Four knights on a 3x3 board, and there's only one way to swap them
Place two white knights on the top corners of a 3x3 chessboard and two black knights on the bottom corners, leaving the centre and edge squares empty. Using only legal knight moves, can you swap every white knight with every black knight, and if so, is there any real choice in how you do it?
Reveal the answer
Yes, and remarkably there's no choice at all. The eight usable squares form a single unbroken loop under the knight's move, so all four knights are forced to shuffle around that loop in the same direction until their positions are exactly reversed, taking 16 moves. Posed in 1512 by Paolo Guarini di Forlì, it's considered one of the earliest recreational chess puzzles ever recorded.