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# Colorful cubes

Best Answer Prime, 15 March 2013 - 02:31 PM

Actually, we should split the difference and go with 27.

Spoiler for missed symmetry

Go to the full post

11 replies to this topic

### #1 bonanova

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Posted 13 March 2013 - 12:51 PM

I have 12 sticks and I have painted 8 of them red and 4 of them blue.

I then glued the sticks together to form the frame of a cube.

So now I'm wondering how many total ways could I have assembled the sticks into cubes that could be distinguished from each other.

Assume I can pick up the cube and move it around any way I like, but I cannot deform or re-assemble it

• 0

Vidi vici veni.

### #2 BobbyGo

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Posted 13 March 2013 - 02:49 PM

Spoiler for guess

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### #3 k-man

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Posted 13 March 2013 - 03:38 PM

Spoiler for I found

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### #4 bonanova

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Posted 14 March 2013 - 04:43 PM

Is there a consensus?

Can you construct the possible configurations in groups, using words or a sketch?

My first try to solve this was to take 12 things 4 at a time, then remove the symmetrically equivalent solutions.

But I kept removing too many cases. Next try was to group the edges and distribute 4 blues among the groups.

I'm not convinced yet of my answer.

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Vidi vici veni.

### #5 k-man

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Posted 14 March 2013 - 08:07 PM

Spoiler for my approach

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### #6 bonanova

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Posted 15 March 2013 - 04:47 AM

Spoiler for my approach

Very nice approach. Nice categories and elimination of symmetric cases.

Spoiler for I have one question

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Vidi vici veni.

### #7 Prime

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Posted 15 March 2013 - 09:42 AM

Good spacial vision exercise. Without looking at an actual model of a cube, I am not sure I got it right.

Next, let's try it in 4-D.

Spoiler for connections

Edited by Prime, 15 March 2013 - 09:50 AM.

• 0

Past prime, actually.

### #8 bonanova

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Posted 15 March 2013 - 11:20 AM

Spoiler for my approach

Very nice approach. Nice categories and elimination of symmetric cases.

Spoiler for I have one question
Never mind, I think I see two cases after all. I think that's it.
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Vidi vici veni.

### #9 Prime

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Posted 15 March 2013 - 11:54 AM

Good spacial vision exercise. Without looking at an actual model of a cube, I am not sure I got it right.

Next, let's try it in 4-D.

Spoiler for connections

Correction: It is 10 arrangements for the variation 4.

Then the answer is the same as K-man has found.

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Past prime, actually.

### #10 Prime

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Posted 15 March 2013 - 02:31 PM   Best Answer

Actually, we should split the difference and go with 27.

Spoiler for missed symmetry

• 0

Past prime, actually.

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