Mathematics, 21.02.2020 07:55 ineedhelpplz40
A monkey has filled in a 3 Γ 3 grid with the numbers 1, 2, . . . , 9. A cat writes down the three numbers obtained by multiplying the numbers in each horizontal row. A dog writes down the three numbers obtained by multiplying the numbers in each vertical column. Can the monkey fill in the grid in such a way that the cat and dog obtain the same set of three numbers? What if the monkey writes the numbers 1, 2, . . . , 25 in a 5Γ5 grid? Or 1, 2, . . . , 121 in a 11 Γ 11 grid? Can you find any conditions on n that guarantee that it is possible or any conditions that guarantee that it is impossible for the monkey to write the numbers 1, 2, . . . , n2 in an n Γ n grid so that the cat and the dog obtain the same set of numbers?
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A monkey has filled in a 3 Γ 3 grid with the numbers 1, 2, . . . , 9. A cat writes down the three nu...
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