{"id":3575,"date":"2025-04-16T07:16:46","date_gmt":"2025-04-16T07:16:46","guid":{"rendered":"https:\/\/blogs.ua.es\/dimates\/?p=3575"},"modified":"2025-04-16T07:16:48","modified_gmt":"2025-04-16T07:16:48","slug":"solucion-a-arbol-factorial","status":"publish","type":"post","link":"https:\/\/blogs.ua.es\/dimates\/2025\/04\/16\/solucion-a-arbol-factorial\/","title":{"rendered":"Soluci\u00f3n a &#8220;\u00c1rbol factorial&#8221;"},"content":{"rendered":"<pre>\nProblema 0 del concurso Marat\u00f3 de problemes 2025\nSe dirige a una edad de: 14-15 a\u00f1os<\/pre>\n\n\n<p>Busca 5 cifras, llamadas A, B, C D y E, de forma que cumplan las siguientes igualdades:<\/p>\n\n\n\n<p>C\u00b7C = D<\/p>\n\n\n\n<p>E\u00b7D = BE<\/p>\n\n\n\n<p>C\u00b7E = AE<\/p>\n\n\n\n<p>C\u00b7BE = ACE<\/p>\n\n\n\n<p>AE\u00b7ACE = 2025<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"300\" src=\"https:\/\/blogs.ua.es\/dimates\/files\/2025\/04\/380.factorial.png\" alt=\"\" class=\"wp-image-3573\" \/><\/figure>\n\n\n\n<p>Soluci\u00f3n:<\/p>\n\n\n\n<!--more-->\n\n\n\n<p>Para poder trabajar con cifras, empecemos por alg\u00fan sitio. Si pensamos que AE\u00b7ACE = 2025, claramente E tiene que ser 5.<\/p>\n\n\n\n<p>Como E\u00b7D = BE, D tiene que ser un n\u00famero impar y B tiene que ser menor que 5.<\/p>\n\n\n\n<p>De manera similar, C es impar y A menor que 5.<\/p>\n\n\n\n<p>Puesto que C\u00b7C s\u00f3lo tiene una cifra, C vale 1 o vale 3.<\/p>\n\n\n\n<p>Vamos a empezar por eliminaci\u00f3n.<\/p>\n\n\n\n<p>Si C = 1, D = 1 y no puede ser, porque 1\u00b75 no tiene 2 cifras.<\/p>\n\n\n\n<p>Si C = 3, D = 9, B = 4, y por tanto A = 1 y cuadra todo (es la \u00fanica posibilidad).<\/p>\n\n\n\n<p>En efecto,<\/p>\n\n\n\n<p>3\u00b73 = 9<\/p>\n\n\n\n<p>5\u00b79 = 45<\/p>\n\n\n\n<p>3\u00b75 = 15<\/p>\n\n\n\n<p>3\u00b745 = 135<\/p>\n\n\n\n<p>15\u00b7135 = 2025<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Problema 0 del concurso Marat\u00f3 de problemes 2025 Se dirige a una edad de: 14-15 a\u00f1os Busca 5 cifras, llamadas A, B, C D y E, de forma que cumplan las siguientes igualdades: C\u00b7C = D E\u00b7D = BE C\u00b7E = AE C\u00b7BE = ACE AE\u00b7ACE = 2025 Soluci\u00f3n:<\/p>\n","protected":false},"author":4267,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2242030,2242026,1738,2849,3303],"tags":[],"class_list":["post-3575","post","type-post","status-publish","format-standard","hentry","category-marato","category-marato-de-problemes","category-olimpiadas","category-problemas","category-soluciones"],"_links":{"self":[{"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/posts\/3575","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=3575"}],"version-history":[{"count":1,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/posts\/3575\/revisions"}],"predecessor-version":[{"id":3578,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/posts\/3575\/revisions\/3578"}],"wp:attachment":[{"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/media?parent=3575"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/categories?post=3575"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/tags?post=3575"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}