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FIGURE it out ! (Posted on 2004-09-10) Difficulty: 4 of 5
  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?

No Solution Yet Submitted by SilverKnight    
Rating: 3.3333 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): My take - correction | Comment 10 of 12 |
(In reply to re: My take by Richard)

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.

  Posted by Tristan on 2004-09-10 23:44:31
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