{"id":1097,"date":"2024-12-14T08:00:00","date_gmt":"2024-12-14T07:00:00","guid":{"rendered":"https:\/\/control-advent.com\/?p=1097"},"modified":"2025-11-28T19:05:46","modified_gmt":"2025-11-28T18:05:46","slug":"14-o-enigma-das-bolachas-no-forno-quantas-estarao-prontas","status":"publish","type":"post","link":"https:\/\/control-advent.com\/?p=1097","title":{"rendered":"14 &#8211; O enigma das bolachas no forno: Quantas estar\u00e3o prontas?"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\"><strong><strong><strong>Autores desta quest\u00e3o:<\/strong><\/strong><\/strong> Francesco Dolce &amp; Adriano Fagiolini, <em>Dipartimento di Ingegneria, Mobile &amp; Intelligent Robots Panormus Laboratory (MIRPALab), <\/em>Universit\u00e0 di Palermo, It\u00e1lia<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">O Pai Natal est\u00e1 a preparar bolachas de gengibre com os seus duendes, mas n\u00e3o consegue ver quantas bolachas est\u00e3o no forno, pois este est\u00e1 fechado e n\u00e3o tem um vidro transparente que permita espreitar para o interior. Mas quer mesmo muito saber quantas est\u00e3o prontas, sem abrir o forno demasiadas vezes para evitar que a temperatura baixe e correr o risco de algumas n\u00e3o ficarem bem cozidas. Como poder\u00e1 o Pai Natal estimar quantas bolachas j\u00e1 est\u00e3o prontas sem as ver diretamente?<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"1024\" src=\"https:\/\/control-advent.com\/wp-content\/uploads\/2024\/11\/14-Dec-2024-1024x1024.jpeg\" alt=\"\" class=\"wp-image-428\" style=\"width:auto;height:600px\" srcset=\"https:\/\/control-advent.com\/wp-content\/uploads\/2024\/11\/14-Dec-2024-1024x1024.jpeg 1024w, https:\/\/control-advent.com\/wp-content\/uploads\/2024\/11\/14-Dec-2024-300x300.jpeg 300w, https:\/\/control-advent.com\/wp-content\/uploads\/2024\/11\/14-Dec-2024-150x150.jpeg 150w, https:\/\/control-advent.com\/wp-content\/uploads\/2024\/11\/14-Dec-2024-768x768.jpeg 768w, https:\/\/control-advent.com\/wp-content\/uploads\/2024\/11\/14-Dec-2024-1536x1536.jpeg 1536w, https:\/\/control-advent.com\/wp-content\/uploads\/2024\/11\/14-Dec-2024-2048x2048.jpeg 2048w, https:\/\/control-advent.com\/wp-content\/uploads\/2024\/11\/14-Dec-2024-640x640.jpeg 640w, https:\/\/control-advent.com\/wp-content\/uploads\/2024\/11\/14-Dec-2024-24x24.jpeg 24w, https:\/\/control-advent.com\/wp-content\/uploads\/2024\/11\/14-Dec-2024-36x36.jpeg 36w, https:\/\/control-advent.com\/wp-content\/uploads\/2024\/11\/14-Dec-2024-48x48.jpeg 48w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">a. \ud83e\udddd\u200d\u2642\ufe0f\ud83e\udd14\ud83d\udd75\ufe0f\u200d\u2642\ufe0f Pode pedir a um duende que se lembre de quantas bolachas estavam no tabuleiro. Afinal, \u00e9 pouco prov\u00e1vel que os duendes mintam\u2026 n\u00e3o v\u00e3o tirar uma ou duas bolachas enquanto ningu\u00e9m estiver a olhar, pois n\u00e3o?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">b. \ud83d\udcca\ud83e\udddd\u200d\u2640\ufe0f\ud83c\udf6a Pode pedir a cada duende que se lembre de quantas bolachas estavam no tabuleiro e, em seguida, calcular uma m\u00e9dia ponderada, onde os pesos refletem a &#8220;fiabilidade&#8221; de cada duende: uma conjuga\u00e7\u00e3o entre a sua capacidade de mem\u00f3ria e a sua honestidade em rela\u00e7\u00e3o a bolachas.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">c. \ud83d\udcda\ud83d\udcc8\ud83d\udd22 Pode recorrer a dados hist\u00f3ricos sobre o n\u00famero m\u00e9dio de bolachas por tabuleiro para estimar quantas bolachas os duendes colocaram no tabuleiro anterior. Afinal, o que poderia correr mal com um pouco de matem\u00e1tica natal\u00edcia aplicada \u00e0s bolachas &#8212; especialmente com os duendes envolvidos?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">d. \ud83e\uddea\ud83d\udd25\ud83d\udcdf Pode determinar o modelo matem\u00e1tico que quantifique como a introdu\u00e7\u00e3o das bolachas influencia a temperatura do forno e a velocidade com que esta regressa ao valor desejado definido pelo termostato. Depois, pode desenvolver um dispositivo que combine este modelo com as medi\u00e7\u00f5es da temperatura do forno para calcular, \u00e0 posteriori, quantas bolachas os duendes adicionaram. Seria a fus\u00e3o perfeita entre ci\u00eancia e pastelaria!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">e. \ud83c\udf6a\ud83c\udf6a\ud83c\udf6a Pode simplesmente encher o pr\u00f3ximo tabuleiro com o maior n\u00famero poss\u00edvel de bolachas para garantir que haja o suficiente para todos. Afinal, a vida \u00e9 demasiado curta para ter arrependimentos com bolachas \u2014&#8211; especialmente com os duendes a amea\u00e7ar entrar em greve se o frasco das bolachas ficar vazio!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">f. \ud83e\udd8c\ud83c\udf2c\ufe0f\u2728 Pode pedir ao Rudolph para farejar o ar e estimar quantas bolachas est\u00e3o no forno pelo cheiro. Afinal, h\u00e1 uma raz\u00e3o para ele ser uma lenda natal\u00edcia, famosa pela sua incr\u00edvel habilidade em encontrar bolachas!<\/p>\n\n\n<div class=\"yop-poll-container\" data-yop-poll-id=\"19\"><script type=\"application\/json\" data-yop-poll-init>{\"poll\":{\"id\":\"19\",\"name\":\"14-Dec-2024\",\"template\":\"3\",\"template_base\":\"classic\",\"skin_base\":\"red-v1\",\"status\":\"published\",\"meta_data\":{\"style\":{\"poll\":{\"backgroundColor\":\"#b70004\",\"borderSize\":0,\"borderStyle\":\"none\",\"borderColor\":\"#b70004\",\"borderRadius\":0,\"paddingLeftRight\":10,\"paddingTopBottom\":10},\"questions\":{\"paddingLeftRight\":0,\"paddingTopBottom\":10,\"textColor\":\"#ffffff\",\"textSize\":14,\"textWeight\":\"normal\",\"textAlign\":\"center\"},\"answers\":{\"paddingLeftRight\":0,\"paddingTopBottom\":0,\"textColor\":\"#ffffff\",\"textSize\":14,\"textWeight\":\"normal\",\"skin\":\"minimal\",\"colorScheme\":\"black\"},\"buttons\":{\"backgroundColor\":\"#ffffff\",\"borderSize\":1,\"borderStyle\":\"solid\",\"borderColor\":\"#000000\",\"borderRadius\":0,\"paddingLeftRight\":10,\"paddingTopBottom\":5,\"textColor\":\"#000000\",\"textSize\":14,\"textWeight\":\"normal\",\"align\":\"center\"},\"errors\":{\"borderLeftColorForSuccess\":\"#008000\",\"borderLeftColorForError\":\"#ff0000\",\"borderLeftSize\":10,\"paddingTopBottom\":0,\"textColor\":\"#000000\",\"textSize\":14,\"textWeight\":\"normal\"},\"captcha\":[],\"custom\":{\"css\":\"\"}},\"options\":{\"poll\":{\"voteButtonLabel\":\"&gt;&gt;&gt;\",\"showResultsLink\":\"no\",\"resultsLabelText\":\"Results\",\"showTotalVotes\":\"no\",\"showTotalAnswers\":\"no\",\"startDateOption\":\"now\",\"startDateCustom\":\"\",\"endDateOption\":\"never\",\"endDateCustom\":\"\",\"redirectAfterVote\":\"no\",\"redirectUrl\":\"\",\"redirectAfter\":\"\",\"pageLink\":\"\",\"useCaptcha\":\"no\",\"enableGdpr\":\"no\",\"gdprSolution\":\"ask_consent\",\"gdprConsentText\":\"\",\"loadWithAjax\":\"no\",\"notificationMessageLocation\":\"top\"},\"results\":{\"showResultsMoment\":[\"never\"],\"customDateResults\":\"\",\"showResultsTo\":[],\"resultsDetails\":[\"percentages\"],\"backToVoteOption\":\"no\",\"backToVoteCaption\":\"Back to vote\",\"sortResults\":\"as-defined\",\"sortResultsRule\":\"asc\",\"displayResultsAs\":\"bar\"},\"access\":{\"votePermissions\":[\"wordpress\"]}}}},\"elements\":[{\"id\":\"19\",\"poll_id\":\"19\",\"etext\":\"Choose an option:\",\"etype\":\"question-text\",\"status\":\"active\",\"sorder\":\"1\",\"meta_data\":{\"allowOtherAnswers\":\"no\",\"otherAnswersLabel\":\"Other\",\"addOtherAnswers\":\"no\",\"displayOtherAnswersInResults\":\"no\",\"resultsColorForOtherAnswers\":\"#000000\",\"allowMultipleAnswers\":\"no\",\"multipleAnswersMinim\":\"1\",\"multipleAnswersMaxim\":\"1\",\"answersDisplay\":\"horizontal\",\"answersColumns\":\"\",\"answersSort\":\"as-defined\"},\"subelements\":[{\"id\":\"118\",\"poll_id\":\"19\",\"element_id\":\"19\",\"stext\":\"a\",\"stype\":\"text\",\"status\":\"active\",\"sorder\":\"1\",\"meta_data\":{\"makeDefault\":\"0\",\"makeLink\":\"0\",\"link\":\"\",\"resultsColor\":\"#000000\"}},{\"id\":\"119\",\"poll_id\":\"19\",\"element_id\":\"19\",\"stext\":\"b\",\"stype\":\"text\",\"status\":\"active\",\"sorder\":\"2\",\"meta_data\":{\"makeDefault\":\"0\",\"makeLink\":\"0\",\"link\":\"\",\"resultsColor\":\"#000000\"}},{\"id\":\"120\",\"poll_id\":\"19\",\"element_id\":\"19\",\"stext\":\"c\",\"stype\":\"text\",\"status\":\"active\",\"sorder\":\"3\",\"meta_data\":{\"makeDefault\":\"0\",\"makeLink\":\"0\",\"link\":\"\",\"resultsColor\":\"#000000\"}},{\"id\":\"178\",\"poll_id\":\"19\",\"element_id\":\"19\",\"stext\":\"d\",\"stype\":\"text\",\"status\":\"active\",\"sorder\":\"4\",\"meta_data\":{\"makeDefault\":\"0\",\"makeLink\":\"0\",\"link\":\"\",\"resultsColor\":\"#000000\"}},{\"id\":\"179\",\"poll_id\":\"19\",\"element_id\":\"19\",\"stext\":\"e\",\"stype\":\"text\",\"status\":\"active\",\"sorder\":\"5\",\"meta_data\":{\"makeDefault\":\"0\",\"makeLink\":\"0\",\"link\":\"\",\"resultsColor\":\"#000000\"}},{\"id\":\"224\",\"poll_id\":\"19\",\"element_id\":\"19\",\"stext\":\"f\",\"stype\":\"text\",\"status\":\"active\",\"sorder\":\"6\",\"meta_data\":{\"makeDefault\":\"0\",\"makeLink\":\"0\",\"link\":\"\",\"resultsColor\":\"#000000\"}}]}],\"messages\":{\"captcha\":{\"accessibility-alt\":\"Sound icon\",\"accessibility-title\":\"Accessibility option: listen to a question and answer it!\",\"accessibility-description\":\"Type below the [STRONG]answer[\\\/STRONG] to what you hear. 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