Three philosophers are taking a nap under a tree. While they’re asleep, a small boy smears their noses with red berries. When they awake, they each begin to laugh, thinking the other two are laughing at each other.
But then one philosopher stops laughing, realizing his nose is red too. How did he come to this conclusion?
Let’s call the philosopher’s A, B and C. A reasoned that B was confident his nose wasn’t red. If B saw A’s nose wasn’t red, he would be surprised that C was laughing, because C would have nothing to laugh at. But B wasn’t surprised, therefore, A correctly reasoned his nose was smeared.
The riddle refers to a variety of meanings of the word fine.
Feeling normal refers to when you feel fine. Extremely thin refers to a fine thread. A punishment refers to being charged a fee. The one who wins refers to an athlete who is physically trained and hardened close to the limit of efficiency. Free from impurity refers to measuring the fineness of precious metals. A keen edge refers to a knife with a fine edge. Refined refers to fine manners or elegance.
You’re in a room with two doors. There’s a guard at each door. One door is the exit, but behind the other door is something that will kill you. You’re told that one guard always tells the truth and the other guard always lies. You don’t know which guard is which. You are allowed to ask one question to either of the guards to determine which door is the exit.
Ask either guard what door the other guard would say is the exit, then choose the opposite door.
If you ask the guard who always tells the truth, he knows the other guard would lie, so he’ll point you to the door leading to death. If you ask the guard who always lies, he knows the other guard would truthfully show you the exit, so he’ll lie and point you to the door leading to death.
An alternate solution is to ask a guard what they would answer if you were to ask them which door was the exit, then choose that door. The truthful guard will point to the correct exit, but the lying guard will too. Here’s why. If you asked him what door was the exit, he would normally lie and point to the death door, but you asked him what he would say if you asked what door was the exit, and in order to lie to that question, he will point you to the exit.