7. A monkey has filled in a 3 x 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 lists of three numbers? What if the monkey writes the numbers 1, 2, ..., 25 in a 5 x 5 grid? Or 1, 2, ..., 121 in a 11 x 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 x n grid so that the cat and the dog obtain the same lists of numbers?

7. A monkey has filled in a 3 x 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 lists of three numbers? What if the monkey writes the numbers 1, 2, ..., 25 in a 5 x 5 grid? Or 1, 2, ..., 121 in a 11 x 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 x n grid so that the cat and the dog obtain the same lists of numbers?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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