{"id":2160,"date":"2021-08-22T10:50:18","date_gmt":"2021-08-22T10:50:18","guid":{"rendered":"https:\/\/blogs.ua.es\/dimates\/?p=2160"},"modified":"2021-08-28T04:50:35","modified_gmt":"2021-08-28T04:50:35","slug":"un-tablero-cuadrado","status":"publish","type":"post","link":"https:\/\/blogs.ua.es\/dimates\/2021\/08\/22\/un-tablero-cuadrado\/","title":{"rendered":"Un tablero cuadrado"},"content":{"rendered":"<pre>Problema 2 de la fase catalana de la 57 Olimpiada Matem\u00e1tica Espa\u00f1ola (2020\/21)\r\nSe dirige a una edad de: 16-17 a\u00f1os<\/pre>\n<p>Tenemos un tablero nxn, con n &gt; 2.<\/p>\n<p>Escribimos en cada casilla un n\u00famero natural entre el 1 y el n\u00b2 diferente, en cualquier orden.<\/p>\n<p>Demuestra que siempre existen dos casillas adyacentes tales que los n\u00fameros que x, y que contienen satisfacen la siguiente desigualdad: |x \u2013 y| \u2265 n\/2 + 1.<\/p>\n<p>Entendemos que son casillas adyacentes aquellas que comparten un lado.<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.ua.es\/dimates\/files\/2021\/08\/210.tablerocuadrado.png\" alt=\"\" width=\"300\" height=\"300\" class=\"aligncenter size-full wp-image-2161\" srcset=\"https:\/\/blogs.ua.es\/dimates\/files\/2021\/08\/210.tablerocuadrado.png 300w, https:\/\/blogs.ua.es\/dimates\/files\/2021\/08\/210.tablerocuadrado-150x150.png 150w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><br \/>\nSoluci\u00f3n: <a href=\"https:\/\/blogs.ua.es\/dimates\/2021\/08\/28\/solucion-a-un-tablero-cuadrado\/\">Aqu\u00ed<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Problema 2 de la fase catalana de la 57 Olimpiada Matem\u00e1tica Espa\u00f1ola (2020\/21) Se dirige a una edad de: 16-17 a\u00f1os Tenemos un tablero nxn, con n &gt; 2. Escribimos en cada casilla un n\u00famero natural entre el 1 y el n\u00b2 diferente, en cualquier orden. Demuestra que siempre existen dos casillas adyacentes tales que [&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-2160","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\/2160","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=2160"}],"version-history":[{"count":3,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/posts\/2160\/revisions"}],"predecessor-version":[{"id":2173,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/posts\/2160\/revisions\/2173"}],"wp:attachment":[{"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/media?parent=2160"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/categories?post=2160"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/tags?post=2160"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}