Question 89
Given a $20 \times 20$ table with one of two signs "+" or "-" in any of its cells. Per move one can replace the signs in all cells of some row (or of some column) by the opposite signs. At the beginning there are $8$ minuses in the table (all other signs are pluses). After some moves the table with exactly $50$ minuses is obtained.
Prove that exactly one initial minus is in the same cell.
Prove that exactly one initial minus is in the same cell.