Puzzles

Turn the wheel and one of thirteen warriors disappears

A card shows a circle of Chinese warriors printed around a rotating disc set into a rectangular background of the Earth. Rotate the disc slightly one way and you can count thirteen warriors; rotate it the other way and only twelve remain, with no warrior obviously removed. Where does the thirteenth one go?

Reveal the answer

Nobody vanishes — the warriors are drawn in overlapping slivers of body parts, and rotating the disc redistributes those slivers so that twelve figures absorb the material that used to look like thirteen. Sam Loyd patented this 'vanishing area' puzzle in 1896; it sold over ten million copies and remains one of the most famous optical-geometric paradoxes ever made.

Sam Loyd, edited by Martin Gardner, Mathematical Puzzles of Sam Loyd — Dover, 1959 (puzzle originally published 1896)
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