Puzzles
The sliding puzzle with a $1,000 prize that could never be won
The 15 puzzle has fifteen numbered tiles sliding in a 4x4 frame. In 1880, puzzle-maker Sam Loyd offered $1,000 to anyone who could take a puzzle with tiles 14 and 15 swapped and slide it back into normal numerical order. Why couldn't anyone claim the prize?
Reveal the answer
It's mathematically impossible. Sliding moves can only ever produce even permutations of the tiles; swapping two tiles (like 14 and 15) creates an odd permutation, which no sequence of legal slides can ever undo. Loyd's prize was safe because he understood — and the public didn't — that some scrambles are permanently unsolvable.
— Sam Loyd (popularizer); Noyes Chapman (inventor), The 15 Puzzle — c. 1874-1880