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?

Thank you!

I think I know what I did wrong.  When I was considering type 3, I forgot to subtract double the number of pairs that are type 2.

So that means there are (n^4-n-n*(n-1))/4 unique type 3 squares.  This simplifies to n/4(n^3-n).

In total, there are n+n*(n-1)/2+n/4(n^3-n) squares.  This simplifies to n/4(n^3+n+2), which agrees with the other solutions.