How Many Combinations are Possible for Octahedron?

bennyJ

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Tough question.
 
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tkhunny

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Yes, it appears to want you to consider all types of symmetry.

All White - Only one way to do that.
All Black - Only one way to do that.
One White (same thing as 7 black) - You can paint any one of the 8 surfaces, but various symmetries show they are all the same. - Just one distinct way.
One Black (7 white) - Again, just one.
Two White (6 black) -- What say you? More than one distinct way?
 

tkhunny

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For two triangles, I think three patterns are possible for each color. So, we would have three for white and three for black.
I have to agree with this. We have:

With reference to the provided drawing:
1) Adjacent horizontally
2) Adjacent vertically
3) No Adjacent

Well, that covers a lot of he problem. Why quit now?

8W0B - 1
7W1B - 1
6W2B - 3
5W3B - ?? - Still some thinking to do.
4W4B - ?? - Still some thinking to do.
3W5B - ?? (by symmetry)
2W6B - 3 (by symmetry)
1W7B - 1 (by symmetry)
0W8B - 1 (by symmetry)

What say you of 5W3B?
 

tkhunny

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Start with the three 2-6 patterns and explore the 3-5s.
 
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