What is the knight's tour?
The knight's tour is one of the oldest chess puzzles: move a single knight so that it lands on every square of the board exactly once. There is no opponent and no capture, only the knight's L-shaped jump, two squares in one direction and one square to the side. What makes it hard is that a knight in a corner has only two exits and one on the edge has three or four, so a tour that leaves the edges for later runs out of ways back in.
Open vs closed tour
A closed tour ends on a square one knight's move from where it started, so the knight could jump straight back and go round again: the tour is a loop. An open tour visits every square too, but its last square is not a knight's move from the first, so the loop does not close. Both exist on 8×8. A closed tour is impossible on a board with an odd number of squares, such as 5×5, because the knight changes colour on every move and a loop must have as many light squares as dark ones. This page tells you which kind you finished.
Warnsdorff's rule
In 1823 H. C. von Warnsdorff proposed a simple rule: always jump to the square from which the knight will have the fewest onward moves. The idea is to visit the awkward squares (corners, edges) while they can still be reached, and to keep the open centre for later. Followed blindly, it finds a complete tour from most starting squares without any backtracking.
It is a heuristic, not a guarantee. When two squares tie, the choice between them matters, and the rule can still walk into a dead end: with the tie-break the hint button uses, it completes the 8×8 tour from 63 starting squares and gets stuck from e3. Use the hint to learn the idea, not as a solver.
Why it trains blindfold visualization
Blindfold players do not see the board, they compute it, and the knight is the piece that exposes weak board vision fastest: its jumps contradict the straight lines the eye follows. A tour forces you to list a knight's targets from every square, over and over, and to keep track of which squares are already used. Switch on Blindfold above to hide the visited marks: you then have to remember the squares you used, which is position memory, not just geometry.
To build the reflex first, drill single jumps in knight movement, learn the pattern in the knight moves lesson, then race to a target square in the knight maze. The blindfold chess guide shows where knight calculation fits in the whole path to playing without a board.
Frequently asked questions
Is a knight's tour always possible on an 8×8 board?
Yes. Both closed tours (ending one knight's move from the start) and open tours (ending on a square that is not) exist on the standard 8×8 board. Smaller boards are harder: 5×5 has open tours but no closed one, and 2×2, 3×3 and 4×4 have no tour at all.
How many knight's tours are there?
On 8×8 there are 26,534,728,821,064 directed closed tours, counted by Brendan McKay in 1997. Counting a tour and its reverse once, that is 13,267,364,410,532.
Can a knight's tour start on any square?
On 8×8, yes. A closed tour is a loop through all 64 squares, so you can enter it anywhere and follow it round. On 5×5, a tour can only start on one of the 13 squares that share a1's colour.
Does Warnsdorff's rule always find a tour?
No. It is a heuristic: always jump to the square with the fewest onward moves. It finds a full tour from most starting squares, but how ties are broken matters, and it can still walk into a dead end. The hint on this page uses it, so it can occasionally lead you astray too.