Question 24
There are two boards $A$ and $B$, both $8 \times 8$.
Juan writes a number in each cell of board $A$. For each cell of board $A$, Juan adds the number written in that cell to the sum of the numbers written in its neighbouring cells, and then writes the result in the cell occupying the same position on board $B$.
Juan gives board $B$ to Esteban and challenges him to reconstruct board $A$.
For which cells can Esteban determine with certainty the number written on board $A$?
Note: Two cells are neighbours if they share a side or a vertex.
Juan writes a number in each cell of board $A$. For each cell of board $A$, Juan adds the number written in that cell to the sum of the numbers written in its neighbouring cells, and then writes the result in the cell occupying the same position on board $B$.
Juan gives board $B$ to Esteban and challenges him to reconstruct board $A$.
For which cells can Esteban determine with certainty the number written on board $A$?
Note: Two cells are neighbours if they share a side or a vertex.