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A king has 1000 bottles of water, exactly one of which is poisoned. Servants die the day after consuming the poison. The king holds a party and has his servants drink the bottles. The next morning, the king finds out which servants are dead. What is the minimum number of servants that the king needs at the party to determine which bottle is poisoned?
The king needs 10 servants. Label the bottles in binary: 0000000000, 0000000001, 0000000010, 0000000011, ... The 1st servant drinks all bottles where the 1st digit is 1, not 0. The 2nd servant drinks all bottles where the 2nd digit is 1, not 0. The 3rd servants drinks all bottles where the 3rd digit is 1, not 0. The rest of the servants drink similarly. After finding out which servants are dead, the king can match the unique binary number to determine which bottle is poisoned.
You need 6 servants.
Since the king has to wait to the next morning to know, it will require 999 servants.
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