A monkey has filled in a $33$ grid with the numbers $1,2,$dots,$9.$ 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 $1,2,$dots,$25$ in a $55$ grid? Or $1,2,$dots,$121$ in a $1111$ 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 $1,2,$dots,$n^2$ in an $nn$ grid so that the cat and the dog obtain the same lists of numbers?