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HMMT November 2015 H2

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Consider a 2×22 \times 2 grid of squares. David writes a positive integer in each of the squares. Next to each row, he writes the product of the numbers in the row, and next to each column, he writes the product of the numbers in each column. If the sum of the eight numbers he writes down is 2015, what is the minimum possible sum of the four numbers he writes in the grid?

Dataset text NuminaMath olympiads. Quoted with source.

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