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Puzzle 2 | (Finding the poisoned juice)
You have 240 vessels of juice, one of which has been poisoned. After drinking the poisoned juice, one dies exactly 24 hours. You have 5 slaves whom you are willing to sacrifice in order to determine which vessel contains the poisoned juice. How do you achieve this in 48 hours?
Let us number the vessels with 5 digit numbers consisting of 0, 1 and 2. Let us number the slaves as 1, 10, 100, 1000, 10000.
Number 0 on a vessel represents the juice in the vessel will not be taken by the slave.
Number 1 on a vessel represents the juice in the vessel will taken by the slave on 1st day.
Number 2 on a vessel represents the juice in the vessel will be taken by the slave on 2nd day(after 24 hours).
The action corresponding to the digit in the unit place will be executed by slave numbered 1.
The action corresponding to the digit in the tenth place will be executed by slave numbered 10.
The action corresponding to the digit in the 100th place will be executed by slave numbered 100.
The action corresponding to the digit in the 1000th place will be executed by slave numbered 1000.
The action corresponding to the digit in the 10000th place will be executed by slave numbered 10000.
Example: Let us say the vessel is numbered 11201. The juice in this vessel is taken on the first day by the slave numbered 10000, 1000 and 1. It is taken on the second day by slave numbered 100. And it is not taken by the slave numbered 10.
So if the slave numbered 10000, 1000 and 1 die within first 24 hours, slave numbered 100 dies in the next 24 hours and the slave numbered 10 does not die, then the poisoned vessel has to be 11201.
This way total number possible is 3 * 3 * 3 * 3 * 3 = 3^5 = 243 vessels!! So with the help of 5 slaves and within 48 hours we will be able to find a poisoned vessel among 243 vessels.