Challenge - Keypad puzzle

[Albert Chan]

(02-14-2020 11:57 AM)Albert Chan Wrote:  

(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.

Here is another, with geometry.
sum of diagonals, if divided by 2, is their mid-point, say point M

M = (B+D)/2 = (A+C)/2

RHS = (B+D) - (A+C) = 2M - 2M = 0