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, 2016

Combinatorics Difficulty 5.0 AIME, harder Prove it United Kingdom

Dean wishes to place the positive integers $1, 2, 3, \ldots, 9$ in the cells of a $3 \times 3$ square grid so that: (i) there is exactly one number in each cell; (ii) the product of the numbers in each row is a multiple of four; (iii) the product of the numbers in each column is a multiple of four. Is Dean's task possible? Prove that your answer is correct.

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