Question

A king has 1000 bottles of wine and one has been poisoned. Even a sip of the poisoned wine is enough to kill a person.

The king asks the royal jailor to identify the poisoned wine bottle by testing them on the prisoners.

It takes up to 24 hours for the poison to take effect. There are unlimited number of prisoners at the jailer’s disposal. What is the minimum number of prisoners the jailer needs to identify the poisoned wine bottle in 24 hours?

Answer 1

The minimum number of prisoners the jailer needs to identify the poisoned wine bottle in 24 hours is 10. The jailer can assign each bottle a number from 1 to 1000 and then use a binary representation to test the bottles. Each prisoner will drink from the bottles corresponding to the 1's in their binary number.

Step-by-step explanation:

The minimum number of prisoners the jailer needs to identify the poisoned wine bottle in 24 hours is 10.

To determine this, the jailer can assign each bottle a number from 1 to 1000 and then use a binary representation to test the bottles. Each prisoner will drink from the bottles corresponding to the 1's in their binary number. For example, if a prisoner has the binary number 1010, they will drink from bottles 1, 3, and 4. By the end of 24 hours, if any prisoner dies, the bottle they drank from is poisoned.

This method allows the jailer to test all 1000 bottles with a minimum number of prisoners, as the binary representation can cover all possible combinations.