Quiz

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.