You have a handful of coins spread out on the table in front of you. You put on a blindfold, and someone flips over some of the coins, then tells you how many are showing heads. You can now move the coins around and turn them over.
Each day you must take an A pill and a B pill. After you tap an A pill into your palm you inadvertently tap two B pills into your hand. The A and B pills are indistinguishable. The pills are expensive and you must not overdose. Can you still use the pills you have mixed up?
You and two other logicians (Alice and Bob) are in a room. A controller comes in and paints a spot onto each of your foreheads. You can each see the others’ spots (Alice and Bob both have black spots) but not your own. The controller tells you all that all the spots are black or white, and at least one of you has a black spot. Then the controller asks if anyone knows the colour of their spot. Everyone says no. The controller asks the same question a second time: again, everyone says no. The controller then asks the same question a third time. What do you say now?