1. With an unlimited supply of toothpicks of n different colors, how many different triangles can be formed on a flat surface, using three toothpicks for the sides of each triangle?
   (Reflections are considered different, but rotations are not.)

2. How many different squares?

"T = n + n*(n-1) + 1/3*n*(n-1)*(n-2) = n^3 + 2n = n/3*(n^2 + 2)"

I some how lost my 1/3 factor, and then it appeared again.  If that confused you, I apologize.  It should read:

T = n + n*(n-1) + 1/3*n*(n-1)*(n-2) = 1/3(n^3 + 2n) = n/3*(n^2 + 2)