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.
10 red, 10 blue, 10 green matches are used to build a regular icosahedron, how many possible solutions are there?
2 answers
You decided to post them the day before the due date? :P