Question 8
In the following $3\times3$ board, some cells are already filled in with positive integers:
Our goal is to write a positive integer in each of the remaining empty cells in such a way that the following conditions are met:
- All nine integers written on the board must be different from each other.
- The sum of the four integers in any $2\times2$ square is always the same.
Find the smallest possible value for the sum of the nine integers on the board.
Our goal is to write a positive integer in each of the remaining empty cells in such a way that the following conditions are met:
- All nine integers written on the board must be different from each other.
- The sum of the four integers in any $2\times2$ square is always the same.
Find the smallest possible value for the sum of the nine integers on the board.