49 empty cups are arranged in a 7×7 square. Each cup can hold up to 50 marbles.

Every time you add marbles to a cup you must add the same number of marbles to the adjacent cups.
Similarly, every time you remove marbles from a cup you must remove the same number of marbles from the adjacent cups. The central cup has 4 neighbors.

What is the largest number of marbles you can have in the center cup when all of the other cups are empty?

(In reply to re: Symmetric solution by Steven Lord)

I can't say if my symmetric solution is the only solution without going through the labor of the entire 49 variable matrix.  For all I know it could be underdetermined, and thus have more solutions.

Posted by Brian Smith on 2024-05-26 19:16:05