How about this (choices are random):
1) Choose two bottles and one device
2) Measure the two. If they're the same, choose another device, if they're different, choose another bottle
When bottles appear identical, make more measurements with different detectors on them (there's no way around doing that)
When a device has accumulated n/2 0 or 1 measurements, the remainder are the opposite number (call this column constraint as per your table)
When selecting the next detector, prefer the one that is closest to meeting the column constraint (otherwise choose randomly)
Sorry about the poor formatting of the algorithm but I'm typing on my phone and don't want to submit something AI generated
I was trying to figure out the runtime of this…it captures your best case scenario, and I think the worst as well, but what about the average?
Lol