## Penrose Tiles to Trapdoor Ciphers: And the Return of Dr MatrixHere is another collection drawn from Martin Gardner's 'Mathematical Games' column in Scientific American. Each chapter explores a different theme, for example fractals, surreal numbers, the sculptures of Berrocal, tiling the plane, Ramsey theory and code breaking, all combining to create a rich diet of recreational mathematics. Most chapters can be readily understood by the uninitiated: at each turn there are challenges for the reader and a wealth of references for further reading. Gardner's clarity of style and ability systematically to simplify the complex make this an excellent vehicle in which to start or continue an interest in recreational mathematics. |

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### Contents

Penrose Tiling | 1 |

Mandelbrots Fractals | 31 |

Conwas Surreal Numbers | 49 |

Back from the Klondike and Other Problems | 63 |

The Oulipo | 79 |

The Oulipo II | 95 |

Wythoffs Him | 103 |

PoolBall Triangles and Other Problems | 119 |

Trapdoor Ciphers | 183 |

Hyperbolas | 205 |

The New Eleusis | 219 |

Ramsey Theory 231 | 246 |

From Burrs to Berrocal | 249 |

Sicherman Dice the Kruskal Count and Other Cun CHAPTER 20 Raymond Smullyans Logic Puzzles | 281 |

The Return of Dr Matrix | 293 |

Postscript | 307 |

Mathematical Induction and Colored Hats | 137 |

Negative Numbers | 151 |

Cutting Shapes into N Congruent Parts | 165 |

315 | |

### Common terms and phrases

adam algorithm Ammann Ammann bars answer Aviezri Fraenkel Beatty sequences Berrocal BIBLIOGRAPHY bisecting called chapter checkers chess cipher circle color column combinatorial complete graph congruent Conway Conway's counters cube curve dealer diagonal dice digits dimension Eleusis ellipse example Fibonacci Quarterly Fibonacci sequence finite flowsnake force four fractals golden ratio hole hyperbola hyperboloid infinite infinity Journal knave knight letter Loyd's magic square Mandelbrot mathematicians Mathews Matrix move negative numbers No-Three-in-Line Problem nonperiodic tiling Oulipo paradox pattern Penrose tiling pieces plane play player points positive integer positive number possible prime problem proof Prophet proved puzzle Quasicrystals queen Ramsey number Ramsey theory readers Recreational Mathematics region rotations safe cells safe pairs say yes Science Scientific American shown in Figure shows Smith Numbers Smullyan solution solved straight line symmetry theorem torus triangle two-colored University words Wythoff's