## Across the Board: The Mathematics of Chessboard Problems
Each main topic is treated in depth from its historical conception through to its status today. Many beautiful solutions have emerged for basic chessboard problems since mathematicians first began working on them in earnest over three centuries ago, but such problems, including those involving polyominoes, have now been extended to three-dimensional chessboards and even chessboards on unusual surfaces such as toruses (the equivalent of playing chess on a doughnut) and cylinders. Using the highly visual language of graph theory, Watkins gently guides the reader to the forefront of current research in mathematics. By solving some of the many exercises sprinkled throughout, the reader can share fully in the excitement of discovery. Showing that chess puzzles are the starting point for important mathematical ideas that have resonated for centuries, |

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### Contents

Introduction | 1 |

Knights Tours | 25 |

The Knights Tour Problem | 39 |

Magic Squares | 53 |

The Torus and the Cylinder | 65 |

The Klein Bottle and Other Variations | 79 |

Domination | 95 |

Queens Domination | 113 |

Domination on Other Surfaces | 139 |

Independence | 163 |

Other Surfaces Other Variations | 191 |

Eulerian Squares | 213 |

Polyominoes | 223 |

247 | |

251 | |