10 red, 10 blue, 10 green matches are used to build a regular icosahedron, how many possible solutions are there?

Answer 1

first, how many edges are there on an icosohedron?

Then, since there are duplicates, you will have

30Pn/(10!10!10!) ways to arrange the toothpicks.

But, there are rotational symmetries which make multiple solutions really the same thing.

Answer 2

You decided to post them the day before the due date? :P