You are hosting a party where you will be serving 1000 bottles of wine, one of which, regrettably, contains poison. You also have 10 rats that are ready to sacrifice their lives for the cause of keeping your guests alive. The party begins in one hour and the rats show the effect of the poison, also in one hour. Your assignment: administer samples of the wine to the rats so that from their mortality you can pick out the bad bottle, or at least minimize the number you have to throw out.

This is an easy puzzle (an altered version appeared on "Car Talk"). My talk will be about the extension to the case of exactly two poisoned bottles, which has proven to be surprisingly hard.

This is joint work with Michael Kleber.