{"id":2773,"date":"2023-02-25T06:52:13","date_gmt":"2023-02-25T06:52:13","guid":{"rendered":"https:\/\/blogs.ua.es\/dimates\/?p=2773"},"modified":"2023-03-08T16:40:44","modified_gmt":"2023-03-08T16:40:44","slug":"reduciendo-una-lista","status":"publish","type":"post","link":"https:\/\/blogs.ua.es\/dimates\/2023\/02\/25\/reduciendo-una-lista\/","title":{"rendered":"Reduciendo una lista"},"content":{"rendered":"<pre>Problema 5 de la Fase Local de la Olimpiada Espa\u00f1ola de Matem\u00e1ticas 2023 (viernes ma\u00f1ana)\r\nSe dirige a una edad de: 16-17 a\u00f1os<\/pre>\n<p>Los inversos de los n\u00fameros enteros positivos de 2 a 2023 se escriben en una pizarra.<\/p>\n<p>En cada paso se seleccionan dos de los n\u00fameros de la pizarra, x e y, y se reemplazan con el n\u00famero xy\/(xy + (1 \u2013 x)(1 \u2013 y)).<\/p>\n<p>Este proceso se repite 2021 veces, hasta que s\u00f3lo quede un n\u00famero.<\/p>\n<p>\u00bfCu\u00e1les pueden ser los posibles n\u00fameros que se obtengan al repetir este proceso?<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.ua.es\/dimates\/files\/2023\/02\/286.reduciendo.png\" alt=\"\" width=\"300\" height=\"300\" class=\"alignnone size-full wp-image-2774\" srcset=\"https:\/\/blogs.ua.es\/dimates\/files\/2023\/02\/286.reduciendo.png 300w, https:\/\/blogs.ua.es\/dimates\/files\/2023\/02\/286.reduciendo-150x150.png 150w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><br \/>\nSoluci\u00f3n: <a href=\"https:\/\/blogs.ua.es\/dimates\/2023\/03\/04\/solucion-a-reduciemdo-una-lista\/\">Aqu\u00ed<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Problema 5 de la Fase Local de la Olimpiada Espa\u00f1ola de Matem\u00e1ticas 2023 (viernes ma\u00f1ana) Se dirige a una edad de: 16-17 a\u00f1os Los inversos de los n\u00fameros enteros positivos de 2 a 2023 se escriben en una pizarra. En cada paso se seleccionan dos de los n\u00fameros de la pizarra, x e y, y [&hellip;]<\/p>\n","protected":false},"author":4267,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2242021,1738,2849],"tags":[],"class_list":["post-2773","post","type-post","status-publish","format-standard","hentry","category-olimpiada-matematica-espanola","category-olimpiadas","category-problemas"],"_links":{"self":[{"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/posts\/2773","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/users\/4267"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/comments?post=2773"}],"version-history":[{"count":3,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/posts\/2773\/revisions"}],"predecessor-version":[{"id":2784,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/posts\/2773\/revisions\/2784"}],"wp:attachment":[{"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/media?parent=2773"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/categories?post=2773"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/tags?post=2773"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}