290.A Thousand Bottles, One Poisoned
★★★puzzlesTower Research Capital
You have 1000 bottles of wine, exactly one of which is poisoned. You may give each test rat any mixture of bottles, but you can run the test only once and read the results only once afterwards; a rat that drank from the poisoned bottle reacts, and the others do not. What is the minimum number of rats needed to identify the poisoned bottle with certainty?
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Each rat ends up as a yes/no readout, so the rats jointly spell out a binary number. How many bits do you need to label 1000 bottles?
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