Puzzle Details:

240 Barrels of Wine, 5 Slaves and 48 hours Puzzle || 240 Barrels of Wine, 5 Prisoners and 48 hours Puzzle Details: 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). a number can be represented in multiple ways, such as base10, base2,
base8, similarly a number can also be represented, in base 3.

base 3 uses only, 0 1 and 2 to represent any number. If you
are not familiar this is easy, binary system uses 0 and 1 to represent the
number whereas ternary system uses 0 1 and 2 to represent the number. conversion
technique remains same for binary and ternary systems.

Let the barrels be numbered from 1 to 240, this is
represented in base 10. The same number can be represented in base 3 from,
00001 to 22220. Here 00001 represents number 1 whereas as 22220 represents
240. hence, there are 3 digits in ternary system, corresponding to 3
outcomes, in the given problem for each slave.

let’s assign the digits to the outcomes, when it is 0 the
slave does not die, when 1 the slave dies within the first 24 hours, when
2 the slave dies in the last 24 hours

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) |

now arrange 5 slaves and let’s give the wine from each
barrel to the slaves, convert each number associated with the barrel to its
equivalent base 3 presentation which will be 5-digit representation.

**Assume for Barrel 139**

here barrel number is 139 which is represented in base 10
and its equivalent base3 representation is 12011, you can use online calculator
to convert the number from base10 to base 3 representations.

**HERE**

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.

if slave 1 4 and 5 dies at first 24th hour and slave 2 dies at 48th hour then barrel 139 is poisonous.

**Consider one more Barrel 231**

Here barrel number is 231 which is represented in base 10 and its equivalent base3 representation is 22120. 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.

if slave 3 dies at first 24th hour and slave 1 2 and 4 dies at 48th hour then barrel 231 is poisonous.

with these simple steps we can find which barrel is poisonous, based on which slaves die.

one more 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) which is base 3 representation and its equivalent base 10
representation is 48 hence barrel 48 is poisonous in this case.

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