2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/226636Richomme asked the following question: what is the infimum of the real numbers $α$ > 2 such that there exists an infinite word that avoids $α$-powers but contains arbitrarily large squares beginning at every position? We resolve this question in the case of a binary alphabet by showing that the answer is $α$ = 7/3.12 pages; minor revisions and clarificationsCombinatoricsFormal Languages and Automata Theory68R15text