Problem of the Week
Problem E
To Tell the Truth?

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

• one person lied in both statements;

• one person told the truth in both statements; and

• two people told the truth in one statement and a lie in the other statement.

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?