### The Room With Two Doors

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. What question should you ask?

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.

### The Eight Coins

You are given eight coins and told that one of them is counterfeit. The counterfeit one is slightly heavier than the other seven. Otherwise, the coins look identical. Using a simple balance scale, how can you determine which coin is counterfeit using the scale only twice?