There are $n$ large bottles of wine, out of which $n-1$ have been poisoned.
However, consuming a single bottle does no harm, it requires all $n-1$ bottles (or small samples of them) to be consumed by the same person to get poisoned. A person dies of poisoning only at the end of the day. The poison consumed by a person remains in his/her body forever, but does not activate until all the other poisons are also consumed.

You have $100$ people and unlimited time for performing the tests.

What is the largest value of $n$ for which you can identify the good bottle?

P.S. This is not a , nor is it a one.


Anyone who has drank fewer than $n-1$ bottles is guaranteed not to be poisoned, so we get no information from that.

Anyone who drinks $n$ bottles is guaranteed to be poisoned, so this also gives no information.

The only situation that does provide information is if someone drinks exactly $n-1$ bottles. If they die, the good bottle is the one they didn't drink, otherwise it is one of the bottles they did drink. At this point, the person is useless for getting any more information (repeating a drink is pointless, and drinking the last bottle is guaranteed death).

Each person can only rule out one bottle, so the maximum $n$ is $101$.


Well, as a first guess, n = 101.

Just line all 100 people and all 101 bottles up and have each person drink from all but bottle number x, where x is their number in line. Wait a day. If a person y dies, then y was the good bottle and they drank every other poison. If nobody dies, then 101 was the good bottle, since it's the only one everybody drank from.


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