The horse problem…

The problem of the horse is an old mathematical problem in which it is requested that, having a grid of n x n squares and a chess horse placed in any position (x, y), the horse passes through all the squares and only once. What results in n2-1 movements.

- Solution for 63 horse jumps for the 64 squares.

- Many mathematicians have looked for a mathematical solution to this problem, among them    Leonhard Euler.

Many solutions have been found to this problem and in fact it is not known for sure how many different ways it is possible to solve it.

Some variations of this problem have been studied by mathematicians, such as:

• Look for cyclical solutions, in which you must reach the same box from which you started.
• Boards of different number of columns or different number of rows.
• Two-player games based on the idea.
• Problems using slight variations in the way the horse moves.
• The problem of the horse is a form of the problem more general problem of the Hamiltonian route in the theory of graphs.

On the right we can see one of the possible solutions in a conventional chessboard of eight columns by eight rows. Below, a cyclical solution in which the destination box is just the one before the departure.

Recommendation: The chapters of Georges Perec's novel The Life Directions of Use (1978) follow an order that corresponds to a solution of the horse problem on a 10 × 10 grid. The solution was found experimentally by the same author.