A and B are two opposite vertices of an n×n board. Within each small square of the board, the diagonal parallel to AB is drawn, so that the board is divided in 2n2 equal triangles. A coin moves from A to B along the grid, and for every segment of the grid that it visits, a seed is put in each triangle that contains the segment as a side. The path followed by the coin is such that no segment is visited more than once, and after the coins arrives at B, there are exactly two seeds in each of the 2n2 triangles of the board. Determine all the values of n for which such scenario is possible. analytic geometrycombinatorics proposedcombinatorics