For what values of n can we fill an n-by-n grid with + and-signs, such that each square has exactly one neighbor of the opposite sign? A neighbor is an adjacent square that is in the same row or column. Hint: Try to solve the puzzle for n-2, n-3, n-4 For all "valid" n, show (or describe) all the ways of tiling the grid. For "invalid" n, show that it cannot be done. Mathematical induction is necessary here