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I think Ment's solution is correct. I figured it out like this: One condemned person can identify the poison in two barrels. Give one person a taste from one barrel; if they die, the poison is in that barrel; if not, it's in the other. Two people in four barrels. The first drinks from the first barrel, the second from the second, both from the third, and neither from the fourth. Therefore, the third barrel is among eight. Four people in sixteen. Five people in thirty-two. Or, the number of barrels is 2ⁿ, where n is the number of condemned people. Therefore, the first time, we'll select 5 groups of 16 barrels each, and one condemned person will drink from each. If only one dies, the poison is definitely in one of those 16 barrels, and the remaining four are enough to figure out which one. That's 16 * 5 = 80 barrels. The number of combinations of five groups of two barrels each, with two prisoners drinking from all possible combinations, is 5!/(2!*3!) = 120/(2*6) = 10 groups of 8 barrels - 80 barrels. If two prisoners die, the remaining three are enough to identify the poison in the group of 8 barrels. The number of combinations of five groups of three barrels each, with four barrels in each, is 5!/(3!*2!) = 10 groups of 4 barrels - 40 barrels. If three die, the remaining two are enough to identify the poison in the four barrels. The number of combinations of five groups of four barrels each, with two barrels in each, is 5!/(4!*1!) = 5. In total, 5 * 2 = 10 barrels. If four die, even one is enough to identify the poison in the two barrels from which all four drank. In one of them, they will all drink the poison together. If they all die, the poison is in that barrel, which is one more barrel. So, let's calculate how many barrels we've already used: 80 + 80 + 40 + 10 + 1 = 211 barrels. If none of them die, the poison is in the remaining 29 barrels, and as shown above, five people can identify the poison in 32 barrels - let alone 29. So, the poison can be identified in a total of 211 + 32 = 243 barrels. Ment, you're the one who came up with the solution. You're great. I'll try to understand your solution again.

Yes, I calculated the outcomes incorrectly. There are 20 possible outcomes because the order matters, and I thought it didn't.

Ment, go ahead and guess. You're doing great. I'll try to understand your solution again.

I can explain it again. In short, the main idea is to give the barrels to the prisoners in such an order that each barrel has a unique "death trail." And based on how the prisoners died (if they died at all), we could determine which barrel poisoned them.
I consider the combination of this death trail to be a simple combinatorial problem, considering that the prisoners who have already died reduce the number of options for a repeat experiment (which takes place after 12 hours).
C5^5, for example, is the number of ways to give the contents of a barrel to five prisoners out of five. It is equal to one.
C2^5 is the number of ways to give one barrel to two out of five prisoners.
Perhaps if I hadn't been lazy and written the formulas in a formula editor and somehow displayed them, they would be easier to understand...
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However, your explanation seems to be equivalent.

It's not really that complicated.
The death of the prisoner or their life after the trial is an indicator (yes or no), and we collect a unique combination of indicators.

Warehouse rental used to be a significant burden. In particular, Scottish companies that produced whiskey suffered. But one company in the 19th century found an original solution to the problem. In fact, they even named one of their whiskey varieties after the solution to this problem... Australian.

Write a word with a doubled consonant that is the solution to the problem.

This is a trivia question.

Gentlemen, if anything is unclear, I initially made a mistake in the wording, and this is important, so please reread it.

We can recall everything we know about Australia: convicts, kangaroos, winter in summer, most cities are ports. (also rabbits and theater, but that's not the era yet)
And about Scotland: thistle, whiskey (doesn't make sense), kilt, cello, an inflated sense of sovereignty...

Added 2 minutes later
At first, I thought about something related to ships, like storing them directly in the holds, but it seems that would be even more expensive.

Is that a prison or something? )))))))

Is that Tyuragga? )))))))

No.

I can't think of any words with doubled consonants, except for the capital of Australia.)
It's easier to bury whiskey, for example, in some sand, like on a beach. It's cheap and effective.

It's easier to bury whiskey, for example, in some sand, like on a beach. It's cheap and effective.

That's where all these stories about pirates and treasures come from! You find a map with the location of a whiskey stash buried in the sand – and you're set for life...

Initially, I thought about something related to ships, like storing it directly in the holds, but it seems that would be even more expensive.

What if the land was expensive for a warehouse, and it was cheaper to store it on a ship? )

Although there are many islands where they could also have transported the whiskey.

I can understand the difficulty with warehouses. Whiskey is essentially moonshine that is aged for several years. I don't know about strictly maintaining temperature and humidity, but there must be some restrictions.

I can understand the difficulty with warehouses. Whiskey is essentially moonshine that is aged for several years. I don't know about strictly maintaining temperature and humidity, but there must be some limitations.

Some kind of swamp or bog.

peat bog

No, not that. Either provide specific examples, because there's always a chance that I don't know something.