The numbers from 1 to n2 are written in order in a grid of n×n, one number in each square, in such a way that the first row contains the numbers from 1 to n from left to right; the second row contains the numbers n+1 to 2n from left to right, and so on and so forth. An allowed move on the grid consists in choosing any two adjacent squares (i.e. two squares that share a side), and add (or subtract) the same integer to both of the numbers that appear on those squares. Find all values of n for which it is possible to make every squares to display 0 after making any number of moves as necessary and, for those cases in which it is possible, find the minimum number of moves that are necessary to do this. MexicocombinatoricsParity