It is not easily solvable by graph theory..
Unless you know how to solve a diophantine equation by converting an elliptic curve into its weisertrass form and then finding many integer solutions by plotting tangents to curve and moving to the next point and so on till u find positive integral solutions..
I never solved this sum as I don't consider myself to be top 5% xD
Below are the smallest positive whole solutions attached
APPLES = 154476802108746166441951315019919837485664325669565431700026634898253202035277999,