Puzzle showman Sam Loyd offered $1,000 for a slide puzzle he knew was impossible to solve
Around 1880, Sam Loyd popularised a 4x4 sliding tile puzzle numbered 1 to 15, but with the 14 and 15 tiles swapped, and offered a cash prize to anyone who could slide them back into plain numerical order. Thousands tried and failed. Can you work out why no amount of sliding could ever fix it?
Reveal the answer
Every slide move is equivalent to swapping two tiles, which always flips the puzzle's permutation parity. Starting from the swapped 14-15 arrangement, reaching the fully ordered arrangement would require an odd number of swaps, which is mathematically impossible from a board of that size. Loyd's prize was always safe.
— Noyes Palmer Chapman (inventor); popularised by Sam Loyd, 15 puzzle — United States, 1880