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On each side of an equilateral triangle with side length $$n$$ units, where $$n$$ is an integer, $$1\le n\le 100$$, consider $$n-1$$ points that divide the side into $$n$$ equal segments. Through these points, draw lines parallel to the sides of the triangle, obtaining a net of equilateral triangles of side length one unit. On each of the vertices of these small triangles, place a coin head up. Two coins are said to be adjacent if the distance between them is $$1$$ unit. A move consists of flipping over any three mutually adjacent coins. Find the number of values of $$n$$ for which it is possible to turn all coins tail up after a finite number of moves.
Correct Answer: 67
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