{"id":169466,"date":"2020-11-11T22:00:59","date_gmt":"2020-11-12T00:00:59","guid":{"rendered":"http:\/\/clubes.obmep.org.br\/blog\/?page_id=169466"},"modified":"2024-06-26T20:47:47","modified_gmt":"2024-06-26T23:47:47","slug":"problema-para-ajudar-na-escola-cinco-idiomas","status":"publish","type":"page","link":"https:\/\/clubes.obmep.org.br\/blog\/problema-para-ajudar-na-escola-cinco-idiomas\/","title":{"rendered":".Problema para ajudar na escola: Cinco idiomas"},"content":{"rendered":"<p class=\"g2\" ><strong><a href=\"http:\/\/clubes.obmep.org.br\/blog\/?p=220940\" rel=\"noopener\" target=\"_blank\">&#9999; <span style=\"color:#A0522D;font-size:14px;\">Link do problema para dispositivos da <em>Apple<\/em>.<\/span><\/a><\/strong><\/p>\n<div class=\"g1n\" style=\"line-height:25px;padding-bottom:15px; margin-bottom:40px;\">\n<p class=\"tit\" style=\"line-height:20px;margin:10px\">Problema<br \/>\n<span style=\"font-size:12px;color:#00BF00;\"> (A partir do 8\u00ba ano do E. F.- <span style=\"font-weight: normal;\"> N\u00edvel de dificuldade: Dif\u00edcil<\/span>)<\/span><\/p>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 10px; margin-bottom: 20px;border: 0 none\"\/>\nOs amigos Andr\u00e9, Bianca, Caio, D\u00e9bora e Ellen moram em pa\u00edses diferentes, mas conversam muito pela Internet.<br \/>\nQuando Bianca e Caio se encontram em algum bate-papo, eles conversam em franc\u00eas; mas quando D\u00e9bora conversa com eles, os tr\u00eas conversam em portugu\u00eas. Al\u00e9m disso: <\/p>\n<ul>\n\u2022 O \u00fanico idioma comum a Andr\u00e9, Bianca e Ellen \u00e9 o italiano.<br \/>\n\u2022 O \u00fanico idioma comum a Caio e Ellen \u00e9 o espanhol.<br \/>\n\u2022 Tr\u00eas dos cinco amigos falam ingl\u00eas.<br \/>\n\u2022 O idioma mais falado \u00e9 o portugu\u00eas.<br \/>\n\u2022 Um dos amigos fala os cinco idiomas, outro quatro, outro tr\u00eas, outro dois e o amigo restante fala apenas um idioma.<\/ul>\n<p style=\"text-align:center; font-size:12px;\">\n<img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2020\/06\/prob481_p.png\"  style=\"border: none;\" alt=\"\" width=\"300\" height=\"271\" class=\"aligncenter size-full wp-image-155688\" \/>Imagem das pessoas extra\u00edda de <a href=\"https:\/\/www.vecteezy.com\/free-vector\/caring\"rel=\"noopener\" target=\"_blank\">Vecteezy<\/a><\/p>\n<p><strong>Quais s\u00e3o os idiomas falados por cada um dos cinco amigos?<\/strong><\/p>\n<p style=\"margin:10px;\">\n<p style=\"font-size: 12px;text-align:right;line-height:10px;\">Adaptado da <strong> XXXI OPM<\/strong>, 2013.<\/p>\n<\/div>\n<p style=\"margin:40px\">\n<div class=\"g1n\" style=\"line-height:25px;\">\n<p class=\"tit\" style=\"line-height:30px;margin:10px\">Solu\u00e7\u00e3o<\/p>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 1px; margin-bottom: 20px;border: 0 none\"\/>\nInicialmente, observe que:<\/p>\n<ul>\n<li>Os cinco amigos citados s\u00e3o: Andr\u00e9, Bianca, Caio, D\u00e9bora e Ellen.<\/li>\n<li>Os cinco idiomas citados s\u00e3o: espanhol, franc\u00eas, ingl\u00eas, italiano e portugu\u00eas.<\/li>\n<\/ul>\n<p>Para ajudar na solu\u00e7\u00e3o do problema, vamos construir uma tabela com o nome dos cinco amigos e com os idiomas informados e vamos analisando as informa\u00e7\u00f5es do problema.<\/p>\n<ul>\n<li>A partir da informa\u00e7\u00e3o de que &quot;Quando Bianca e Caio se encontram em algum bate-papo, eles conversam em franc\u00eas; mas quando D\u00e9bora conversa com eles, os tr\u00eas conversam em portugu\u00eas&quot;, conclu\u00edmos que <\/li>\n<ul>\n<li><strong>Bianca e Caio falam franc\u00eas.<\/strong><\/li>\n<li><strong>Bianca, Caio e D\u00e9bora falam portugu\u00eas.<\/strong><span style=\"font-size:12px\"> (Cuidado, n\u00e3o podemos concluir daqui que D\u00e9bora n\u00e3o fala franc\u00eas.)<\/span><\/li>\n<\/ul>\n<li>A partir da informa\u00e7\u00e3o de que &quot;O \u00fanico idioma comum a Andr\u00e9, Bianca e Ellen \u00e9 o italiano&quot;, conclu\u00edmos que:<\/li>\n<ul><li<strong><strong>Andr\u00e9, Bianca e Ellen falam italiano.<\/strong><\/strong><\/li>\n<\/ul>\n<li>A partir da informa\u00e7\u00e3o de que &quot;O \u00fanico idioma comum a Caio e Ellen \u00e9 o espanhol&quot;, conclu\u00edmos que <\/li>\n<ul>\n<li><strong>Caio e Ellen falam espanhol.<\/strong><\/li>\n<li>Como espanhol \u00e9 o \u00fanico idioma que eles falam em comum e Caio fala portugu\u00eas e franc\u00eas, ent\u00e3o <strong>Ellen n\u00e3o fala portugu\u00eas e n\u00e3o fala franc\u00eas<\/strong>.<\/li>\n<li>Como espanhol \u00e9 o \u00fanico idioma que eles falam em comum e Ellen fala italiano, ent\u00e3o <strong>Caio n\u00e3o fala italiano<\/strong>.<\/li>\n<\/ul>\n<\/ul>\n<p>Faremos um primeiro preenchimento.<\/p>\n<table class=\"bf\" style=\"border: 2px solid #000000; width:50%; margin-left:auto; margin-right:auto\">\n<tr >\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center; width:30%;\">Idiomas\/Amigos<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><strong>A<\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><strong>B<\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><strong>C<\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><strong>D<\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><strong>E<\/strong><\/td>\n<\/tr>\n<tr >\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:left;padding-left:20px;\"><strong>Espanhol<\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<\/tr>\n<tr >\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:left;padding-left:20px;\"><strong>Franc\u00eas<\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10006;<\/td>\n<\/tr>\n<tr >\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:left;padding-left:20px;\"><strong>Ingl\u00eas<\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><\/td>\n<\/tr>\n<tr >\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:left;padding-left:20px;\"><strong>Italiano <\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10006;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<\/tr>\n<tr >\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:left;padding-left:20px;\"><strong>Portugu\u00eas<\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10006;<\/td>\n<\/tr>\n<\/table>\n<ul>\n<li>Agora, a partir da informa\u00e7\u00e3o de que &quot;O idioma mais falado \u00e9 o portugu\u00eas&quot;, como at\u00e9 agora sabemos que tr\u00eas pessoas falam italiano, tr\u00eas falam portugu\u00eas e uma n\u00e3o fala portugu\u00eas, ent\u00e3o uma quarta pessoa fala portugu\u00eas e ningu\u00e9m mais fala italiano. Ent\u00e3o conclu\u00edmos que:<\/li>\n<ul>\n<li><strong>Andr\u00e9 fala portugu\u00eas e D\u00e9bora n\u00e3o fala italiano.<\/strong><\/li>\n<\/ul>\n<\/ul>\n<table class=\"bf\" style=\"border: 2px solid #000000; width:50%; margin-left:auto; margin-right:auto\">\n<tr >\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center; width:30%;\">Idiomas\/Amigos<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><strong>A<\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><strong>B<\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><strong>C<\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><strong>D<\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><strong>E<\/strong><\/td>\n<\/tr>\n<tr >\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:left;padding-left:20px;\"><strong>Espanhol<\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<\/tr>\n<tr >\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:left;padding-left:20px;\"><strong>Franc\u00eas<\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10006;<\/td>\n<\/tr>\n<tr >\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:left;padding-left:20px;\"><strong>Ingl\u00eas<\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><\/td>\n<\/tr>\n<tr >\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:left;padding-left:20px;\"><strong>Italiano <\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10006;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10006;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<\/tr>\n<tr >\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:left;padding-left:20px;\"><strong>Portugu\u00eas<\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10006;<\/td>\n<\/tr>\n<\/table>\n<ul>\n<li>A partir da informa\u00e7\u00e3o de que &quot;um amigo fala apenas um idioma&quot;, como j\u00e1 sabemos que Andr\u00e9, Bianca, Caio e Ellen falam, pelo menos, dois idiomas, conclu\u00edmos que:<\/li>\n<ul>\n<li>D\u00e9bora fala apenas um idioma, o portugu\u00eas.<\/li>\n<\/ul>\n<\/ul>\n<table class=\"bf\" style=\"border: 2px solid #000000; width:50%; margin-left:auto; margin-right:auto\">\n<tr >\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center; width:30%;\">Idiomas\/Amigos<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><strong>A<\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><strong>B<\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><strong>C<\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><strong>D<\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><strong>E<\/strong><\/td>\n<\/tr>\n<tr >\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:left;padding-left:20px;\"><strong>Espanhol<\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10006;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<\/tr>\n<tr >\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:left;padding-left:20px;\"><strong>Franc\u00eas<\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10006;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10006;<\/td>\n<\/tr>\n<tr >\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:left;padding-left:20px;\"><strong>Ingl\u00eas<\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10006;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><\/td>\n<\/tr>\n<tr >\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:left;padding-left:20px;\"><strong>Italiano <\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10006;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10006;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<\/tr>\n<tr >\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:left;padding-left:20px;\"><strong>Portugu\u00eas<\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10006;<\/td>\n<\/tr>\n<\/table>\n<ul>\n<li>Analisemos a informa\u00e7\u00e3o de que &quot;Tr\u00eas dos cinco amigos falam ingl\u00eas&quot;. Observe que  &quot;o \u00fanico idioma comum a Caio e Ellen \u00e9 o espanhol&quot;; assim, o ingl\u00eas n\u00e3o pode ser um idioma comum aos dois. Como D\u00e9bora n\u00e3o fala ingl\u00eas e, no m\u00e1ximo, um dentre os amigos Caio e Ellen fala ingl\u00eas, conclu\u00edmos que:<\/li>\n<ul>\n<li><strong>Andr\u00e9 e Bianca, falam ingl\u00eas.<\/strong><\/li>\n<\/ul>\n<\/ul>\n<table class=\"bf\" style=\"border: 2px solid #000000; width:50%; margin-left:auto; margin-right:auto\">\n<tr >\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center; width:30%;\">Idiomas\/Amigos<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><strong>A<\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><strong>B<\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><strong>C<\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><strong>D<\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><strong>E<\/strong><\/td>\n<\/tr>\n<tr >\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:left;padding-left:20px;\"><strong>Espanhol<\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10006;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<\/tr>\n<tr >\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:left;padding-left:20px;\"><strong>Franc\u00eas<\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10006;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10006;<\/td>\n<\/tr>\n<tr >\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:left;padding-left:20px;\"><strong>Ingl\u00eas<\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10006;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><\/td>\n<\/tr>\n<tr >\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:left;padding-left:20px;\"><strong>Italiano <\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10006;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10006;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<\/tr>\n<tr >\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:left;padding-left:20px;\"><strong>Portugu\u00eas<\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10006;<\/td>\n<\/tr>\n<\/table>\n<ul>\n<li>J\u00e1 sabemos que D\u00e9bora fala apenas um idioma. Como j\u00e1 sabemos que Andr\u00e9, Bianca e Caio falam, pelo menos, tr\u00eas idiomas, conclu\u00edmos que:<\/li>\n<ul>\n<li> Ellen fala exatamente dois idiomas e, portanto, <strong> Ellen n\u00e3o fala ingl\u00eas<\/strong>.<\/strong><\/li>\n<\/ul>\n<li>Como tr\u00eas amigos falam ingl\u00eas, o terceiro que est\u00e1 faltando \u00e9 Caio. Logo:<\/li>\n<ul>\n<li><strong> Caio fala ingl\u00eas<\/strong>.<\/strong><\/li>\n<\/ul>\n<\/ul>\n<table class=\"bf\" style=\"border: 2px solid #000000; width:50%; margin-left:auto; margin-right:auto\">\n<tr >\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center; width:30%;\">Idiomas\/Amigos<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><strong>A<\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><strong>B<\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><strong>C<\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><strong>D<\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><strong>E<\/strong><\/td>\n<\/tr>\n<tr >\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:left;padding-left:20px;\"><strong>Espanhol<\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10006;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<\/tr>\n<tr >\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:left;padding-left:20px;\"><strong>Franc\u00eas<\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10006;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10006;<\/td>\n<\/tr>\n<tr >\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:left;padding-left:20px;\"><strong>Ingl\u00eas<\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10006;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10006;<\/td>\n<\/tr>\n<tr >\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:left;padding-left:20px;\"><strong>Italiano <\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10006;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10006;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<\/tr>\n<tr >\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:left;padding-left:20px;\"><strong>Portugu\u00eas<\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10006;<\/td>\n<\/tr>\n<\/table>\n<ul>\n<li>Finalmente, observe que j\u00e1 sabemos quem fala um idioma (D\u00e9bora), dois idiomas (Ellen) e quatro idiomas (Caio). Sabemos tamb\u00e9m que Andr\u00e9 fala, no m\u00ednimo, tr\u00eas idiomas e Bianca fala no m\u00ednimo quatro idiomas. Como Bianca n\u00e3o pode ser o amigo que fala tr\u00eas idiomas, conclu\u00edmos que:<\/li>\n<ul>\n<li><strong> Bianca fala cinco idiomas<\/strong>.<\/strong><\/li>\n<\/ul>\n<ul>\n<li><strong> Andr\u00e9 fala tr\u00eas idiomas<\/strong>.<\/strong><\/li>\n<\/ul>\n<\/ul>\n<p>A \u00faltima tabela mostra quantos e quais idiomas cada amigo fala!<\/p>\n<table class=\"bf\" style=\"border: 2px solid #000000; width:50%; margin-left:auto; margin-right:auto\">\n<tr >\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center; width:30%;\">Idiomas\/Amigos<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><strong>A<\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><strong>B<\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><strong>C<\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><strong>D<\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\"><strong>E<\/strong><\/td>\n<\/tr>\n<tr >\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:left;padding-left:20px;\"><strong>Espanhol<\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10006;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10006;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<\/tr>\n<tr >\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:left;padding-left:20px;\"><strong>Franc\u00eas<\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10006;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10006;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10006;<\/td>\n<\/tr>\n<tr >\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:left;padding-left:20px;\"><strong>Ingl\u00eas<\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10006;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10006;<\/td>\n<\/tr>\n<tr >\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:left;padding-left:20px;\"><strong>Italiano <\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10006;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10006;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<\/tr>\n<tr >\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:left;padding-left:20px;\"><strong>Portugu\u00eas<\/strong><\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10003;<\/td>\n<td class=\"bf\" style=\"border: 2px solid #000000;text-align:center;\">&#10006;<\/td>\n<\/tr>\n<\/table>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 10px; margin-bottom: 15px;border: 0 none\"\/>\n<p class=\"g2\" style=\"line-height:20px;\">Solu\u00e7\u00e3o elaborada pelos <strong>Moderadores do Blog<\/strong>.<\/p>\n<\/div>\n<p style=\"margin:20px\">\n<table style=\" height:auto; margin-left: auto; margin-right: auto;width:640px;\">\n<tr>\n<td class=\"bf\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1001 alignright\" style=\"border: 0px;\" alt=\"\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2013\/01\/menino.jpg\" width=\"80\" height=\"115\" \/><\/td>\n<td class=\"bf\">\n<p class=\"fala\" style=\"width:520px;background-color: #FFF5EE; padding:10px; font-family: calibri; font-size: 13px;color: #1C1C1C; line-height: 20px; \"> Se for conveniente, voc\u00ea pode obter um arquivo PDF desta p\u00e1gina, com o problema e a solu\u00e7\u00e3o, clicando no bot\u00e3o abaixo.<br \/>\nVoc\u00ea pode abrir o arquivo diretamente no seu navegador (<em>Chrome<\/em>, <em>Edge<\/em>, <em>Firefox<\/em>, <em>Safari<\/em>, entre outros), mas tamb\u00e9m pode utilizar o software gratuito <em><strong>Adobe Acrobat Reader<\/strong><\/em>.<br \/>\nCaso o dispositivo que voc\u00ea est\u00e1 utilizando n\u00e3o tenha o <strong><em>Acrobat Reader<\/em><\/strong> instalado, \u00e9 s\u00f3 clicar <a href=\"http:\/\/get.adobe.com\/br\/reader\/\" rel=\"noopener\" target=\"_blank\"><strong>AQUI<\/strong><\/a> para fazer o download adequado ao seu dispositivo.<\/p>\n<\/td>\n<\/tr>\n<\/table>\n<div style=\" float:right;  width: 100px;\">\n<p style=\"text-align: center; border-style: dotted; border-color :#FFFAFA; border-width :thin; width:90px;  height:40px;  padding: 5px; background-color: #800000;\">\n<a href=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2020\/11\/Cinco-idiomassss_c.pdf\" title=\" Arquivo PDF\" download=\"Clubes_ Cinco idiomas.pdf\"><span style=\"color: #FFFAFA; font-family: georgia; font-size: 16px;\"><strong>Arquivo <\/strong><\/span><\/a>\n <\/p>\n<\/div>\n<div style=\"clear: both;\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>&#9999; Link do problema para dispositivos da Apple. Problema (A partir do 8\u00ba ano do E. F.- N\u00edvel de dificuldade: Dif\u00edcil) Os amigos Andr\u00e9, Bianca, Caio, D\u00e9bora e Ellen moram em pa\u00edses diferentes, mas conversam muito pela Internet. Quando Bianca e Caio se encontram em algum bate-papo, eles conversam em franc\u00eas; mas quando D\u00e9bora conversa &hellip; <\/p>\n<p><a class=\"more-link btn\" href=\"https:\/\/clubes.obmep.org.br\/blog\/problema-para-ajudar-na-escola-cinco-idiomas\/\">Continue lendo<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"template-onecolumn.php","meta":{"footnotes":""},"class_list":["post-169466","page","type-page","status-publish","hentry","nodate","item-wrap"],"_links":{"self":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/169466","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/comments?post=169466"}],"version-history":[{"count":78,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/169466\/revisions"}],"predecessor-version":[{"id":220942,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/169466\/revisions\/220942"}],"wp:attachment":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/media?parent=169466"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}