2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/167794We count the number of walks of length n on a k-node circular digraph that cover all k nodes in two ways. The first way illustrates the transfer-matrix method. The second involves counting various classes of height-restricted lattice paths. We observe that the results also count so-called k-balanced strings of length n, generalizing a 1996 Putnam problem.12 pages, 1 figure, 2 tables. Submitted.AcceptedCombinatorics05A05; 05A15text