{"id":2135,"date":"2021-08-01T15:36:24","date_gmt":"2021-08-01T15:36:24","guid":{"rendered":"https:\/\/blogs.ua.es\/dimates\/?p=2135"},"modified":"2021-08-09T16:01:26","modified_gmt":"2021-08-09T16:01:26","slug":"malas-fichas","status":"publish","type":"post","link":"https:\/\/blogs.ua.es\/dimates\/2021\/08\/01\/malas-fichas\/","title":{"rendered":"Malas fichas"},"content":{"rendered":"<pre>Problema 3 de la fase nacional de la 57 Olimpiada Matem\u00e1tica Espa\u00f1ola (2021)\r\nSe dirige a una edad de: 16-17 a\u00f1os<\/pre>\n<p>Tenemos 2021 colores y 2021 fichas de cada color.<\/p>\n<p>Colocamos las 2021\u00b2 fichas en fila.<\/p>\n<p>Se dice que una ficha F es \u201cmala\u201d si a cada lado queda un n\u00famero impar de las 2020\u00b72021 fichas que no comparten color con F.<\/p>\n<p>(a) Determina cu\u00e1l es el m\u00ednimo n\u00famero posible de fichas malas.<\/p>\n<p>(b) Si se impone la condici\u00f3n de que cada ficha ha de compartir color con al menos una ficha adyacente. \u00bfCu\u00e1l es el m\u00ednimo n\u00famero posible de fichas malas?<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.ua.es\/dimates\/files\/2021\/07\/207.malasposiciones.png\" alt=\"\" width=\"300\" height=\"300\" class=\"aligncenter size-full wp-image-2136\" srcset=\"https:\/\/blogs.ua.es\/dimates\/files\/2021\/07\/207.malasposiciones.png 300w, https:\/\/blogs.ua.es\/dimates\/files\/2021\/07\/207.malasposiciones-150x150.png 150w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><br \/>\nSoluci\u00f3n: <a href=\"https:\/\/blogs.ua.es\/dimates\/2021\/08\/09\/solucion-a-malas-fichas\/\">Aqu\u00ed<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Problema 3 de la fase nacional de la 57 Olimpiada Matem\u00e1tica Espa\u00f1ola (2021) Se dirige a una edad de: 16-17 a\u00f1os Tenemos 2021 colores y 2021 fichas de cada color. Colocamos las 2021\u00b2 fichas en fila. Se dice que una ficha F es \u201cmala\u201d si a cada lado queda un n\u00famero impar de las 2020\u00b72021 [&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-2135","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\/2135","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=2135"}],"version-history":[{"count":2,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/posts\/2135\/revisions"}],"predecessor-version":[{"id":2156,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/posts\/2135\/revisions\/2156"}],"wp:attachment":[{"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/media?parent=2135"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/categories?post=2135"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/tags?post=2135"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}