During a math exam, Willy asks Ms. Matilda, the teacher, how much time is left. Ms. Matilda is known for being obtuse and answers that the amount of time left is 1/5 of the time already completed and that is also how much time is left, in a manner of speaking.
15 minutes. The total exam time is 90 minutes. If 15 minutes are left, 75 minutes have already passed, and one fifth of 75 is 15. However, if you follow Ms. Matilda’s hint and pay attention to only the numbers in 1/5, you get the answer of 15 minutes as well.
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.