You are on a strict medical regimen that requires you to take two types of pills each day. You must take exactly one A pill and exactly one B pill at the same time. The pills are very expensive, and you don’t want to waste any. So you open the bottle of A pills, and tap one out into your hand. Then you open the bottle of B pills and do the same thing – but you make a mistake, and two B pills come out into your hand with the A pill. But the pills are all exactly identical. There is no way to tell A pills apart from B pills. Is it possible to satisfy your regimen and take exactly one of each pill at the same time, without wasting any pills?