Fish Switch: Clarence’s favorite joke is to switch the signs on the fish barrels. Today he mixed up the signs on the carp barrel, the catfish barrel, and the carp-and-catfish barrel, deliberately hanging each sign on the wrong barrel. Clarence will let you see only one fish, but it can be from any barrel you choose. Using only this information, can you restore the signs to their rightful barrels? How?
Here’s how: Start by choosing a fish from the “carp-and-catfish” barrel. Since every barrel is incorrectly signed, you already know that this barrel cannot contain “carp-and-catfish”… it has to contain only one type of fish. Say you drag out a carp… you can correctly place the carp label on this barrel. Next ask, what fish are in the barrel labeled “catfish”? They cannot be carp, and the can’t be cat-fish either or the label would be correct. They must be “carp-and-catfish”. The “carp” barrel,then, must contain the catfish. That clever Clarence!