The King has 1000 bottles of wine, exactly one of which is poisoned. Your job is to identify and throw out the poisoned bottle as quickly as possible by having the royal taste-testers drink the wines. Since the poison takes a little while to take effect, quickly means that the taste-testers only have the time to take a single drink—so you can’t have a single taste-tester go through the wines one by one. On the other hand, you can mix the wines in arbitrary ways before handing them out. What is the fewest number of taste-testers needed to identify the poisoned wine, and why?