Question 162
Let $n$ be a positive integer. In each cell of an $n \times n$ grid, we place a coin with either the head or the tail facing upwards. Each time we can select one cell, and flip all the $2n - 1$ coins that lie in the same row or the same column as this cell. Find all $n$ such that it is always possible to have all the coins with the heads facing upwards after finitely many moves, no matter how we place the coins initially.