{"id":11280,"date":"2012-11-12T00:50:09","date_gmt":"2012-11-12T00:50:09","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=11280"},"modified":"2022-01-02T23:11:27","modified_gmt":"2022-01-02T23:11:27","slug":"desafio","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=11280","title":{"rendered":"Desafio"},"content":{"rendered":"<p><ul id='GTTabs_ul_11280' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_11280' class='GTTabs_curr'><a  id=\"11280_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_11280' ><a  id=\"11280_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_11280'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Constr\u00f3i uma tabela como a indicada e coloca um algarismo em cada uma das seis casas, de modo que os dois n\u00fameros de tr\u00eas algarismos formados na horizontal e os tr\u00eas n\u00fameros de dois algarismos formados na vertical sejam quadrados perfeitos.<\/p>\n<table class=\"aligncenter\" style=\"width: 40%;\" border=\"1\" align=\"center\">\n<tbody>\n<tr>\n<td>?<\/td>\n<td>?<\/td>\n<td>?<\/td>\n<\/tr>\n<tr>\n<td>?<\/td>\n<td>?<\/td>\n<td>?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_11280' onClick='GTTabs_show(1,11280)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_11280'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>Ser\u00e1 \u00fatil come\u00e7armos por construir uma tabela com os quadrados perfeitos com dois e com tr\u00eas algarismos.<\/p>\n<table class=\" aligncenter\" style=\"width: 90%;\" border=\"0\" align=\"center\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$n$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$4$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$5$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$6$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$7$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$8$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$9$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$10$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$11$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$12$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$13$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$14$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$15$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$16$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$17$<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">${n^2}$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #0000ff;\">$16$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$25$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$36$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #0000ff;\">$49$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$64$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #0000ff;\">$81$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$100$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$121$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$144$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$169$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #0000ff;\">$196$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$225$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$256$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$289$<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table class=\" aligncenter\" style=\"width: 90%;\" border=\"0\" align=\"center\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$n$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$18$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$19$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$20$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$21$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$22$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$23$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$24$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$25$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$26$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$27$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$28$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$29$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$30$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$31$<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">${n^2}$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$324$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$361$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$400$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$441$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$484$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$629$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$576$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$625$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$676$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$729$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$784$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #0000ff;\">$841$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$900$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\">$961$<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Depois de algumas tentativas, obt\u00e9m-se a solu\u00e7\u00e3o:<\/p>\n<table class=\"aligncenter\" style=\"width: 40%;\" border=\"1\" align=\"center\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #0000ff;\">$8$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #0000ff;\">$4$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #0000ff;\">$1$<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #0000ff;\">$1$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #0000ff;\">$9$<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #0000ff;\">$6$<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_11280' onClick='GTTabs_show(0,11280)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Constr\u00f3i uma tabela como a indicada e coloca um algarismo em cada uma das seis casas, de modo que os dois n\u00fameros de tr\u00eas algarismos formados na horizontal e os tr\u00eas&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19267,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[317,97,318],"tags":[319,340],"series":[],"class_list":["post-11280","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-7-o-ano","category-aplicando","category-numeros-inteiros","tag-numeros-inteiros-2","tag-quadrado-perfeito"],"views":2061,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat88.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/11280","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=11280"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/11280\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=11280"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=11280"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=11280"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=11280"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}