Alice and Bob sit down, face to face, with a chessboard in front of them. They are going to play a little game, but this game only has a single knight... Who will win?

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A chess knight
Photo by Piotr Makowski on Unsplash

Problem statement

Alice and Bob will play a special game of “chess”. Alice will take the knight and place it in some square of the chessboard, any square she likes.

Chessboard with a knight

Then, Bob will take the knight and move it (according to chess rules) to a square of his choosing.

Chessboard after another move

Then it's Alice's turn to do the same, and they will alternate moving the knight. There is only a catch:

They cannot move the knight to a position that has already been visited by the knight.

In the example image below, the knight cannot be moved one row down and two columns right, as that is the place the knight started at.

Same chessboard with some squares already visited

Thus, the player who cannot make a valid move loses.

Can any of them guarantee a win? Who? How?

Give it some thought...

If you want, you can try playing the game against the computer here.

If you need any clarification whatsoever, feel free to ask in the comment section below.

This problem was posed to me by a university colleague that plays a lot of chess!


You can read the solution here to compare with your own solution. You can also use that link to post your own solution in the comments! Please do not post spoilers in the comments here.

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