Self-avoiding walks of a knight on a square chessboard

4x4 chessboard

Closed: 4 moves, 2 solutions

Open: 5 moves, 5 solutions

5x5 chessboard

Closed: 8 moves, 6 solutions

Open: 10 moves, 4 solutions

6x6 chessboard

Closed: 12 moves, 51 solutions

Open: 17 moves, 1 solution

7x7 chessboard

Closed: 24 moves, 1 solution

Open: 24 moves, 13 solutions

8x8 chessboard

Closed: 32 moves, 2 solutions

Open: 35 moves, 4 solutions

9x9 chessboard

Closed: 42 moves, 15 solutions