MathDB

A

and

B

are two opposite vertices of an

n \times n

board. Within each small square of the board, the diagonal parallel to

AB

is drawn, so that the board is divided in

2n^{2}

equal triangles. A coin moves from

A

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

2n^{2}

triangles of the board. Determine all the values of

n

for which such scenario is possible.

Problem Statement