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Problem of the Week
Problem E
To Tell the Truth?

Four people, Nathaniel, Elizabeth, Libby, and Joel, each said two statements such that:

Nathaniel said “Elizabeth lied exactly once” and “Joel lied twice”.

Elizabeth said “I never lie” and “Nathaniel never lied”.

Libby said “Joel lied twice” and “Elizabeth never lied”.

Joel said “Nathaniel lied twice” and “I never lie”.

Who lied twice? Who never lied? Who lied exactly once?