Daily Brain Teaser & Logic Puzzle

The Scenario

In the damp, decaying cellars beneath a tyrant's fortress sit 1,000 wooden barrels of wine. An enemy assassin successfully laced exactly one barrel with an undetectable, agonizing poison. The toxin is absolute: even a single drop will kill a person, but it acts with a cruel, delayed precision—showing zero symptoms for exactly 24 hours, after which the victim instantly collapses.

The tyrant's grand banquet begins in precisely 24 hours and one hour. He demands to know which specific barrel is poisoned so it can be discarded. To accomplish this, he forces 10 condemned prisoners to act as taste-testers.

You have only enough time for one single round of testing (since the toxin takes 24 hours to act). If you fail to identify the precise barrel, the tyrant will execute you, and hundreds of banquet guests will consume the poison anyway.

Is it mathematically possible to guarantee the identification of the single poisoned barrel out of 1,000 using only 10 testers in one attempt? If so, how do you mitigate the overwhelming statistical probability of catastrophe?

The Hint

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Consider how information is stored in digital systems. Each prisoner represents a binary state: alive (0) or dead (1). How many distinct combinations can 10 bits represent?

The Solution

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Yes, it is possible—though ethically horrifying.

To solve this within a single 24-hour window, you must utilize binary numbering:

1. Number the Barrels: Label each barrel from 1 to 1,000.
2. Convert to Binary: Express each barrel's number as a 10-digit binary sequence (since $2^{10} = 1,024$, which is greater than 1,000).
   • Barrel 1 = 0000000001
   • Barrel 2 = 0000000010
   • Barrel 3 = 0000000011
   • ...
   • Barrel 1,000 = 1111101000
3. Assign Prisoners to Bits: Line up the 10 prisoners, assigning each to one of the 10 binary positions (from Bit 1 to Bit 10).
4. Administer the Test: Mix a tiny drop from every barrel where a prisoner's corresponding bit is 1 into a single cup for that prisoner.
   • Prisoner 1 drinks a drop from every barrel whose binary code has a 1 in the 1st digit.
   • Prisoner 2 drinks from every barrel with a 1 in the 2nd digit, and so on.
5. Analyze the Tragedy: Exactly 24 hours later, observe which prisoners die.
   • If a prisoner dies, record their position as 1.
   • If a prisoner survives, record their position as 0.

The resulting 10-digit binary number translates directly back to the exact poisoned barrel number. (For instance, if only Prisoners 3, 5, and 10 die, the code is 0010100001, pointing inexorably to Barrel #161).

Naturally, this assumes no prisoner misplaces their cup, dies of sheer terror beforehand, or that the poison doesn't react unpredictably with mixed wines. In reality, relying on absolute precision under such grim stakes is a recipe for fatal failure.