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Director
Joined: 14 Oct 2003
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http://www.manhattangmat.com This week, I'm going to sit [#permalink]  05 Jan 2004, 09:23
http://www.manhattangmat.com

This week, I'm going to sit back on this one.
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Director
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[#permalink]  05 Jan 2004, 09:39
Lets call the colors R O Y G B V

Opposite R, we can have O Y G B V

For each case, there are 3 ways to configure the remainder.

For example, if R is opposite O, than we can have Y opposite G, Y opposite B, or Y opposite V.

5*3 is 15.

So I'm certain that the answer is a multiple of fifteen, but I don't know why 30 or 60 would be correct.

I doubt they made a mistake, but I'm a bit befuddled.
Director
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[#permalink]  05 Jan 2004, 09:48
To add to my last post, I would think that the configuration of opposite sides can be the only "variant" (for lack of a better word), since any two cubes with opposite sides configured the same way can be reoriented to look alike...
Director
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[#permalink]  05 Jan 2004, 09:49
And, titleist, why are you sitting this one out?

I'd like to hear your reasoning for agreeing/disagreeing...
Director
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[#permalink]  05 Jan 2004, 09:51
stoolfi wrote:
To add to my last post, I would think that the configuration of opposite sides can be the only "variant" (for lack of a better word), since any two cubes with opposite sides configured the same way can be reoriented to look alike...

You definitely have a knack for solving these types of problems stoolfi! I'll go with what you say - I've run to the same conclusion. I'll report back after lunch!
Senior Manager
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[#permalink]  05 Jan 2004, 10:07
I think the answer should be 5!/2 = 60
Director
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[#permalink]  05 Jan 2004, 11:44
This:

" since any two cubes with opposite sides configured the same way can be reoriented to look alike..."

is wrong.

Consider a cube with O and B on East and West

We need to have V Y R G ordered in the middle. Their positions are unimportant, but their order, relative to one another, is.

Six ways to arrange them in a circle.

Times five E-W orientations

equals thirty.

Crap.
Director
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[#permalink]  05 Jan 2004, 11:58
Crap again.

Forgetting anything about orientation, there are 6! ways that the cube can be painted.

There are 24 ways to orient the cube (six sides facing you, four edges per side)

6!/6*4

30.
[#permalink] 05 Jan 2004, 11:58
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