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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: Solution for Squares | Comment 5 of 12 |
(In reply to Solution for Squares by nikki)

"abcd: 2*[n!/(4!(n-4)!)] = 1/12*n*(n-1)*(n-2)*(n-3) (the "times 2" is because reflections are different)"

With 4 colors, that comes out to only 2 possible orders, presumably abcd and dcba.  But there are 6 possible orders: abcd (a between b and d), acbd (a between c and d), abdc (a between b and c) and their reversals.



  Posted by Charlie on 2004-09-10 16:44:33
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