## Aha! A Two Volume Collection: Aha! Gotcha Aha! InsightPreviously published separately, the two books aha! Gotcha and aha! Insight are here combined as a single volume. The aha! books, as they are referred to by fans of Martin Gardner, contain 144 wonderful puzzles from the reigning king of recreational mathematics. In this combined volume, you will find puzzles ranging over geometry, logic, probability, statistics, number, time, combinatorics, and word play. Gardner calls these puzzles aha! problems, that 'seem difficult, and indeed are difficult if you go about trying to solve them in traditional ways. But if you can free your mind from standard problem solving techniques, you may be receptive to an aha! reaction that leads immediately to a solution. Don't be discouraged if, at first, you have difficulty with these problems. After a while you will begin to catch the spirit of offbeat, nonlinear thinking, and you may be surprised to find your aha! ability improving.' |

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### Contents

Preface xvu The Ubiquitous Number 9 38 | 9 |

Logic 1 The Missing Dollar | 42 |

The Liar Paradox 4 The Amazing Code | 48 |

Infinite Regress 10 3 Geometry | 55 |

The Barber Paradox 16 Mirror Magic | 61 |

Semantics and Set Theory 20 The Vanishing Leprechaun | 67 |

The Unexpected Tiger 26 The Inescapable Point | 74 |

Paradoxes about integers fractions and an infinite | 81 |

Surprising Swords | 39 |

Quibbles Matches | 45 |

Miss Euclids Cubes | 51 |

Broken Records | 61 |

Eyes and Legs | 69 |

6 | 75 |

The Crafty Cabbie | 90 |

The Big Holdup | 97 |

Population Implosion 37 The Gamblers Fallacy | 87 |

Four Kittens 90 The Voting Paradox 128 | 100 |

6 Time | 137 |

Statistics 111 Zenos Paradoxes | 143 |

Contents | 175 |

A Sticky Gum Problem | 4 |

The Bewildered Babies | 12 |

The Troublesome Tiles | 18 |

The Medicine Mixup | 24 |

Crafty Cheese Cuts | 32 |

Holiday Haircut | 105 |

Fifteen Finesse | 116 |

Dividing the Chores | 123 |

The Lazylover | 131 |

Dr W O Wordle | 140 |

Mother of the Year 116 Can Time Go Backward? 150 | 150 |

Patterns in Pi 122 Time Dilation 156 | 156 |

87 | 172 |

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### Common terms and phrases

algorithm answer arithmetic balls binary bottle called cards cells centimeters circle clock coins color combinatorial count cube deck digital root digits divided dollar easy equations exactly example famous four geometry girl Helen hole Hotel Infinity infinite number insight integers Josephus problem kilometers knights length letters liar paradox logic magic square Martin Gardner match Mathematical Games mathematical induction mathematician mathematics metalanguage meters minutes mirror Miss move pair palindrome palindromic prime paradox parity Pascal's triangle path person phone number pieces plane play player principle of indifference probability problem procedure puzzle question remains rope Scientific American sentence sequence shown in Figure side simple solution solved spot square straight line supertasks Suppose symmetry theorem theory tile tion triangle Uncle Henry word Wordle Zeno's Paradoxes