An 1880 sliding-tile craze offered $1,000 for a mathematically impossible solution
The 15 puzzle, numbered tiles 1 through 15 in a 4x4 grid with one gap, became a craze across the United States and Europe in 1880. Puzzle-maker Sam Loyd claimed to have invented it and offered a cash prize to anyone who could swap just two tiles, numbers 14 and 15, back into order from an otherwise-solved state. Can it be done?
Reveal the answer
No. Swapping any two tiles changes the puzzle's parity, and only half of all tile arrangements are reachable from any given starting position by legal slides; Loyd's target was in the unreachable half, so the $1,000 was never at real risk. Mathematicians Johnson and Story proved the parity rule in 1879. Loyd's claim to have invented the puzzle is also disputed: the earliest documented version was patented by Noyes Chapman in 1880.