# Problem 163: Cross-hatched triangles

![graphic](img163.gif)

Consider an equilateral triangle in which straight lines are drawn from
each vertex to the middle of the opposite side, such as in the size 1
triangle in the sketch below. Sixteen triangles of either different
shape or size or orientation or location can now be observed in that
triangle. Using size 1 triangles as building blocks, larger triangles
can be formed, such as the size 2 triangle in the above sketch.
One-hundred and four triangles of either different shape or size or
orientation or location can now be observed in that size 2 triangle. It
can be observed that the size 2 triangle contains 4 size 1 triangle
building blocks. A size 3 triangle would contain 9 size 1 triangle
building blocks and a size n triangle would thus contain n2 size 1
triangle building blocks. If we denote T(n) as the number of triangles
present in a triangle of size n, then T(1) = 16 T(2) = 104 Find T(36).