Solution: Desert

Ask a question similar to the following:

"If I had asked you yesterday about the way to the oasis,
would you have told me to take the way to the left?"

If the nomad answers with "yes", pick the right way, otherwise go
to the left.

If you phrase a question in combination with the previous day,
you can be sure that one (and only one) lie is in the answer;
either he lied yesterday and is telling the truth today or he told
the truth yesterday and is lying today.

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