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Solutions

The number of triangles:
single small triangles = 16
Big triangle comprises of all 16 elements = 1
Triangles with 4 elements (1,2,3,4), (2,5,6,7), (4,7,8,9), (6,7,8,13), (5,10,11,12), (7,12,13,14), (9,14,15,16) = 7
Triangles with 9 elements (1,2,3,4,5,6,7,8,9), (2,5,6,7,10,11,12,13,14), (4,7,8,9,12,13,14,15,16) = 3
Total = 16+1+7+3 =27