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TUYMAADA 2022 J5

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Each row of a 24×824 \times 8 table contains some permutation of the numbers 1,2,⋯ ,8.1, 2, \cdots , 8. In each column the numbers are multiplied. What is the minimum possible sum of all the products? (C. Wu)

Dataset text AI-MO AoPS. Quoted with source.

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