# aha! Gotcha

### Paradoxes to puzzle and delight

## Martin Gardner

# Contents

### Preface

**Logic.**Paradoxes about truth-tellers, liars, crocodiles, and barbers.The Liar Paradox

Buttons and Graffiti

A Sentence and Its Opposite

The Crazy Computer

Infinite Regress

The Plato-Socrates Paradox

Alice and the Red King

Crocodile and Baby

The Don Quixote Paradox

The Barber Paradox

Astrologer, Robot, and Catalog

Dull Versus Interesting

Semantics and Set Theory

Metalanguages

Theory of Types

The Swami's Prediction

The Unexpected Tiger

Newcomb's Paradox

**Number.**Paradoxes about integers, fractions, and an infinite ladderThe Six-Chair Mystery

The Elusive Profit

Population Implosion

The Ubiquitous Number 9

The Bewildered Bus Driver

The Missing Dollar

Magic Matrix

The Curious Will

The Amazing Code

Hotel Infinity

The Ladder of Alephs

**Geometry.**Paradoxes about plane, solid, and impossible shapesGetting Around a Girl

The Great Moon Mystery

Mirror Magic

Cubes and Ladies

Randi's Remarkable Rugs

The Vanishing Leprechaun

The Great Bank Swindle

The Amazing Inside-Out Doughnut

The Bewildering Braid

The Inescapable Point

Impossible Objects

A Pathological Curve

The Unknown Universe

Antimatter

**Probability.**Paradoxes about chance, wagers, and belieThe Gambler's Fallacy

Four Kittens

Three-Card Swindle

The Elevator Paradox

The Bewildered Girlfriends

Three-Shell Game

Chuck-A-Luck

Puzzling Parrots

The Wallet Game

The Principle of Indifference

Pascal's Wager

**Statistics.**Paradoxes about gismos, clumps, ravens, and grueThe Deceptive "Average"

Mother of the Year

Jumping to Conclusions

The Small-World Paradox

What's Your Sign?

Patterns in Pi

Jason and the Sun

Crazy Clumps

An Amazing Card Trick

The Voting Paradox

Miss Lonelyhearts

Hempel's Ravens

Goodman's Grue

**Time.**Paradoxes about motion, supertasks, time and reversed timeCarroll's Crazy Clocks

The Perplexing Wheel

The Frustrated Skier

Zeno's Paradoxes

The Rubber Rope

Supertasks

Mary, Tom, and Fido

Can Time Go Backward?

Time Machines

The Tachyon Telephone

Parallel Worlds

Time Dilation

Fate, Chance, and Free Will

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Copyright © 1996-2018 Alexander Bogomolny