There is a king who wants to throw a party in 48 hours and he wants to serve a total of 700 barrels of wine at the party. Unfortunately, he knows that one of the barrels has been poisoned and he does not know which one. When consumed, the poison takes **up to 24 hours** to kill.

In order to determine which barrel the poison is in, the king wants to use his prisoners as taste testers. What is the fewest number of prisoners that he needs to test the barrels in 48 hours?

Note: The king doesn't care about the number of prisoners that die. He just wants to minimize the number of prisoners used.

**Assumption**: The time it takes for the poison to kill is unknown, and may differ from prisoner to prisoner, from case to case. We only know that it always kills a person within 24 hours after consumption.

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