2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/165979We give a new proof that any candy-passing game on a graph G with at least 4|E(G)|-|V(G)| candies stabilizes. (This result was first proven in arXiv:0807.4450.) Unlike the prior literature on candy-passing games, we use methods from the general theory of chip-firing games which allow us to obtain a polynomial bound on the number of rounds before stabilization.3 pagesCombinatoricsDiscrete Mathematics05C35, 05C85, 68Q25 (Primary); 37B15, 68R10, 68Q80 (Secondary)text