The police commissioner hired a mathematician to help at a crime scene. At the scene were between 100 and 200 glasses of wine. Exactly one glass was poisoned. The police lab could test any sampling for poison. A group of glasses could be tested simultaneously by mixing a sample from each glass. The police commissioner desired only to minimize the maximum possible tests required to determine which exact glass was poisoned.

The mathematician started by asking a detective to select a single glass at random for testing. "Wouldn't that waste a test?", the detective asked. "No, besides I'm in a gambling mood.", the mathematician replied. How many glasses were there?

I want t o guess 111. Just a guess, though. Do they (the mathematician and detective) know how many glasses there were?