Flying Rook Cycles

A flying rook moves like a rook, but each move must have length at least 2 (no single-step moves).

So the board becomes a custom move graph: vertices are squares, edges are allowed flying-rook moves. The puzzle asks for a Hamiltonian cycle: visit every square exactly once and return to the start.

Why this puzzle matters

• Same idea as Knight''s Tour (Hamiltonian path/cycle on a move graph), but with a different piece and move rule.
• The flying-rook graph has different connectivity and degree structure; exploring 4x4 up to 8x8 shows how the problem scales.

Board sizes in this set

• 4x4: compact; good first check that a cycle exists.
• 5x5, 6x6, 7x7: larger search spaces.
• 8x8: the classical board.

Use the problems below to practice each size. The interactive validates your cycle when you close the loop back to the start.

Return to the Mathematics in Chess overview for the full collection.