The Barber Paradox is a strange riddle that goes like this: In a small village, there is a single barber who shaves all the people in the village who don't shave themselves. The question is, does the barber shave himself?
If the barber shaves himself, he would be shaving someone who shaves themselves, which doesn't make sense. But if the barber doesn't shave himself, he would be someone in the village who doesn't shave themselves, which also doesn't make sense because then he wouldn't be the barber.
It's a paradox because it doesn't matter what answer you pick, you can't be right. It's like trying to pick between two boxes that are the same color - no matter which you pick, the answer is the same.