{"id":1603,"date":"2019-12-25T06:06:09","date_gmt":"2019-12-25T05:06:09","guid":{"rendered":"http:\/\/xmau.com\/wp\/ilpost\/?p=1603"},"modified":"2019-12-19T16:43:17","modified_gmt":"2019-12-19T15:43:17","slug":"quizzini-per-natale-2019","status":"publish","type":"post","link":"https:\/\/xmau.com\/ilpost\/2019\/12\/25\/quizzini-per-natale-2019\/","title":{"rendered":"Problemini per Natale 2019"},"content":{"rendered":"<p>\u00c8 Natale, tornano i problemini&#8230; e quest&#8217;anno tornano quelli relativi al numero che corrisponde all&#8217;anno prossimo, con la soluzione che verr\u00e0 postata, assieme alle fonti per i problemi e per le soluzioni, il 31 dicembre; in questo modo potete forse evitare la solita tombola :-) Attenzione! L&#8217;ultimo problema non \u00e8 facilissimo.<\/p>\n<p><b><big>1. 2020 in tono minore<\/big><\/b><br \/>\nQual \u00e8 il numero pi\u00f9 grande che potete ottenere se prendete le cifre 2020 e senza cambiarne l&#8217;ordine aggiungete a piacere le quattro operazioni aritmetiche di base, spazi e parentesi? Beh, \u00e8 2020. Se fosse permesso l&#8217;elevamento a potenza avremmo 20<sup>20<\/sup>, ma niente da fare. E qual \u00e8 invece il numero pi\u00f9 piccolo che potete ottenere?<br \/>\n<img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" data-attachment-id=\"1617\" data-permalink=\"https:\/\/xmau.com\/ilpost\/2019\/12\/25\/quizzini-per-natale-2019\/q431a\/\" data-orig-file=\"https:\/\/i0.wp.com\/xmau.com\/ilpost\/wp-content\/uploads\/sites\/5\/2019\/12\/q431a.png?fit=452%2C109&amp;ssl=1\" data-orig-size=\"452,109\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"q431a\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/xmau.com\/ilpost\/wp-content\/uploads\/sites\/5\/2019\/12\/q431a.png?fit=452%2C109&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/xmau.com\/wp\/ilpost\/wp-content\/uploads\/sites\/4\/2019\/12\/q431a.png?resize=452%2C109\" alt=\"\" width=\"452\" height=\"109\" class=\"aligncenter size-full wp-image-1617\" srcset=\"https:\/\/i0.wp.com\/xmau.com\/ilpost\/wp-content\/uploads\/sites\/5\/2019\/12\/q431a.png?w=452&amp;ssl=1 452w, https:\/\/i0.wp.com\/xmau.com\/ilpost\/wp-content\/uploads\/sites\/5\/2019\/12\/q431a.png?resize=300%2C72&amp;ssl=1 300w\" sizes=\"auto, (max-width: 452px) 100vw, 452px\" \/><!-- La risposta non \u00e8 -2020, perch\u00e9 ha un meno unario e non un simbolo di sottrazione --><\/p>\n<p><b><big>2. Da 1 a 10<\/big><\/b><br \/>\nPartite dalla lista 1 2 3 4 5 6 7 8 9 10 e inserite a piacere i simboli delle quattro operazioni oppure parentesi per comporre un&#8217;operazione che vi faccia ottenere 2020. Non siete obbligati a mettere simboli ovunque: se volete partire con 1234 o finire con 910, va benissimo.<br \/>\n<img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" data-attachment-id=\"1618\" data-permalink=\"https:\/\/xmau.com\/ilpost\/2019\/12\/25\/quizzini-per-natale-2019\/q432a\/\" data-orig-file=\"https:\/\/i0.wp.com\/xmau.com\/ilpost\/wp-content\/uploads\/sites\/5\/2019\/12\/q432a.png?fit=520%2C68&amp;ssl=1\" data-orig-size=\"520,68\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"q432a\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/xmau.com\/ilpost\/wp-content\/uploads\/sites\/5\/2019\/12\/q432a.png?fit=520%2C68&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/xmau.com\/wp\/ilpost\/wp-content\/uploads\/sites\/4\/2019\/12\/q432a.png?resize=520%2C68\" alt=\"\" width=\"520\" height=\"68\" class=\"aligncenter size-full wp-image-1618\" srcset=\"https:\/\/i0.wp.com\/xmau.com\/ilpost\/wp-content\/uploads\/sites\/5\/2019\/12\/q432a.png?w=520&amp;ssl=1 520w, https:\/\/i0.wp.com\/xmau.com\/ilpost\/wp-content\/uploads\/sites\/5\/2019\/12\/q432a.png?resize=300%2C39&amp;ssl=1 300w\" sizes=\"auto, (max-width: 520px) 100vw, 520px\" \/><!-- A parte il 10, ci sono solo due numeri di due cifre. --><\/p>\n<p><b><big>3. Alla radice<\/big><\/b><br \/>\nQuanto vale la somma qui raffigurata?<br \/>\n<img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" data-attachment-id=\"1619\" data-permalink=\"https:\/\/xmau.com\/ilpost\/2019\/12\/25\/quizzini-per-natale-2019\/q433a\/\" data-orig-file=\"https:\/\/i0.wp.com\/xmau.com\/ilpost\/wp-content\/uploads\/sites\/5\/2019\/12\/q433a.png?fit=435%2C42&amp;ssl=1\" data-orig-size=\"435,42\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"q433a\" data-image-description=\"\" data-image-caption=\"&lt;p&gt;1\/(1 + \u221a2) + 1\/(\u221a2 + \u221a3) + &amp;#8230; + 1\/(\u221a2019 + \u221a2020)&lt;\/p&gt;\n\" data-large-file=\"https:\/\/i0.wp.com\/xmau.com\/ilpost\/wp-content\/uploads\/sites\/5\/2019\/12\/q433a.png?fit=435%2C42&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/xmau.com\/wp\/ilpost\/wp-content\/uploads\/sites\/4\/2019\/12\/q433a.png?resize=435%2C42\" alt=\"1\/(1 + \u221a2) + 1\/(\u221a2 + \u221a3) + ... + 1\/(\u221a2019 + \u221a2020)\" width=\"435\" height=\"42\" class=\"aligncenter size-full wp-image-1619\" srcset=\"https:\/\/i0.wp.com\/xmau.com\/ilpost\/wp-content\/uploads\/sites\/5\/2019\/12\/q433a.png?w=435&amp;ssl=1 435w, https:\/\/i0.wp.com\/xmau.com\/ilpost\/wp-content\/uploads\/sites\/5\/2019\/12\/q433a.png?resize=300%2C29&amp;ssl=1 300w\" sizes=\"auto, (max-width: 435px) 100vw, 435px\" \/><!-- Togliete le radici dai denominatori. --><\/p>\n<p><b><big>4. Iterazioni<\/big><\/b><br \/>\n\u00c8 data la funzione <i>f<\/i>(<i>x<\/i>) = (1+<i>x<\/i>)\/(1&minus;<i>x<\/i>). Qual \u00e8 il valore dell&#8217;espressione qui sotto, dove la graffa significa che ci sono 2020 iterazioni della funzione <i>f<\/i>?<br \/>\n<img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" data-attachment-id=\"1626\" data-permalink=\"https:\/\/xmau.com\/ilpost\/2019\/12\/25\/quizzini-per-natale-2019\/q434a\/\" data-orig-file=\"https:\/\/i0.wp.com\/xmau.com\/ilpost\/wp-content\/uploads\/sites\/5\/2019\/12\/q434a.png?fit=249%2C75&amp;ssl=1\" data-orig-size=\"249,75\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"q434a\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/xmau.com\/ilpost\/wp-content\/uploads\/sites\/5\/2019\/12\/q434a.png?fit=249%2C75&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/xmau.com\/wp\/ilpost\/wp-content\/uploads\/sites\/4\/2019\/12\/q434a.png?resize=249%2C75\" alt=\"\" width=\"249\" height=\"75\" class=\"aligncenter size-full wp-image-1626\" \/><!-- Calcolate le prime iterazioni dela funzione. --><\/p>\n<p><b><big>5. Soldi<\/big><\/b><br \/>\nAl corso di Economia della Condivisione, 2020 monete vengono divise in un certo modo tra gli studenti, e si chiede loro di scambiarsele secondo questa regola: quando due studenti si incontrano, mettono insieme le loro monete e se le dividono in parti uguali, mettendone una nella Cassa della Classe nel caso il totale sia dispari. Dopo (tanti&#8230;) scambi, gli studenti scoprono che tutte le monete sono finite nella Cassa. Qual \u00e8 il numero minimo possibile di studenti nella classe perch\u00e9 ci\u00f2 possa avvenire?<br \/>\n<img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" data-attachment-id=\"1633\" data-permalink=\"https:\/\/xmau.com\/ilpost\/2019\/12\/25\/quizzini-per-natale-2019\/q435a\/\" data-orig-file=\"https:\/\/i0.wp.com\/xmau.com\/ilpost\/wp-content\/uploads\/sites\/5\/2019\/12\/q435a.png?fit=300%2C300&amp;ssl=1\" data-orig-size=\"300,300\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"q435a\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/xmau.com\/ilpost\/wp-content\/uploads\/sites\/5\/2019\/12\/q435a.png?fit=300%2C300&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/xmau.com\/wp\/ilpost\/wp-content\/uploads\/sites\/4\/2019\/12\/q435a.png?resize=300%2C300\" alt=\"\" width=\"300\" height=\"300\" class=\"aligncenter size-full wp-image-1633\" srcset=\"https:\/\/i0.wp.com\/xmau.com\/ilpost\/wp-content\/uploads\/sites\/5\/2019\/12\/q435a.png?w=300&amp;ssl=1 300w, https:\/\/i0.wp.com\/xmau.com\/ilpost\/wp-content\/uploads\/sites\/5\/2019\/12\/q435a.png?resize=150%2C150&amp;ssl=1 150w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><!-- Ci deve essere almeno uno studente che parte senza monete. Lavorate all'indietro sul numero massimo di monete con due, tre, ... studenti --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Cinque problemini matematici che hanno a che fare con il 2020<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"activitypub_content_warning":"","activitypub_content_visibility":"","activitypub_max_image_attachments":4,"activitypub_interaction_policy_quote":"anyone","activitypub_status":"","footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[1],"tags":[129],"class_list":["post-1603","post","type-post","status-publish","format-standard","hentry","category-uncategorized","tag-quizzini"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/phh2yP-pR","jetpack-related-posts":[{"id":2468,"url":"https:\/\/xmau.com\/ilpost\/2011\/12\/31\/risposte-ai-problemini-natalizi-2011\/","url_meta":{"origin":1603,"position":0},"title":"Risposte ai problemini natalizi 2011","author":".mau.","date":"31\/12\/2011","format":false,"excerpt":"Le risposte ai problemini natalizi!","rel":"","context":"Similar post","block_context":{"text":"Similar post","link":""},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/www.ilpost.it\/wp-content\/uploads\/bloggers\/2011\/12\/8fiammiferi-risp.png?resize=350%2C200&ssl=1","width":350,"height":200},"classes":[]},{"id":2466,"url":"https:\/\/xmau.com\/ilpost\/2011\/12\/25\/problemini-natalizi-2011\/","url_meta":{"origin":1603,"position":1},"title":"Problemini natalizi &#8211; 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Fibonacci I numeri di Fibonacci li conoscete tutti: si parte da F1=F2=1 (e se volete, F0=0) e da l\u00ec ogni numero \u00e8 la somma dei\u2026","rel":"","context":"Similar post","block_context":{"text":"Similar post","link":""},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":482,"url":"https:\/\/xmau.com\/ilpost\/2014\/12\/25\/problemini-per-natale-2014\/","url_meta":{"origin":1603,"position":3},"title":"Problemini per Natale 2014","author":".mau.","date":"25\/12\/2014","format":false,"excerpt":"Auguri!","rel":"","context":"In \"problemi\"","block_context":{"text":"problemi","link":"https:\/\/xmau.com\/ilpost\/tag\/problemi\/"},"img":{"alt_text":"[quattro e sedici angoli]","src":"https:\/\/i0.wp.com\/xmau.com\/wp\/ilpost\/wp-content\/uploads\/sites\/4\/2014\/12\/dic2014-angoli.png?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":1459,"url":"https:\/\/xmau.com\/ilpost\/2019\/04\/21\/problemini-per-pasqua-2019\/","url_meta":{"origin":1603,"position":4},"title":"Problemini per Pasqua 2019","author":".mau.","date":"21\/04\/2019","format":false,"excerpt":"Gli usuali cinque problemini da risolvere... stavolta pi\u00f9 semplici del solito","rel":"","context":"In \"quizzini\"","block_context":{"text":"quizzini","link":"https:\/\/xmau.com\/ilpost\/tag\/quizzini\/"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/xmau.com\/wp\/ilpost\/wp-content\/uploads\/sites\/4\/2019\/04\/q381a.png?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":1468,"url":"https:\/\/xmau.com\/ilpost\/2019\/04\/28\/risposte-ai-problemini-per-pasqua-2019\/","url_meta":{"origin":1603,"position":5},"title":"Risposte ai problemini per Pasqua 2019","author":".mau.","date":"28\/04\/2019","format":false,"excerpt":"A domande, risposte!","rel":"","context":"In \"quizzini\"","block_context":{"text":"quizzini","link":"https:\/\/xmau.com\/ilpost\/tag\/quizzini\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]}],"_links":{"self":[{"href":"https:\/\/xmau.com\/ilpost\/wp-json\/wp\/v2\/posts\/1603","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/xmau.com\/ilpost\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/xmau.com\/ilpost\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/xmau.com\/ilpost\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/xmau.com\/ilpost\/wp-json\/wp\/v2\/comments?post=1603"}],"version-history":[{"count":9,"href":"https:\/\/xmau.com\/ilpost\/wp-json\/wp\/v2\/posts\/1603\/revisions"}],"predecessor-version":[{"id":1637,"href":"https:\/\/xmau.com\/ilpost\/wp-json\/wp\/v2\/posts\/1603\/revisions\/1637"}],"wp:attachment":[{"href":"https:\/\/xmau.com\/ilpost\/wp-json\/wp\/v2\/media?parent=1603"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/xmau.com\/ilpost\/wp-json\/wp\/v2\/categories?post=1603"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/xmau.com\/ilpost\/wp-json\/wp\/v2\/tags?post=1603"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}