Question 76
In a $50 \times 50$ grid, an integer is written in each of the $2500$ cells. Let $G$ be the configuration of $8$ cells formed by removing the central cell of a $3 \times 3$ grid. It is given that for any group of $8$ cells in the $50 \times 50$ grid forming the configuration $G$, the sum of the numbers written in the $8$ cells is positive. Prove that there is a $2 \times 2$ grid so that the sum of the numbers in the $4$ cells is positive.