2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/109135In a monotonic sequence game, two players alternately choose elements of a sequence from some fixed ordered set. The game ends when the resulting sequence contains either an ascending subsequence of length a or a descending one of length d. We investigate the behaviour of this game when played on finite linear orders or Q and provide some general observations for play on arbitrary ordered sets.20 pages, 1 tableCombinatorics05A05; 05E10text