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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)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: # 1-4, possible errors | Comment 9 of 11 |
(In reply to # 1-4, possible errors by Tristan)

Tristan - Thanks for saving me.  I was about to commence #4 using brute force. I was at the point of coloring three sides when your post arrived.

While I will let someone else find the flaw in my logic for #3 (94 vs 96), I worked through Charlie's answer for #2 and concur with his answer.

In both cases Polya's theory is 2 variations higher . . .

  Posted by Leming on 2006-03-06 09:14:45
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