A Bottle of Poisoned Wine

Discrete Mathematics Level pending

Once upon a time there was a king who had owned 1000 bottles of wine, which were going to be used to treat his guest at a huge party. However, 22 hours before the party, the king received a message saying that one (and only one) of the a thousand bottles was poisoned. The poison was specially designed so that the person poisoned would not show symptom until 20 hours later.

The king had tens of thousands of slaves (sorry if you are against slavery) working for him on a construction project, all of whom the king could use to test the poisoned bottle. Taking out laboring slaves, however, would make the project progress slower; therefore, the king wanted as few slaves a possible.

Question: what is the minimum number of slaves needed to test the poisoned bottle? Assuming the process of drinking sample wine takes very little time compared to 20 hours.

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