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A paradox is a situation or puzzle that appears to contradict itself, or appears to contradict what is obviously true through valid assumptions and logic.
A well known family of paradoxes involve self-reference, such as the statement "this statement is untrue", or the old joke "How do you keep a fool busy? Hand him a card with this question and 'see other side' on both sides". Others involve creative signs (such as one that reads "Keep Left" with an arrow pointing right, or "Reading This Sign Is Forbidden").