A Thousand Bottles, Three Rounds

A cellar holds 1000 bottles of wine, exactly one of which is poisoned. A taster who drinks any amount from the poisoned bottle dies at the end of the round in which they drank; a taster who has not drunk the poison survives. A taster can drink from any number of bottles in a round, and survivors can be used again in later rounds. You have three rounds, and you see who died at the end of each round before planning the next. What is the minimum number of tasters that is guaranteed to find the poisoned bottle?

• combinatorial games
• pigeonhole

Source: Version of the 'poisoned wine / pigs' puzzle popularised in interview collections and on LeetCode; no traceable original source. Statement written for AxiomIQ.