After excavating for weeks, you finally arrive at the burial chamber. The room is empty except for two large chests. On each is carved a message (strangely in English) : "If this chest is empty, then the other chest's message is true." and "This chest is filled with treasure or the other chest contains deadly scorpions."

You know exactly one of these messages is true. What should you do?

You should open the second chest.

Step-by-step explanation:

Let's analyze this problem with logic. If you know exactly one of these messages is true, this means than the other chest message is false.

Let's call A to the first chest (The one with the message "If this chest is empty, then the other chest's message is true.").

Let's call B to the second Chest (the one with the message "This chest is filled with treasure or the other chest contains deadly scorpions.").

Case 1: A is true:

If A is true, B should be false. But in A is read "If this chest is empty, then the other chest's message is true". Knowing that the other message is false means that, for message A be true, this chest shouldn't be empty. Therefore this chest has something inside.

Case 2: B is true:

If B is true, A should be false. This means that either B is full of treasure or A is full of scorpions. We have a problem with this now:

If B is empty, A is full of scorpions. The message A only talks about B been true if A is empty (which is not). But message A is false, therefore, B would be true if A is not Empty (double negation).

If B is full of treasure, A should be empty. If the message of A is false, this contradicts than B is true. This is absurd. Therefore A isn't empty, therefore B doesn't have treasure so B is true.

Therefore if B is true, A is full of scorpions.

If A is true, A is full of something, but B can be false by been true both of its statements instead of only one of them ("This chest is filled with treasure and the other chest contains deadly scorpions"). This means than A is full of scorpions. It's safer to open B.