2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/227592We give a new interpretation of the derangement numbers d_n as the sum of the values of the largest fixed points of all non-derangements of length n-1. We also show that the analogous sum for the smallest fixed points equals the number of permutations of length n with at least two fixed points. We provide analytic and bijective proofs of both results, as well as a new recurrence for the derangement numbers.7 pagesCombinatorics05A05 (Primary); 05A15 (Secondary)text