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My Question on Maxwell's Paradox

Maxwell's devil, according to his Pardox, the gas in both boxes is the same temperature. The devil uses the door in the middle to allow the fast(hot) molecules on the left to pass to the right. But, we said the boxes same temerature in both gases. So, on the right box is not completely hot. There exist still cold gases molecules on the right. But according to the thought experiment, the cold gas molecules are all collected on the left side of the chamber. Is this contradiction in paradox? How do slow molecules move as fast as other hot gas molecules? How can you explain it? Thank you.