Winning ways for your mathematical plays. Volume 3

Description

Content: Cover Half Title Title Page Copyright Page Dedication Table of Contents Preface to the Second Edition Preface to the Original Edition Games in Clubs! 14 Turn and Turn About Turning Turtles Mock Turtles Odious and Evil Numbers Moebius, Mogul and Gold Moidores The Mock Turtle Theorem Why Moebius? Mogul Motley Twins, Triplets, Etc. The Ruler Game Circumscribed Games Turnips (or Ternups) Grunt Sym Two-Dimensional Turning Games Acrostic Twins Turning Corners Nim-Multiplication Swirling Tartans The Tartan Theorem Rugs, Carpets, Windows and Doors Acrostic Games Stripping and StreakingUglification and Derision Unlocking Doors Sparring, Boxing and Fencing "Coins" (or Heaps) with Infinitely Many (or 22N) ""Sides References and Further Reading 15 Chips and Strips The Silver Dollar Game Profit from Gaming Tables Antonim Synonim Simonim Staircase Fives Twopins (pronounced "Tuppins") Cram Welter's Game Four-Coin Welter is Just Nim And So's Three-Coin Welter! The Congruence Modulo 16 Frieze Patterns Inverting the Welter Function The Abacus Positions The Abacus Strategy The Misère Form of Welter's Game Kotzig's Nim Fibonacci Nim More Generally Bounded NimEpstein's Put-or-Take-a-Square Game Tribulations and Fibulations Third One Lucky Hickory, Dickory, Dock D.U.D.E.N.E.Y Strings of Pearls Schuhstrings The Princess and the Roses One-Step, Two-Step More on Subtraction Games Smallest Nim, Largest Nim Moore's Nimk The More the Merrier Moore and More Not with a Bang but a Whim Did You Win the Silver Dollar? How Was Your Arithmetic? In Put-or-Take-a-Square , 92 Is an N-Position Tribulations and Fibulations Our Code of Behavior for Princes References and Further Reading 16 Dots-and-Boxes Double-Dealing Leads to Double-CrossesHow Long Is ''Long''? The 4-Box Game The 9-Box Game The 16-Box Game Other Shapes of Board Dots-and-Boxes and Strings-and-Coins Nimstring Why Long Is Long To Take or Not to Take a Coin in Nimstring Sprague-Grundy Theory for Nimstring Graphs All Long Chains Are the Same Which Mutations Are Harmless? Chopping and Changing Vines Dots + Doublecrosses = Turns How Dodie Can Win the 4-Box Game When Is it Best to Lose Control? Computing the Values of Vines Loony Endgames Are NP-Hard Solutions to Dots-and-Boxes Problems Some More Nimstring ValuesNimbers for Nimstring Arrays References and Further Reading 17 Spots and Sprouts Rims Rails Loops-and-Branches Contours Lucasta A Child's Guide to Normal Lucasta The Misère Form of Lucasta The Positions (7, 3, 1) and (11, 1, 1) Cabbages or Bugs, Caterpillars and Cocoons Jocasta Sprouts Brussels Sprouts Stars-and-Stripes Bushenhack Genetic Codes for Nim Bushenhack Positions Have Genetic Codes! Von Neumann Hackenbush The Joke in Jocasta The Worm in Brussels Sprouts Bushenhack References and Further Reading 18 The Emperor and His Money