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This isn't a complete answer, just something to get you started. I think it would useful to think of a function, say countOpenGates, which would look something like this: countOpenGates[mat : {{(0 | 1) ..} ..}] /; MatrixQ[mat] := Total[Times @@@ mat] If "open" means "all subunits are open", i.e. have value 1, then their product is 1. And if any ...

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