 As shown here, a 2 in the upper left corner requires a 1 in the second position due to the first inequality; but a 1 in the second position allows only a 3 in the fifth position.This continues until we conclude that two 4s would need to be placed in the same column.Likewise, a 3 in the upper left corner would require the top row to be 3 2 5 4 1 and the bottom again to be 1 2 3 4 5, which would lead to the same contradiction.