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?

Charlie, from yours and other posters' supplied solutions it seems the interpretation was that a triangle was made up of three toothpicks.  Yet, as SilverKnight added the parenthetical comment -- (Reflections are considered different, but rotations are not.) -- I suspect he meant that EACH side of the triangle was made up of THREE toothpicks.

I have not yet found a solution, but I offer you and all other Perplexians a chance to re-address this.