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Part of 2021 Saudi Arabia Training Tests

Problems(1)

fill cells of an 8x 8 table with numbers from 1 to 64

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

Prove that it is impossible to fill the cells of an

8 \times 8

table with the numbers from

1

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

combinatoricstablesquare table