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If the initial test size is 64 and contains a positive, split into two groups of 32 and test each. Continue splitting and testing when a positive is encountered.

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Yeah, but this version is not necessarily optimal. If you have 4 positive samples, then you will test 2+2+1+1+1+1 = 8, instead of 4 in the naive case.

It feels like a problem for information theory.

I didn’t say it was optimal, but it is a huge improvement on doing 64 tests for 64 samples.

Oh, sure!

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