A puzzle in which a seemingly impossible situation is presented, or any sort of construction that results in a logical contradiction.
A paradox is any statement that appears to contradict itself, and yet is still presented as true. Many paradoxes require lateral thinking to solve.
This statement is false.
If the statement is true, then "this statement is false" is true, and therefore it is false. But if the statement is false, then "this statement is false" is false, and therefore it is true.
Either way, a logical contradiction is arrived at. "This statement is false" is a paradoxical statement.