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Thread: How Many Combinations are Possible for Octahedron?

  1. #1
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    How Many Combinations are Possible for Octahedron?

    Tough question.
    Last edited by bennyJ; 04-23-2018 at 01:51 PM.

  2. #2
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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?
    "Unique Answers Don't Care How You Find Them." - Many may have said it, but I hear it most from me.

  3. #3
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    Quote Originally Posted by bennyJ View Post
    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?
    "Unique Answers Don't Care How You Find Them." - Many may have said it, but I hear it most from me.

  4. #4
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    Start with the three 2-6 patterns and explore the 3-5s.
    "Unique Answers Don't Care How You Find Them." - Many may have said it, but I hear it most from me.

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