Logic puzzle: Solution

You can ask, pointing to one of the envelopes:

Are you the truth-teller if and only if this envelope contains the prize?

The truth-teller will answer "yes" if the envelope contains the prize, and "no" otherwise. The liar will again answer "yes" if the envelope contains the prize, and "no" otherwise. So in any case you can identify the two envelopes.

An alternative solution is: What would the other person answer to the question

Does this envelope contain the prize?

Now the truth-teller has to lie and the liar has to lie too, so both the truth-teller and the liar will answer "no" if the envelope contains the prize, and "yes" otherwise.

This riddle is a reformulation of the Two door riddle which became famous because of the movie Labyrinth (1986).

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