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* * * * * * * * * * * * * * * * The 16 points above lie in a plane on an equilateral triangular lattice. Certain sets of three points of the figure correspond to the vertices of equilateral triangles. Suppose you were to form all of the equilateral triangles possible, such that, for any given equilateral triangle, it must have its three vertices coincide with three of the 16 points. How many total equilateral triangles can be formed this way in the figure?

Thank you for posting, it was a really good exercise. Even more so because I was able to do it without any trial and error. After solving this, it somehow reminded me of your signature (not that I did anything great). "The greatest challenge to any thinker is stating the problem in a way that will allow a solution."