A good kids definition for a paradox for kids is this:
Say you build a time machine right? And you go stand on top of a deep pit. The pit is closed because no one has pressed the button to open it. Following me? OK, next you go into the time machine and set it to five minutes ago so your brought back to when you just finished the time machine. You would have had to design the machine to make invisible to your past self otherwise you would have had caused a few serious problems. When your past self reached the pit you go and press the button to open the pit. Your past self falls into the pit. Oh no! You have caused a Paradox! Trapping yourself in the pit makes it so you could not have returned to the time machine so you could not have trapped yourself in the pit so you go trap your self in the pit and so on. Understand?
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A paradox is something that seems like it doesn't make sense or is impossible, but actually has a hidden truth or can be explained in a clever way. It's like a puzzle that makes you think in a different way to understand it.