{"id":1585,"date":"2025-12-14T08:01:24","date_gmt":"2025-12-14T07:01:24","guid":{"rendered":"https:\/\/control-advent.com\/?p=1585"},"modified":"2025-12-14T08:01:25","modified_gmt":"2025-12-14T07:01:25","slug":"12-which-workshop-should-the-sleigh-be-taken-to","status":"publish","type":"post","link":"https:\/\/control-advent.com\/?p=1585","title":{"rendered":"14 &#8211; Which beard-trimming proposal should Santa choose?"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Santa is known for many traits such as his love of red clothing and his long white beard. A well-kept secret is that Santa\u2019s beard grows exactly&nbsp;<strong>1 cm per week<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">What is charming for some, however, causes extra work for others. Santa himself does not worry much about his beard \u2013 he prefers spending his days overseeing the workshop, eating cookies, and sipping hot chocolate, ginger shots, and the occasional mulled wine.<br>The elves, on the other hand, must ensure he remains presentable when going out.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The longer the beard grows, the more crumbs it catches and the larger the stains from hot drinks. Beyond a certain length Santa even begins to trip over it, and a stumbling Santa is not fit to steer a sleigh. In short: an overgrown beard means more work for the elves and could even endanger Christmas.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Since life would be much easier if Santa\u2019s beard stayed close to the\u00a0<strong>mandatory minimal length for Christmas-staff of 20 cm<\/strong>, the elves propose\u00a0<strong>two<\/strong>\u00a0possible trimming schemes to be applied every Sunday:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Barbara\u2019s Proposal:<\/strong> Each Sunday, Barbara tosses a fair coin:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Heads:<\/strong>\u00a0the beard is cut by\u00a0<strong>2 cm<\/strong>,<\/li>\n\n\n\n<li><strong>Tails:<\/strong>\u00a0the beard is left untouched for another week.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Harry\u2019s Proposal:<\/strong> Each Sunday, Harry rolls a fair six-sided die:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>If a 6 appears:<\/strong>\u00a0the beard is cut\u00a0<strong>down to exactly 20 cm<\/strong>,<\/li>\n\n\n\n<li><strong>If 1\u20135 appear:<\/strong>\u00a0nothing is done for that week.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Santa, overwhelmed by several recent \u201cbeard-related incidents\u201d (including the notorious pasta-sauce disaster), must choose\u00a0<strong>one<\/strong>\u00a0of the two schemes\u00a0<em>right now<\/em>. Since today is Sunday, the first coin toss \/ die roll \/ spinner spin will happen immediately after his choice.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Assuming all random devices are fair, and that Santa wants his beard to be&nbsp;<strong>as long as possible on average<\/strong>, which proposal should he choose?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">a. \ud83c\udfb2\u2702\ufe0f\ud83e\ude99 He should choose\u00a0<strong>Barbara\u2019s<\/strong>\u00a0proposal.<br>b. \ud83c\udfb2\ud83c\udfaf\ud83e\uddd4\u200d\u2642\ufe0f He should choose\u00a0<strong>Harry\u2019s<\/strong>\u00a0proposal.<br>c. \ud83c\udfa1\u2702\ufe0f\ud83c\udf84 It does not matter which proposal he chooses.<br>d. \ud83d\udccf\ud83e\udd37\u200d\u2642\ufe0f\ud83d\udd00 When today his beard is shorter than 25 cm, he should choose Harry\u2019s proposal; otherwise Barbara\u2019s.<br>e. \ud83e\uddf9\u23f3\u2728 All three proposals yield the same average length, but Harry&#8217;s requires the least grooming time on average, so he should be chosen.<br>f. \ud83e\uddd4\ud83c\udf85\u274c A man\u2019s beard is a man\u2019s beard. Even if Christmas must be cancelled, he should not cut it ever.<\/p>\n\n\n<div class=\"yop-poll-container\" data-yop-poll-id=\"51\"><script type=\"application\/json\" data-yop-poll-init>{\"poll\":{\"id\":\"51\",\"name\":\"14-Dec-2025\",\"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\":\"51\",\"poll_id\":\"51\",\"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\":\"480\",\"poll_id\":\"51\",\"element_id\":\"51\",\"stext\":\"a\",\"stype\":\"text\",\"status\":\"active\",\"sorder\":\"1\",\"meta_data\":{\"makeDefault\":\"0\",\"makeLink\":\"0\",\"link\":\"\",\"resultsColor\":\"#000000\"}},{\"id\":\"481\",\"poll_id\":\"51\",\"element_id\":\"51\",\"stext\":\"b\",\"stype\":\"text\",\"status\":\"active\",\"sorder\":\"2\",\"meta_data\":{\"makeDefault\":\"0\",\"makeLink\":\"0\",\"link\":\"\",\"resultsColor\":\"#000000\"}},{\"id\":\"482\",\"poll_id\":\"51\",\"element_id\":\"51\",\"stext\":\"c\",\"stype\":\"text\",\"status\":\"active\",\"sorder\":\"3\",\"meta_data\":{\"makeDefault\":\"0\",\"makeLink\":\"0\",\"link\":\"\",\"resultsColor\":\"#000000\"}},{\"id\":\"486\",\"poll_id\":\"51\",\"element_id\":\"51\",\"stext\":\"d\",\"stype\":\"text\",\"status\":\"active\",\"sorder\":\"4\",\"meta_data\":{\"makeDefault\":\"0\",\"makeLink\":\"0\",\"link\":\"\",\"resultsColor\":\"#000000\"}},{\"id\":\"497\",\"poll_id\":\"51\",\"element_id\":\"51\",\"stext\":\"e\",\"stype\":\"text\",\"status\":\"active\",\"sorder\":\"5\",\"meta_data\":{\"makeDefault\":\"0\",\"makeLink\":\"0\",\"link\":\"\",\"resultsColor\":\"#000000\"}},{\"id\":\"498\",\"poll_id\":\"51\",\"element_id\":\"51\",\"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. Numbers or words:\",\"explanation\":\"Click or touch the [STRONG]ANSWER[\\\/STRONG]\",\"refresh-alt\":\"Refresh\\\/reload icon\",\"refresh-title\":\"Refresh\\\/reload: get new images and accessibility option!\"},\"buttons\":{\"anonymous\":\"Anonymous Vote\",\"wordpress\":\"Sign in with WordPress\",\"facebook\":\"Sign in with Facebook\",\"google\":\"Sign in with Google\"},\"voting\":{\"poll-ended\":\"This poll is no longer accepting votes\",\"poll-not-started\":\"This poll is not accepting votes yet\",\"already-voted-on-poll\":\"Thank you for your vote\",\"invalid-poll\":\"Invalid Poll\",\"no-answers-selected\":\"No answer selected\",\"min-answers-required\":\"At least {min_answers_allowed} answer(s) required\",\"max-answers-required\":\"A max of {max_answers_allowed} answer(s) accepted\",\"no-answer-for-other\":\"No other answer entered\",\"no-value-for-custom-field\":\"{custom_field_name} is required\",\"consent-not-checked\":\"You must agree to our terms and conditions\",\"no-captcha-selected\":\"Captcha is required\",\"not-allowed-by-ban\":\"Vote not allowed\",\"not-allowed-by-block\":\"Vote not allowed\",\"not-allowed-by-limit\":\"Vote not allowed\",\"thank-you\":\"Thank you for your vote\",\"too-many-chars-for-custom-field\":\"Text for {custom_field_name} is too long\"},\"results\":{\"single-vote\":\"vote\",\"multiple-votes\":\"votes\",\"single-answer\":\"answer\",\"multiple-answers\":\"answers\"}},\"date_format\":\"F j, Y\",\"nonce\":\"fd14e88770\",\"page_id\":0,\"tracking_id\":\"https:\\\/\\\/control-advent.com\"}<\/script><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Related control theory topic: stochastic systems<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Santa is known for many traits such as his love of red clothing and his long white beard. A well-kept secret is that Santa\u2019s beard grows exactly&nbsp;1 cm per week. What is charming for some, however, causes extra work for &hellip; <span class=\"more-link\"><a href=\"https:\/\/control-advent.com\/?p=1585\" class=\"readmore\">Continue reading<span class=\"screen-reader-text\">14 &#8211; Which beard-trimming proposal should Santa choose?<\/span><\/a><\/span><\/p>\n","protected":false},"author":1,"featured_media":1587,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[22],"tags":[111],"class_list":["post-1585","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-english","tag-2025-en"],"_links":{"self":[{"href":"https:\/\/control-advent.com\/index.php?rest_route=\/wp\/v2\/posts\/1585","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/control-advent.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/control-advent.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/control-advent.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/control-advent.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1585"}],"version-history":[{"count":3,"href":"https:\/\/control-advent.com\/index.php?rest_route=\/wp\/v2\/posts\/1585\/revisions"}],"predecessor-version":[{"id":1589,"href":"https:\/\/control-advent.com\/index.php?rest_route=\/wp\/v2\/posts\/1585\/revisions\/1589"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/control-advent.com\/index.php?rest_route=\/wp\/v2\/media\/1587"}],"wp:attachment":[{"href":"https:\/\/control-advent.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1585"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/control-advent.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1585"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/control-advent.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1585"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}