1990 OIM Problems/Problem 5

Problem

Let $A$ and $B$ be opposite vertices of a gridded board of $n$ by $n$ squares $n \ge 1$ , to each of which its diagonal of direction $AB$ is added, thus forming $2n^2$ equal triangles. A piece is moved along a path that goes from $A$ to $B$ formed by segments of the board, and each time it is traveled, a seed is placed in each of the triangles that accepts that segment as a side. The path is traveled in such a way that no segment is passed more than once, and it is observed, after traveling, that there are exactly two seeds in each of the $2n^2$ triangles of the board. For what values of $n$ is this situation possible?

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

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1990 OIM Problems/Problem 5

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