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Titleist
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stoolfi
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stoolfi
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stoolfi
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And, titleist, why are you sitting this one out?

I'd like to hear your reasoning for agreeing/disagreeing...
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Titleist
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stoolfi
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!
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I think the answer should be 5!/2 = 60
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stoolfi
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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.
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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.



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