Question 92
On each side of an equilateral triangle of side $n \ge 1$ consider $n-1$ points that divide the sides into $n$ equal segments. Through these points draw parallel lines to the sides of the triangle, obtaining a net of equilateral triangles of side length $1$. On each of the vertices of the small triangles put a coin head up. A *move* consists in flipping over three mutually adjacent coins. Find all values of $n$ for which it is possible to turn all coins tail up after a finite number of moves.
Illustration for $n=4$ (AI-generated):
Illustration for $n=4$ (AI-generated):