Suppose there is a cube and we can colour the cube's faces

1. Apr 8, 2006

heman

suppose there is a cube and we can colour the cube's faces with only two colours ..i.e.
black and white ,,how many different patterns are possible....

2. Apr 8, 2006

Muzza

Seems like the perfect place to apply Burnside's theorem (about orbits).

3. Apr 8, 2006

pallidin

Here's my take:

How many faces are on a cube? 6
How many allowable variations per face? 2
Combinations possible: 2*2*2*2*2*2 =64

Oh, but wait, this is not a strictly linear situation!
My mind is melting.

4. Apr 8, 2006

Rach3

all white: 1 version
1 black side: 1 version
3 black: 2 versions (three in a row/three sides with common vertex)
and by symmetry...
4 black = 2 white: 2 versions
5 black: 1 version
6 black: 1 version

Total... 10 indistinguishable ways.

5. Apr 10, 2006

heman

Thanks Rach,,
i am clear with how that value 10 comes..but actually the theory related with Polya's theorem is n't much clear to me...i am actually not clear with how they have derived the formula.