The pattern of possible numbers of non-congruent triangles for different size dot grids.

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If I have four dots, arranged in two rows of two to make a square, and I draw a triangle by joining three of the dots, there are four triangles I can draw, but they are all the same shape (they are congruent). If I start with nine dots, arranged in three rows of three to make a square, how many different (non-congruent) triangles is it possible to draw? What if I start with a square formed of sixteen dots? Can you generalise for n2 dots?