I have a question about transferring water into different glasses. Suppose the capacities of three different glasses are X + Y, X and Y liters respectively where both X and Y are integers with X >= Y > 0 where the largest glass (X+Y) starts full and the others are empty.
How can I show using methods of graph theory that when Y = 1 any configuration is attainable, but that if Y>1, then configurations exist which are unattainable?
I have tried different amounts for X and Y and have noticed that the attainable solutions are always on the boundary but I am having trouble with formalizing the proof. Any help would be awesome!