Hello everyone, I came across this beautiful problem Problem. However in order to solve this problem it assumes that the shortest distance between a king at point (x, y) and any arbitrary point (x', y') is given as max(|x' — x|, |y' — y|).

The above distance is Chebyshev Distance and it is true for Kings on a chessboard. Can someone help me with the proof or at least an intuition why the above formula is true. Thanks in advance :).