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
Symmetric solution by Brian Smith)
Very nice. Doesn't the existence of the symmetric solution you found also prove there are no asymmetric solutions? Otherwise, using the determinant method of solving the 49 linear equations with 49 unknowns would have to yield more than one result and I don't think it can, as it would not be degenerate.
re: Symmetric solution
