# Possible variations in a bilateral symmetric system

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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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 $2^{3\times 5} = 32768$.