Sam Loyd offered $1,000 for solving a puzzle he didn't even invent
The 15 Puzzle — fifteen numbered tiles sliding in a 4x4 grid with one gap — became a national craze in 1880. Puzzle showman Sam Loyd claimed for the rest of his life that he'd invented it, and offered $1,000 to anyone who could swap just two tiles and still solve the puzzle. Why was that reward always perfectly safe?
Reveal the answer
It's mathematically impossible: sliding moves can only ever produce even permutations of the starting arrangement, so swapping any two tiles (an odd permutation) makes the puzzle unsolvable — no sequence of legal moves can undo it. The prize was never paid. As for the invention: it wasn't Loyd's. Puzzle historians trace it to Noyes Chapman, a postmaster in Canastota, New York, who applied for a patent in 1880; Loyd's claim, first made in 1891, is now recognized as false.