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):

a. If this chest is empty, then the other chest's message is true.

b. This chest is filled with treasure or the other chest contains deadly scorpions.

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

Question

Mathematics

Adalynn Pham

19 March, 22:52

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):

a. If this chest is empty, then the other chest's message is true.

b. This chest is filled with treasure or the other chest contains deadly scorpions.

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

+2

Answers (1)

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Lovely · Answer 1

So we will open the chest with the message: a. If this chest is empty, then the other chest's message is true.

Step-by-step explanation:

We know that:

a. If this chest is empty, then the other chest's message is true.

b. This chest is filled with treasure or the other chest contains deadly scorpions.

We know exactly one of these messages is true.

We conclude that the first chest cannot be empty, because then we get that both messages are true.

Since the first chest is not empty, it follows that the message of the second chest is incorrect.

So we will open the chest with the message: a. If this chest is empty, then the other chest's message is true.