Challenge - Keypad puzzle

[Albert Chan]

(02-14-2020 06:45 AM)pinkman Wrote:  A*1000+B*100+C*10+D≡-A+B-C+D (mod 11)

Another perspective, RHS = (B+D) - (A+C), or differences of the diagonals.

For the keypad (or its rotations, or flipped over)

7 8 9
4 5 6
1 2 3

For any 2x2 squares, diagonals sum to the same number, thus (B+D) - (A+C) = 0