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Can someone shed a light on how to solve something like this? I've been looking for permutations but so far I found it very confusing. As I'm not at home atm, I can't reach for my math books either for an answer. Maybe you can help?

Given:

  • a 5x5 grid
  • each cell can have 2 possible values: 0 or 1
  • each resulting grid "layout" must be bilateral-symmetric ( on the vertical axis )

Question: What's the number of possible variations?

Thanks a lot!

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1 Answer 1

up vote 1 down vote accepted

You only need to consider all possible $3\times 5$ grids, from which you can get a symmetrical $5\times 5$ grid by mirroring the first two columns about the third. Each cell in the $3\times 5$ grid has 2 possibilities, independent of all the others, so the total number of possibilities is $2^{3\times 5} = 32768$.

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Thanks Rahul for your very fast and correct answer! I figured out I could drop 2 columns, but the rest of the calculations was more difficult for me. Again thanks! –  Webdevotion Sep 29 '10 at 22:10

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