Question 88
Let $n$ be a positive integer. Equilateral triangle with the side length $n$ is divided into $n^2$ smaller equilateral triangles with the side length $1$ (Fig. 31 shows this division for $n=10$). Initially, one of these triangles is blue and the rest are yellow. The blue triangle is guaranteed not to have any common points with the boundary of the big triangle. It is allowed to consider any of $n^2$ equilateral triangles and change its color together with the colors of its neighbors (blue changes to yellow, yellow changes to blue). Is there any $n$ for which it is possible to make all $n^2$ equilateral triangles of the same color?
(Arsenii Nikolaiev)
(Arsenii Nikolaiev)