Twenty-five of the numbers $1, 2, \cdots , 50$ are chosen. Twenty-five of the numbers$ 51, 52, \cdots, 100$ are also chosen. No two chosen numbers differ by $0$ or $50$. Find the sum of all $50$ chosen numbers.
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Tags: combinatorics proposed, combinatorics
Twenty-five of the numbers $1, 2, \cdots , 50$ are chosen. Twenty-five of the numbers$ 51, 52, \cdots, 100$ are also chosen. No two chosen numbers differ by $0$ or $50$. Find the sum of all $50$ chosen numbers.