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 FIGURE it out ! (Posted on 2004-09-10)
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)

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 re: solution -- numbers | Comment 7 of 12 |
(In reply to solution by Charlie)

For squares, following the formula I gave, the following table breaks down the possibilities:

` n   4-col  3-col  2-col  1-col  total 1      0      0      0      1      1 2      0      0      4      2      6 3      0      9     12      3     24 4      6     36     24      4     70 5     30     90     40      5    165 6     90    180     60      6    336 7    210    315     84      7    616 8    420    504    112      8   1044 9    756    756    144      9   166510   1260   1080    180     10   253011   1980   1485    220     11   369612   2970   1980    264     12   522613   4290   2574    312     13   718914   6006   3276    364     14   966015   8190   4095    420     15  1272016  10920   5040    480     16  1645617  14280   6120    544     17  2096118  18360   7344    612     18  2633419  23256   8721    684     19  3268020  29070  10260    760     20  40110`

 Posted by Charlie on 2004-09-10 16:55:57

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