Sorrelkova N.P.

Under one of the cells of an $8 \times 8$ board, a treasure is buried. Under each of the other cells, there is a sign indicating the minimum number of steps required to reach the treasure from that cell (one step allows moving from a cell to an adjacent cell by side). What is the minimum number of cells that need to be dug up to definitely retrieve the treasure?
Let's dig up the corner cell $U$. Suppose there is a sign there. All cells at the specified distance from $U$ form a diagonal perpendicular to the main diagonal drawn from $U$. Let's dig up the corner cell $W$ on the same side as $U$. If there is also a sign there, then another diagonal perpendicular to the first one is formed. The diagonals intersect at one cell, where the treasure is buried.

Two diggings may not be enough. For example, suppose we were unlucky and found a sign with the number 1 on the first try. Then the treasure is in the adjacent cell, but there are at least two such cells.

## Answer

3 cells.