240 barrels of Wine, 5 Prisoners and 48 hours

You have 240 barrels of wine, one of which has been poisoned. After drinking the poisoned wine, one dies within 24 hours. You have 5 slaves whom you are willing to sacrifice in order to determine which barrel contains the poisoned wine. How do you achieve this in 48 hours?


The number system we generally use is base 10, or decimal system. I am assuming that the reader is familiar with ternary system (base 3) while reading this answer.

The pledge
Let the barrels be numbered from 1 to 240 (base 10)
This means in base 3, they will be numbered from 00001 to 22220.

There are 3 digits in ternary system, corresponding to 3 outcomes in the given problem for each slave. Assigning the digits to the outcomes,
Digit    Outcome
0          - the slave does not die
1           - the slave dies within the first 24 hours (00 to 24)
2           - the slave dies in the last 24 hours (24 to 48)

The turn
We give the wine from each barrel to the slaves, according to the following examples -
Barrel 139
If we take barrel number 139 (base 10) = 12011 (base 3)

3rd digit is 0, so don't feed slave 3 from this barrel.
1st, 4th and 5th digits are 1, so feed slave number 1,4 and 5 from this barrel at time t=0.
2nd digit is 2, so feed slave 2 from this barrel at time t=24.

Barrel 231
If we take barrel number 231 (base 10) = 22120 (base 3)

5th digit is 0, so don't feed slave 5 from this barrel.
3rd digit is 1, so feed slave number 3 from this barrel at time t=0.
1st, 2nd and 4th digits are 2, so feed slave number 1,2 and 4 from this barrel at time t=24.

The prestige
If we do that, then we can find which barrel is poisonous, based on which slaves die.
Example: If slave numbers 2 and 4 die in the first 24 hours, and slave 3 dies in the next 24 hours, then..
Barrel number 01210 (base 3)
That is, barrel number 48 (base 10) is poisonous.

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