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Comments on A knight's sightseeing tour
Parent
A knight's sightseeing tour Question
Puzzle
How short can you make a closed knight’s sightseeing tour?
Terminology
Standard terminology
- A chess board is an 8 by 8 chequerboard.
- A knight is a chess piece that moves 2 squares horizontally then 1 vertically, or 2 vertically then 1 horizontally. The knights in the following diagram can reach any of the correspondingly coloured marked squares in 1 move.
(thanks to Wikipedia)
- A knight’s tour is a sequence of moves that visits every square exactly once.
- A closed knight’s tour visits every square exactly once and then returns to its starting square.
Terminology specific to this puzzle
- A square is visible to a knight if the knight can reach it in 1 move.
- A closed knight’s sightseeing tour is a sequence of moves that visits no square more than once and then returns to its starting square, such that every square on the board is visible from at least one of the squares in the tour. (To avoid doubt: Note that the starting square is included as one of the squares in the tour.)
After completing a sightseeing tour, the knight has not necessarily visited every square, but it has seen every square. A closed knight’s tour automatically also counts as a closed knight’s sightseeing tour, but is longer than it needs to be.
You are free to choose any square on the board as the starting square.
Leaderboard
| Username | Shortest knight's sightseeing tour |
|---|---|
| will.octagon.gibson | 20 |
| trichoplax | 26 |
Post
The following users marked this post as Works for me:
| User | Comment | Date |
|---|---|---|
| trichoplax | (no comment) | Sep 14, 2026 at 17:15 |
My tours are inspired by trichoplax‘s answer.
Spoiler! Key idea
Subdivide the 6x6 grid from trichoplax‘s answer into four 3x3 grids that will be toured one at a time.Spoiler! Tour with 32 moves
The following tour starts at the square labeled 1 and continues 2, 3, 4, ..., 31, 32 and lastly back to 1.
After finding the above tour, I was able to reduce the number of squares visited.
Spoiler! Tour with 28 moves
The following tour starts at the square labeled 1 and continues 2, 3, 4, ..., 27, 28 and lastly back to 1.
I reduced the number of squares visited even further.
Spoiler! Tour with 20 moves
The following tour starts at the square labeled 1 and continues 2, 3, 4, ..., 19, 20 and lastly back to 1.
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