Problem

Source: 2021 Saudi Arabia Training Lists p29 https://artofproblemsolving.com/community/c2758131_2021_saudi_arabia_training_tests

Tags: combinatorics, table, square table



Prove that it is impossible to fill the cells of an $8 \times 8$ table with the numbers from $ 1$ to $64$ (each number must be used once) so that for each $2\times 2$ square, the difference between products of the numbers on it’s diagonals will be equal to $ 1$.