |d 1916-2020 |e Verfasser |0 (DE-588)124655254 |4 aut | |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-034017368 | |
Datensatz im Suchindex
| _version_ | 1819310050283356160 |
|---|---|
| adam_text | Contents Preface to the Second Edition xvii Preface to the Original Edition xviii Games in Clubs! xxi 14 Turn and Turn About 461 Turning Turtles................................................................................................................ 461 Mock Turtles................................................................................................................... 463 Odious and Evil Numbers............................................................................................. 463 Moebius, Mogul and Gold Moidores.......................................................................... 464 The Mock Turtle Theorem............................................................................................. 464 Why Moebius?................................................................................................................ 466 Mogul............................................................................................................................... 467 Motley............................................................................................................................... 469 Twins, Triplets, Etc.......................................................................................................... 469 The Ruler Game............................................................................................................ 469 Circumscribed Games................................................................................................... 470 Turnips (or
Ternups)...................................................................................................... 470 Grunt............................................................................................................................... 472 Sym.................................................................................................................................. 473 Two-Dimensional Turning Games.................................................................................473 Acrostic Twins................................................................................................................ 473 Turning Corners ............................................................................................................ 473 Nim-Multiplication......................................................................................................... 475 Swirling Tartans............................................................................................................ 476 The Tartan Theorem...................................................................................................... 477 Rugs, Carpets, Windows and Doors .......................................................................... 478 ix
Contents x 4 Acrostic Games ............................................................................................................. 482 Stripping and Streaking................................................................................................ 483 Uglification and Derision................................................................................................ 483 Unlocking Doors............................................................................................................. 488 Sparring, Boxing and Fencing .................................................................................... 488 “Coins” (or Heaps) with Infinitely Many (or 22*) “Sides”..................................... 488 References and Further Reading.................................................................................... 489 Ī5 Chips and Strips 491 The Silver Dollar Game................................................................................................ 491 Profit from Gaming Tables .......................................................................................... 492 Antonim............................................................................................................................ 493 Synonim............................................................................................................................ 494 Šimonim............................................................................................................................ 496 Staircase
Fives................................................................................................................ 499 Twopins (pronounced “Tuppins”).................................................................................500 Cram ............................................................................................................................... 502 Welter’s Game................................................................................................................ 506 Four-Coin Welter is Just Nim....................................................................................... 507 And So’s Three-Coin Welter!....................................................................................... 507 The Congruence Modulo 16.......................................................................................... 507 Frieze Patterns................................................................................................................ 509 Inverting the Welter Function....................................................................................... 510 The Abacus Positions ................................................................................................... 512 The Abacus Strategy ....................................................................................................513 The Misère Form of Welter’s Game.............................................................................. 514 Kotzig’s
Nim................................................................................................................... 515 Fibonacci Nim................................................................................................................ 517 More Generally Bounded Nim....................................................................................... 517 Epstein’s Put-or-Take-a-Square Game........................................................................518 Tribulations and Fibulations ....................................................................................... 520 Third One Lucky............................................................................................................. 520 Hickory, Dickory, Dock................................................................................................... 521 D.U.D.E.N.E.Y ............................................................................................................. 521 Strings of Pearls ............................................................................................................. 522 Schuhstrings...................................................................................................................... 523 The Princess and the Roses.......................................................................................... 524 One-Step, Two-Step.......................................................................................................529 More on Subtraction
Games.......................................................................................... 529 Smallest Nim, Largest Nim.......................................................................................... 532 Moore’s Nim₺................................................................................................................... 533 The More the Merrier....................................................................................................533 Moore and More............................................................................................................. 534 Not with a Bang but a Whim....................................................................................... 534
Ą Contents xi Did You Win the Silver Dollar?.................................................................................... 535 How Was Your Arithmetic?.......................................................................................... 535 In Put-or-Take-a-Square , 92 Is an ^Position........................................................... 535 Tribulations and Fibulations ....................................................................................... 535 Our Code of Behavior for Princes................................................................................. 537 References and Further Reading.................................................................................... 538 16 Dots-and-Boxes 541 Double-Dealing Leads to Double-Crosses.................................................................... 543 How Long Is “Long”? ................................................................................................... 546 The 4-Box Game............................................................................................................. 547 The 9-Box Game............................................................................................................. 549 The 16-Box Game..........................................................................................................549 Other Shapes of Board................................................................................................... 550 Dots-and-Boxes and Strings-and-Coins........................................................................550
Nimstring......................................................................................................................... 552 Why Long Is Long..........................................................................................................554 To Take or Not to Take a Coin in Nimstring.............................................................. 555 Sprague-Grundy Theory for Nimstring Graphs........................................................ 556 All Long Chains Are the Same.................................................................................... 561 Which Mutations Are Harmless?................................................................................. 562 Chopping and Changing................................................................................................ 564 Vines ................................................................................................................................564 Dots + Doublecrosses = Turns.................................................................................... 571 How Dodie Can Win the 4-Box Game........................................................................572 When Is it Best to Lose Control?................................................................................. 574 Computing the Values of Vines.................................................................................... 575 Loony Endgames Are NP-Hard.................................................................................... 577 Solutions to Dots-and-Boxes
Problems....................................................................... 578 Some More Nimstring Values....................................................................................... 581 Nimbers for Nimstring Arrays....................................................................................... 581 References and Further Reading.................................................................................... 584 17 Spots and Sprouts 585 Rims.................................................................................................................................. 585 Rails ............................................................................................................................... 586 Loops-and-Branches .......................................................................................................586 Contours ......................................................................................................................... 587 Lucasta............................................................................................................................ 588 A Child’s Guide to Normed Lucasta ...........................................................................589 The Misère Form of Lucasta ....................................................................................... 590 The Positions (7, 3, 1) and (11, 1, 1)...........................................................................594 Cabbages; or Bugs, Caterpillars and Cocoons........................................................... 597
Jocasta ............................................................................................................................ 597
xii Contents Sprouts ............................................................................................................................ 598 Brussels Sprouts .............................................................................................................603 Stars-and-Stripes............................................................................................................. 603 Bushenhack...................................................................................................................... 604 Genetic Codes for Nim................................................................................................... 605 Bushenhack Positions Have Genetic Codes!.............................................................. 606 Von Neumann Hackenbush .......................................................................................... 606 The Joke in Jocasta...................................................................................................... 607 The Worm in Brussels Sprouts.................................................................................... 607 Bushenhack...................................................................................................................... 607 References and Further Reading.................................................................................... 607 18 The Emperor and His Money 609 Sylver Coinage................................................................................................................ 610 How Long Will It
Last?................................................................................................ 610 Some Openings Are Bad................................................................................................ 611 Are All Openings Bad? ................................................................................................ 613 Not All Openings Are Bad............................................................................................. 615 Strategy Stealing.............................................................................................................616 Quiet Ends...................................................................................................................... 617 Doubling and Tripling? ................................................................................................ 620 Halving and Thirding?................................................................................................... 620 Finding the Right Combinations................................................................................. 621 What Shall I do When g is Two.................................................................................... 626 The Great Unknown...................................................................................................... 629 Are Outcomes Computable?.......................................................................................... 630 The Etiquette of Sylver Coinage .................................................................................631
Chomp............................................................................................................................... 632 Zig-Zag............................................................................................................................ 632 More Cliques for Sylver Coinage ................................................................................. 635 5-Pairs............................................................................................................................... 635 Positions Containing 6................................................................................................... 636 Sylver Coinage Has Infinite Nim-Values.................................................................... 636 A Few Final Questions................................................................................................... 640 References and Further Reading.................................................................................... 640 19 The King and the Consumer 641 Chessgo, Kinggo and Dukego....................................................................................... 641 Quadraphage................................................................................................................... 642 The Angel and the Square-Eater................................................................................. 643 Strategy and Tactics.......................................................................................................643 Dukego
............................................................................................................................ 644 The Edge Attack.............................................................................................................646 The Edge Defence ......................................................................................................... 647
Contents xiii A Memoryless Edge Defence.......................................................................................... 648 The Edge-Corner Attack................................................................................................ 650 Strategic and Tactical Stones....................................................................................... 652 Corner Tactics................................................................................................................654 Defence on Large Square Boards.................................................................................657 The 33 x 33 Board......................................................................................................... 658 The Centred King ......................................................................................................... 658 Leaving the Central Region.......................................................................................... 658 The Cornered King......................................................................................................... 661 The Sidelined King......................................................................................................... 661 How Chas. Can Win on a 34 x 34 Board ................................................................. 663 Rectangular Boards ...................................................................................................... 664 Many-Dimensional
Angels............................................................................................. 665 Games of Encirclement................................................................................................... 665 Wolves-and-Sheep ......................................................................................................... 665 Tablut............................................................................................................................... 666 Saxon Hnefatafl................................................................................................................666 King and Rook Versus King.......................................................................................... 667 References and Further Reading....................................................................................668 20 Fox and Geese 669 Some Properties of Our Strategy................................................................................ 672 What Is the Value of Fox-and-Geese?.......................................................................... 673 Fox-Flocks-Fox................................................................................................................673 Towards Greater Precision............................................................................................. 673 The Indefinite Board...................................................................................................... 674 How the Geese Survive Triumphantly .......................................................................
675 Eight Exciting Escapades............................................................................................. 677 Tactics and Startegy for the Fox.................................................................................681 Fox’s Play on Definite Boards....................................................................................... 686 The Scrimmage Sequence............................................................................................. 687 Values of the Initial Positions....................................................................................... 688 Sophisticated New Software.......................................................................................... 690 Values of FOXTAC Positions....................................................................................... 692 High Region...................................................................................................................... 692 Welton’s Region of Value 2over.................................................................................... 693 Lower “Delta” Region................................................................................................... 697 Initial Values................................................................................................................... 697 Parity in the High Scrimmage Region ....................................................................... 697 Early Values ...................................................................................................................
700 The abc’s to Trifúrcate the Two-Ish Transition........................................................ 701 Extending the Backbone to Lower Altitudes.............................................................. 702 Early Values of Other Formations.................................................................................702 Resolving the Exceptions ............................................................................................. 704
xiv Content։ * Museums......................................................................................................................... 705 Solutions to Problems................................................................................................... 709 Open Problems................................................................................................................ 710 Maharajah and Sepoys................................................................................................... 710 References and Further Reading.................................................................................... 710 21 Hare and Hounds 711 The French Military Hunt............................................................................................. 711 Two Trial Games............................................................................................................. 713 History ............................................................................................................................ 713 The Different Kinds of Place ....................................................................................... 713 The Opposition................................................................................................................ 714 When Has the Hare Escaped?....................................................................................... 715 Losing the Opposition................................................................................................... 716 A Strategy for the
Hare................................................................................................ 718 On the Small Board.......................................................................................................721 On the Medium and Larger Boards.............................................................................. 722 Answers to Questions ................................................................................................... 725 A Sound Bound for a Hound?....................................................................................... 725 All Is Found for the Small Board Hound.................................................................... 725 Proof of the Thirty-One Theorem................................................................................. 729 References and Further Reading.................................................................................... 729 22 Lines and Squares 731 Tit-Tat-Toe, My First Go, Three Jolly Butcher Boys All in a Row...................... 731 Magic Fifteen................................................................................................................... 732 Spit Not So, Fat Fop, as if in Pan!.............................................................................. 732 Jam................................................................................................................................... 732 How Long Can You Fool Your Friends? .................................................................... 733 Analysis of Tic-Tac-
Toe................................................................................................ 733 Ovid’s Game, Hopscotch, Les Pendus ........................................................................ 736 Six Men’s Morris............................................................................................................. 737 Nine Men’s Morris.......................................................................................................... 737 Three Up......................................................................................................................... 737 Four-in-a-Row ................................................................................................................ 737 Five-in-ar-Row................................................................................................................... 738 Go-Moku......................................................................................................................... 740 Six, Seven, Eight, Nine, ..., in a Row........................................................................740 n-Dimensional fc-in-a-Row............................................................................................. 742 Strategy Stealing in Tic-Tac-Toe Games.................................................................... 743 Hex................................................................................................................................... 744
Bridgit............................................................................................................................... 744 How Does the First Player Win?................................................................................. 744 The Shannon Switching Game .................................................................................... 744
Contents 4 XV The Black Path Game.......................................................................................................... 746 Lewthwaite’s Game................................................................................................................ 747 Meander.................................................................................................................................... 747 Winners and Losers ............................................................................................................. 748 Dodgem.................................................................................................................................... 749 Dodgerydoo..............................................................................................................................751 Philosopher’s Football.......................................................................................................... 752 Count foxy words And stay awake Using lively wit..................................................... 756 Amazons ................................................................................................................................. 756 Checkers.................................................................................................................................... 757 Chess ........................................................................................................................................757
Cherries.................................................................................................................................... 757 Clobber.................................................................................................................................... 757 Go.............................................................................................................................................. 758 Konane.................................................................................................................................... 759 Reversi-Othello ....................................................................................................................... 760 Scrabble.................................................................................................................................... 760 Shogi................................................................................................................................ 760 Sowing Games ....................................................................................................................... 761 Answers to Problems............................................................................................................. 761 References and Further Reading......................................................................................... 762 Index to Volumes 1-3 770
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| any_adam_object | 1 |
| 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 |
| author_role | aut aut aut |
| author_sort | Berlekamp, Elwyn R. 1940-2019 |
| author_variant | e r b er erb j h c jh jhc r k g rk rkg |
| building | Verbundindex |
| bvnumber | BV048642467 |
| classification_rvk | SN 300 |
| ctrlnum | (OCoLC)1371318853 (DE-599)BVBBV048642467 |
| discipline | Mathematik |
| edition | Second edition, first issued in hardback |
| format | Book |
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| isbn | 9781138427563 |
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| 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_full | Winning ways for your mathematical plays 3 Elwyn R. Berlekamp ; John H. Conway ; Richard K. Guy |
| title_fullStr | Winning ways for your mathematical plays 3 Elwyn R. Berlekamp ; John H. Conway ; Richard K. Guy |
| title_full_unstemmed | Winning ways for your mathematical plays 3 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=034017368&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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