Problem
Three
super spies are caught sending sensitive information to an enemy state.
These three double agents are apprehended and taken out to a remote
spot in the woods. They are told that one of them will be part of a
prisoner exchange, and the other two will be executed.
To
decide who lives, the guards decide to play a game. They show the
captives eight stamps: four red, and four green. They then blindfold the
three men and stick two stamps to each of their foreheads. One of the
guards puts the remaining two stamps in his pocket.
The
guards then take the blindfolds off the captives, who can each see the
stamps on the other two men's heads, but not the two stamps on their own
head, and not the two stamps in the guard's pocket. These spies are
highly intelligent—they're perfect logicians who know they can count on
each other to correctly and quickly interpret the information they have.
The
guard captain tells them that the first man to figure out the color of
the stamps on his own head will be used for the prisoner exchange, and
the other two will be executed. If anyone guesses wrong, they will be
shot dead on the spot.
The captain then asks the spies in order if they know what color stamps they have on their head. The answers are as follows:
- A: "No."
- B: "No."
- C: "No."
- A: "No."
- B: "Yes."
Spy B answers correctly. What color are the stamps on his head, and how does he know?
