Evoookimov M.A.

On one of the cells of an $8 \times 8$ field, a treasure is buried. You are at the center of one of the corner cells of this field with a metal detector and move by transitioning to the centers of adjacent cells along the sides. The metal detector triggers if you are on the cell where the treasure is buried or in one of the adjacent cells along the sides. Can you guarantee to indicate the cell where the treasure is buried by traveling a distance of no more than 26?
Author: $\underline{\text { Aviel Boag }}$

Even 25 moves are sufficient. We will move along the path indicated in the figure. When the mine detector first goes off, the treasure can be in no more than three cells. For example, if it went off in the black cell, then the suspicious cells will be the three marked on the figure. It is easy to see that the correct one can be chosen from them in two moves. If the metal detector first goes off on the 24th move, then there will be two suspicious cells left, and on the $25$-th - one, so the remaining moves will be enough. If the mine detector does not go off at all, then the mine is in the red cell.

![](https://cdn.mathpix.com/cropped/2024_05_06_568737668fd6fdc3aecdg-11.jpg?height=1009&width=1061&top_left_y=1828&top_left_x=1)