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 FIGURE it out (2) (Posted on 2004-09-25)
1. How many different tetrahedrons can be produced by coloring each face a solid color and using n different colors? (Two tetrahedrons are the same if they can be turned and placed side by side so that corresponding sides match in color.)

2. How many cubes with n colors?

 No Solution Yet Submitted by SilverKnight Rating: 4.5000 (4 votes)

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 Numbers | Comment 10 of 14 |

Based on the corrected formulae:

`  n  tetrahedron   cube  1       1           1  2       5          10  3      15          57  4      36         240  5      75         800  6     141        2226  7     245        5390  8     400       11712  9     621       23355 10     925       43450 11    1331       76351 12    1860      127920 13    2535      205842 14    3381      319970 15    4425      482700 16    5696      709376 17    7225     1018725 18    9045     1433322 19   11191     1980085 20   13700     2690800 21   16611     3602676 22   19965     4758930 23   23805     6209402 24   28176     8011200 25   33125    10229375 26   38701    12937626 27   44955    16219035 28   51940    20166832 29   59711    24885190 30   68325    30490050`

using

10   for N=1 to 30
40     Tet=N+3*fnComb(N,2)+3*fnComb(N,3)+2*fnComb(N,4)
50     Cub=N+8*fnComb(N,2)+30*fnComb(N,3)+68*fnComb(N,4)+75*fnComb(N,5)+30*fnComb(N,6)
60     print using(3,0),N;using(8,0),Tet;using(12,0),Cub
90   next
99   end
100   fnComb(N,R)
110   local Ans
120   if R>N then Ans=0:else Ans=combi(N,R)
130   return(Ans)

 Posted by Charlie on 2004-09-25 17:52:53

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