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Black and White Solids (Posted on 2006-03-04) Difficulty: 4 of 5

1)I have lots of black and white squares that can be joined together to make cubes. How many distinguishable cubes can I make?

2)Now I try it with triangles and regular octahedrons?

3)Now pentagons and regular dodecahedrons?

4)Triangles again but making regular icosahedrons!?

Note: Distinguishable means rotations are the same, but reflections are not.

No Solution Yet Submitted by Sir Percivale    
Rating: 4.0000 (1 votes)

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re: #3 - dodecahedron - Part 2 - correction | Comment 7 of 11 |
(In reply to #3 - dodecahedron - Part 2 by Leming)

Error in previous calculation.  Any dodecahedron with six of one color, would automatically take into account the possibilities of six of the other color.

There are 36 variations with less than six black sides, and 22 variations with exactly six black sides.

New answer = (2 x 36) + 22 = 94 variations

  Posted by Leming on 2006-03-04 21:16:08
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