Summer Problem Solving Marathon Solution #27

There are eight triangles of minimal size in the diagram. For convenience, number these 1 through 8, reading left to right on the top half of the square and then left to right on the bottom half of the square.

There are four triangles each made up of two of the smallest triangles -- one made from triangles 2 and 3, one made from 4 and 8, one made from 6 and 7, and one made from 1 and 5.

There are no triangles of size 3. There are four triangles of size 4 -- one made of triangles -- one made from triangles 1, 2, 3, and 5; one made from triangles 2, 3, 4, and 8; one made from triangles 4, 6, 7, and 8; and one made from triangles 1, 5, 6, and 7.

There are no triangles of any other size. Thus there are a total of 8 + 4 + 4 = 16 triangles in the diagram.