## Mathematical Recreations and EssaysThis classic work offers scores of stimulating, mind-expanding games and puzzles: arithmetical and geometrical problems, chessboard recreations, magic squares, map-coloring problems, cryptography and cryptanalysis, much more. "A must to add to your mathematics library" ? The Mathematics Teacher. Index. References for Further Study. Includes 150 black-and-white line illustrations. |

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### Contents

ARITHMETICAL RECREATIONS | 3 |

Other problems with numbers in the denary scale | 14 |

Medieval problems in arithmetic | 27 |

Addendum on solutions | 40 |

The decimal expression for I in | 53 |

Rational rightangled triangles | 57 |

Mersenne numbers | 64 |

Galois fields | 73 |

Magic squares of a singlyeven order | 196 |

Magic squares of nonconsecutive numbers | 210 |

Unbounded surfaces | 232 |

Number of ways of describing a unicursal figure | 250 |

Dragon designs | 266 |

COMBINATORIAL DESIGNS | 271 |

Kirkmans schoolgirl problem | 286 |

Equiangular lines in 3space | 299 |

Geometrical paradoxes | 84 |

Cyclotomy | 94 |

Addendum on a solution | 102 |

Dynamical games of position | 116 |

Paradromic rings | 127 |

POLYHEDRA | 130 |

The Archimedean solids | 136 |

The KeplerPoinsot polyhedra | 144 |

Regular sponges | 152 |

CHESSBOARD RECREATIONS | 162 |

The eight queens problem | 172 |

MAGIC SQUARES | 193 |

MISCELLANEOUS PROBLEMS | 312 |

Arrangements by rows and columns | 325 |

THREE CLASSICAL GEOMETRICAL PROBLEMS | 338 |

The trisection of an angle | 344 |

CALCULATING PRODIGIES | 360 |

Bidder 18061878 | 367 |

Safford 18361901 | 374 |

Alexander Craig Aitken | 386 |

Transposition systems | 391 |

Substitution systems | 402 |

Determination of cryptographic system | 414 |

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### Common terms and phrases

alphabet angle Archimedean solids arithmetic arrangement Bachet calculating cells centre cipher circle circuit colours column construction contains counters cryptanalyst cube cyclic permutation denoted described diagonal diagram digits discs districts divide dodecahedron dominoes edges enantiomorphous equal equiangular lines equivalent Euler's example faces figure finite four geometrical given graph H.S.M. Coxeter Hadamard matrix Hamiltonian circuit Hence icosahedron illustrations instance integers Latin squares letters lines magic square Martin Gardner Mathematics matrix maze method move multiple obtained octahedron odd nodes odd number original orthogonal pack pair pandiagonal pentagon pentominoes permutation Petrie polygon pieces pile placed plain-text plane points polygon polyhedron position prime problem projective plane PUZZLES queens re-entrant rectangle result ring route rule side solution squares of order Steiner triple systems suppose symbols symmetrical tessellation tetrahedra theorem theory tion transposition triangle unicursal vertex vertices