The longest uncrossed (or nonintersecting) knight's path is a mathematical problem involving a knight on the standard 8×8 chessboard or, more generally, on a square n×n board.
A further distinction can be made between a closed path, which ends on the same field as where it begins, and an open path, which ends on a different field from where it begins.
Their lengths for n = 1, 2, …, 9 are: The longest closed paths are known only for n ≤ 10.
The problem for n×m boards, where n doesn't exceed 8 and m might be very large, was given at 2018 ICPC World Finals.
Other standard chess pieces than the knight are less interesting, but fairy chess pieces like the camel ((3,1)-leaper), giraffe ((4,1)-leaper) and zebra ((3,2)-leaper) lead to problems of comparable complexity.