Magnus_RM

(Simplified version an old problem, here with 16 bottles instead of 1000)

A king has 16 bottles of wine of which one (unknown) has deadly poison in it. If one drinks even a drop of the poisoned wine one will die within three weeks.

The king will have a party in four weeks and wants to figure out before that which bottle is poisoned so that he can discard it.

He has some servants who he is willing to sacrifice in order to test this.

The typical solution here is to use the binary system so that you need to sacrifice 4 servants in order to test 16 bottles.

There is a problem though, namely the fact that people sometimes die for other reasons. For example if the the 3 first servants die, then that could be because bottle 7 was poisoned, but it could also be bottle 5 and that servant 2 died for some other reason. This would lead to discarding bottle 7 when it is actually bottle 5 that is poisonous, so a fatal mistake.

My question is, how can one improve the certainty? How many servants are needed with your improved method?