{"id":1593,"date":"2015-06-26T10:52:01","date_gmt":"2015-06-26T08:52:01","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=1593"},"modified":"2015-10-28T15:12:01","modified_gmt":"2015-10-28T13:12:01","slug":"pandigitales-tridivibles","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/pandigitales-tridivibles\/","title":{"rendered":"Pandigitales tridivisibles"},"content":{"rendered":"<p>El n\u00famero 4106357289 tiene la siguientes dos propiedades:<\/p>\n<ul>\n<li>es pandigital, porque tiene todos los d\u00edgitos del 0 al 9 exactamente una vez y<\/li>\n<li>es tridivisible, porque los sucesivos subn\u00fameros de tres d\u00edgitos (a partir del segundo) son divisibles por los sucesivos n\u00fameros primos; es decir, representado por d(i) el i-\u00e9simo d\u00edgito, se tiene <\/li>\n<\/ul>\n<pre lang=\"text\">\n     d(2)d(3)d(4)  = 106 es divisible por 2\n     d(3)d(4)d(5)  = 063 es divisible por 3\n     d(4)d(5)d(6)  = 635 es divisible por 5\n     d(5)d(6)d(7)  = 357 es divisible por 7\n     d(6)d(7)d(8)  = 572 es divisible por 11\n     d(7)d(8)d(9)  = 728 es divisible por 13\n     d(8)d(9)d(10) = 289 es divisible por 17\n<\/pre>\n<p>Definir la constante<\/p>\n<pre lang=\"text\">\n   pandigitalesTridivisibles :: [Integer]\n<\/pre>\n<p>cuyos elementos son los n\u00fameros pandigitales tridivisibles. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   head pandigitalesTridivisibles  ==  4106357289\n   sum pandigitalesTridivisibles   ==  16695334890\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Data.List ((\\\\))\n\npandigitalesTridivisibles :: [Integer]\npandigitalesTridivisibles = \n    [entero [d1,d2,d3,d4,d5,d6,d7,d8,d9,d10] \n     | d2 <- [0..9]\n     , d3 <- [0..9] \\\\ [d2]\n     , d4 <- [0..9] \\\\ [d2,d3]\n     , divisible [d2,d3,d4] 2\n     , d5 <- [0..9] \\\\ [d2,d3,d4]  \n     , divisible [d3,d4,d5] 3\n     , d6 <- [0..9] \\\\ [d2,d3,d4,d5]  \n     , divisible [d4,d5,d6] 5\n     , d7 <- [0..9] \\\\ [d2,d3,d4,d5,d6]  \n     , d8 <- [0..9] \\\\ [d2,d3,d4,d5,d6,d7]  \n     , divisible [d6,d7,d8] 11\n     , divisible [d5,d6,d7] 7\n     , d9 <- [0..9] \\\\ [d2,d3,d4,d5,d6,d7,d8]  \n     , divisible [d7,d8,d9] 13\n     , d10 <- [0..9] \\\\ [d2,d3,d4,d5,d6,d7,d8,d9]  \n     , divisible [d8,d9,d10] 17\n     , d1 <- [1..9] \\\\ [d2,d3,d4,d5,d6,d7,d8,d9,d10]  \n    ]\n\n-- (entero ns) es el n\u00famero cuyos d\u00edgitos son ns. Por ejemplo,\n--    entero [3,2,5]  ==  325\nentero :: [Integer] -> Integer\nentero = read . concatMap show\n\ndivisible :: [Integer] -> Integer -> Bool\ndivisible xs n =\n    entero xs `mod` n == 0\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>El n\u00famero 4106357289 tiene la siguientes dos propiedades: es pandigital, porque tiene todos los d\u00edgitos del 0 al 9 exactamente una vez y es tridivisible, porque los sucesivos subn\u00fameros de tres d\u00edgitos (a partir del segundo) son divisibles por los sucesivos n\u00fameros primos; es decir, representado por d(i) el i-\u00e9simo d\u00edgito, se tiene d(2)d(3)d(4) =&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_kad_post_transparent":"","_kad_post_title":"","_kad_post_layout":"","_kad_post_sidebar_id":"","_kad_post_content_style":"","_kad_post_vertical_padding":"","_kad_post_feature":"","_kad_post_feature_position":"","_kad_post_header":false,"_kad_post_footer":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"footnotes":"","_jetpack_memberships_contains_paid_content":false},"categories":[7],"tags":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1593"}],"collection":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/comments?post=1593"}],"version-history":[{"count":5,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1593\/revisions"}],"predecessor-version":[{"id":1641,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1593\/revisions\/1641"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=1593"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=1593"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=1593"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}