Knight's Tour
Overview
Important
The Knight's Tour problem asks whether it is possible to move a knight on a chessboard so that it visits every square exactly once, following the rules of chess. The sequence of moves forms a path that covers all squares without repeats.
Important properties
-
A tour can be open (the knight does not return to the starting square) or closed (the last move brings the knight back to the starting square).
-
The problem can be represented as finding a Hamiltonian path (or cycle) in a graph where each vertex is a square and edges represent legal knight moves.
-
Not all board sizes allow a Knight's Tour; for example, a 3x3 board is too small.