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My Discrete math teacher said something along the lines of “You go to a town of liars and ask one if he is asleep” in passing the other day. This is aninteresting situation and I think worked out the outcome of it in class, but I couldn’t find any explanations of it on the internet.

Here is what I have written down in my notes:

You ask a liar if he is asleep, there are only 2 answers: yes and no.

Of course one cannot answer if one is asleep so,
1) if he is asleep, he will not answer and appear to be asleep
2) if he is not asleep, he will lie and appear to be asleep.

So there is ambiguity –  the same result occurs for both situations.

Update: I found a video explaining the answer.