The 15 puzzle

Noyes Chapman, a postmaster in Canastota, New York, made the 15 puzzle around 1874. It became a craze in 1880. In 1879 two mathematicians, William Johnson and William Story, proved that half of all starting positions can never be solved.

One thing to hold: Fifteen numbered squares in a box made for sixteen, so one space is always empty.

Why it matters: Counting how the tiles are out of order tells you, before you start, whether a position can be solved at all.

What we don’t know: Sam Loyd later said he invented it and offered $1,000 for a position that cannot be solved. There is no evidence he invented it.

Sources: Jerry Slocum and Dic Sonneveld, The 15 Puzzle (2006) · W. W. Johnson and W. E. Story, “Notes on the 15 Puzzle”, American Journal of Mathematics 2 (1879) · Wikipedia, “15 puzzle”