{"id":230322,"date":"2026-09-01T14:01:11","date_gmt":"2026-09-01T17:01:11","guid":{"rendered":"http:\/\/clubes.obmep.org.br\/blog\/?page_id=230322"},"modified":"2026-09-01T14:01:11","modified_gmt":"2026-09-01T17:01:11","slug":"gabarito-maratona-de-perguntas-e-respostas-torneio-2026","status":"publish","type":"page","link":"https:\/\/clubes.obmep.org.br\/blog\/gabarito-maratona-de-perguntas-e-respostas-torneio-2026\/","title":{"rendered":"Gabarito &#8211; Maratona de Perguntas e Respostas &#8211; Torneio 2026"},"content":{"rendered":"<div class=\"gres cb3dd\" style=\"font-size: 20px;\">\n<p class=\"tiss c3\">Gabarito &#8211; Maratona de Perguntas e Respostas<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter  wp-image-2995\" style=\"border: 0px;\" alt=\"livro_grande\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2013\/02\/livro_grande1.jpg\" width=\"200\" height=\"200\" srcset=\"https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2013\/02\/livro_grande1.jpg 480w, https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2013\/02\/livro_grande1-150x150.jpg 150w, https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2013\/02\/livro_grande1-300x300.jpg 300w\" sizes=\"auto, (max-width: 200px) 100vw, 200px\" \/><br \/>\n<span style=\"color: #1C1C1C;\">O matem\u00e1tico alem\u00e3o, nascido em 1826, que publicou trabalhos em eletrodin\u00e2mica, condu\u00e7\u00e3o de calor, s\u00e9ries hipergeom\u00e9tricas e teoria dos n\u00fameros, \u00e9 Bernhard Riemann, cujo 200\u00ba anivers\u00e1rio motivou a escolha do nome do Torneio 2026. <\/span>\n<\/div>\n<p style=\"margin:30px;\">\n<p style=\"margin:30px;\">\n<div class=\"gris cb3dd\" >\n<p class=\"tiss c3\">N\u00edvel A<\/p>\n<p style=\"margin:10px;\">\n<p><span style=\"color: #1C1C1C;\">1. <strong>[tex]400\\text{ cm}[\/tex]<\/strong><\/span><br \/>\n<span style=\"color: #1C1C1C;\">2. <strong>[tex]16\\text{ cm}^2[\/tex]<\/strong><\/span><br \/>\n<span style=\"color: #1C1C1C;\">3. <strong>[tex]14,53[\/tex]<\/strong><\/span><br \/>\n<span style=\"color: #1C1C1C;\">4. <strong>[tex]24[\/tex]<\/strong><\/span><br \/>\n<span style=\"color: #1C1C1C;\">5. <strong>[tex]15552[\/tex]<\/strong><\/span><br \/>\n<span style=\"color: #1C1C1C;\">6. <strong>O jardineiro<\/strong><\/span><br \/>\n<span style=\"color: #1C1C1C;\">7. <strong>Uma poss\u00edvel solu\u00e7\u00e3o:<\/strong><\/span><br \/>\n<img decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2026\/09\/Quest\u00e3o-7-_-A.png\" alt=\"\" width=\"300\" class=\"aligncenter size-full wp-image-230327\" srcset=\"https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2026\/09\/Quest\u00e3o-7-_-A.png 616w, https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2026\/09\/Quest\u00e3o-7-_-A-300x202.png 300w\" sizes=\"(max-width: 616px) 100vw, 616px\" \/><br \/>\n<span style=\"color: #1C1C1C;\">8. <strong>Uma poss\u00edvel solu\u00e7\u00e3o:<\/strong><\/span><br \/>\n<img decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2026\/09\/pontos-no-quadrado-2.jpg\" alt=\"\" width=\"300\" class=\"aligncenter size-full wp-image-230330\" \/><br \/>\n<span style=\"color: #1C1C1C;\">9. <strong>Uma poss\u00edvel solu\u00e7\u00e3o (COM GAPEM MCPF I):<\/strong><\/span><\/p>\n<div style=\"display: flex; justify-content: center;\">\n    <div style=\"width: 480px;\" class=\"wp-video\"><video class=\"wp-video-shortcode\" id=\"video-230322-1\" width=\"480\" height=\"270\" preload=\"metadata\" controls=\"controls\"><source type=\"video\/mp4\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2026\/09\/converted-video-conversion-30901arHMu6NGkV.mp4?_=1\" \/><a href=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2026\/09\/converted-video-conversion-30901arHMu6NGkV.mp4\">http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2026\/09\/converted-video-conversion-30901arHMu6NGkV.mp4<\/a><\/video><\/div>\n<\/div>\n<p><span style=\"color: #1C1C1C;\">10. <strong>Alan Turing<\/strong><\/span><br \/>\n<img decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2024\/01\/Turin_04.png\" style=\"border:none\"  alt=\"\" width=\"200\" class=\"aligncenter size-full wp-image-210112\" \/><br \/>\n<span style=\"color: #1C1C1C;\">11. <strong>Torneio 2024 &#8211; Beno\u00eet Mandelbrot<\/strong><\/span><br \/>\n<span style=\"color: #1C1C1C;\">12. <strong>Tales de Mileto<\/strong><\/span><br \/>\n<img decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2015\/06\/tales-de-mileto.jpg\" style=\"border: 0px;\" alt=\"tales-de-mileto\" width=\"200\" class=\"aligncenter size-full wp-image-40918\" srcset=\"https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2015\/06\/tales-de-mileto.jpg 325w, https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2015\/06\/tales-de-mileto-243x300.jpg 243w\" sizes=\"(max-width: 325px) 100vw, 325px\" \/>\n<\/div>\n<div class=\"gris cb3dd\" >\n<p class=\"tiss c3\">N\u00edvel B<\/p>\n<p style=\"margin:10px;\">\n<p><span style=\"color: #1C1C1C;\">1. <strong>[tex]72^\\circ[\/tex]<\/strong><\/span><br \/>\n<span style=\"color: #1C1C1C;\">2. <strong>[tex]36[\/tex]<\/strong><\/span><br \/>\n<span style=\"color: #1C1C1C;\">3. <strong>[tex]43,75\\%[\/tex]<\/strong><\/span><br \/>\n<span style=\"color: #1C1C1C;\">4. <strong>[tex]5[\/tex]<\/strong><\/span><br \/>\n<span style=\"color: #1C1C1C;\">5. <strong>[tex]29305[\/tex]<\/strong><\/span><br \/>\n<span style=\"color: #1C1C1C;\">6. <strong>[tex]\\frac{33}{13}\\approx 2,54[\/tex]<\/strong><\/span><br \/>\n<span style=\"color: #1C1C1C;\">7. <strong>Uma poss\u00edvel solu\u00e7\u00e3o (COM GAPEM MCPF I):<\/strong><\/span><\/p>\n<div style=\"display: flex; justify-content: center;\">\n    <div style=\"width: 480px;\" class=\"wp-video\"><video class=\"wp-video-shortcode\" id=\"video-230322-2\" width=\"480\" height=\"270\" preload=\"metadata\" controls=\"controls\"><source type=\"video\/mp4\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2026\/09\/converted-video-conversion-30901arHMu6NGkV.mp4?_=2\" \/><a href=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2026\/09\/converted-video-conversion-30901arHMu6NGkV.mp4\">http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2026\/09\/converted-video-conversion-30901arHMu6NGkV.mp4<\/a><\/video><\/div>\n<\/div>\n<p><span style=\"color: #1C1C1C;\">8. <strong>Uma poss\u00edvel solu\u00e7\u00e3o (COM PHIDIAS!):<\/strong><\/span><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2026\/09\/quest\u00e3o2-Alefes-Home.jpeg\" alt=\"\" width=\"297\" height=\"267\" class=\"aligncenter size-full wp-image-230341\" \/><br \/>\n<span style=\"color: #1C1C1C;\">9. <strong>S\u00e3o necess\u00e1rios 6 movimentos:<\/strong><\/span><br \/>\n<img decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2026\/09\/moedas_solu\u00e7\u00e3o.png\" alt=\"\" width=\"350\" class=\"aligncenter size-full wp-image-230345\" srcset=\"https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2026\/09\/moedas_solu\u00e7\u00e3o.png 1281w, https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2026\/09\/moedas_solu\u00e7\u00e3o-300x253.png 300w, https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2026\/09\/moedas_solu\u00e7\u00e3o-768x647.png 768w, https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2026\/09\/moedas_solu\u00e7\u00e3o-1024x863.png 1024w\" sizes=\"(max-width: 1281px) 100vw, 1281px\" \/><br \/>\n<span style=\"color: #1C1C1C;\">10.<\/span><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2026\/09\/Riemann.png\" alt=\"\" width=\"439\" height=\"685\" class=\"aligncenter size-full wp-image-230343\" srcset=\"https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2026\/09\/Riemann.png 439w, https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2026\/09\/Riemann-192x300.png 192w\" sizes=\"auto, (max-width: 439px) 100vw, 439px\" \/><\/p>\n<p><span style=\"color: #1C1C1C;\">11. <strong>Emmy Noether<\/strong><\/span><br \/>\n<img decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2020\/09\/Noether2.png\"  style=\"border: 0px;\" alt=\"\" width=\"200\" class=\"aligncenter size-full wp-image-165475\" srcset=\"https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2020\/09\/Noether2.png 361w, https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2020\/09\/Noether2-187x300.png 187w\" sizes=\"(max-width: 361px) 100vw, 361px\" \/><br \/>\n<span style=\"color: #1C1C1C;\">12. <strong>Fran\u00e7ois Vi\u00e8te<\/strong><\/span><br \/>\n<img decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2013\/08\/Viete.jpg\" style=\"border: 0px;\" alt=\"Viete\" width=\"200\" class=\"aligncenter size-full wp-image-8448\" \/>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Gabarito &#8211; Maratona de Perguntas e Respostas O matem\u00e1tico alem\u00e3o, nascido em 1826, que publicou trabalhos em eletrodin\u00e2mica, condu\u00e7\u00e3o de calor, s\u00e9ries hipergeom\u00e9tricas e teoria dos n\u00fameros, \u00e9 Bernhard Riemann, cujo 200\u00ba anivers\u00e1rio motivou a escolha do nome do Torneio 2026. N\u00edvel A 1. [tex]400\\text{ cm}[\/tex] 2. [tex]16\\text{ cm}^2[\/tex] 3. [tex]14,53[\/tex] 4. [tex]24[\/tex] 5. [tex]15552[\/tex] &hellip; <\/p>\n<p><a class=\"more-link btn\" href=\"https:\/\/clubes.obmep.org.br\/blog\/gabarito-maratona-de-perguntas-e-respostas-torneio-2026\/\">Continue lendo<\/a><\/p>\n","protected":false},"author":255,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"template-onecolumn.php","meta":{"footnotes":""},"class_list":["post-230322","page","type-page","status-publish","hentry","nodate","item-wrap"],"_links":{"self":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/230322","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\/255"}],"replies":[{"embeddable":true,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/comments?post=230322"}],"version-history":[{"count":26,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/230322\/revisions"}],"predecessor-version":[{"id":230354,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/230322\/revisions\/230354"}],"wp:attachment":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/media?parent=230322"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}