Mathemat question

Question

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?

Answer 1

Taking advantage of the stated rules, we only need 10 testers. Mix up a 50/50 batch of 500 wines and give it to one taster. If the taster gets sick or dies, we know the bad wine is in that batch and can eliminate the other 500. But if the taster does not get poisoned, the poison is in the other batch. Proceed similarly for 250, 125, 63, 32, 16, 8, 4, 2, and 1. This will require 10 testers and we should expect 5 will be poisoned. Good day to all!

Answer 2

To play it safe; 1 taster-1shot. So 1000 tasters are needed.