Siete capaci di ottenere 2021 usando le cifre da 1 a 9 in ordine crescente e in ordine decrescente usando solo somma, moltiplicazione, elevazione a potenza e concatenazione di cifre? Per esempio, 2017 = 12³+ 4\u00d756 + 7\u00d78 + 9 = 98 + 7\u00d76 + 54<\/sup>\u00d73 + 2\u00d71. 2. Le cifre dei quadrati<\/strong><\/p>\n Quanti sono i numeri interi da 1 a 2021 per i quali la somma delle cifre del loro quadrato \u00e8 esattamente 21? 3. Il potere del 7<\/strong><\/p>\n Cominciate con il numero a<\/i>1<\/sub> = 7, e costruite la successione a<\/i>n<\/i><\/sub> := an<\/i>−1<\/sub>7<\/sup>. Qual \u00e8 la cifra meno significativa di a<\/i>2021<\/sub>? 4. N\u00e9 somme n\u00e9 differenze<\/strong><\/p>\n Ho costruito un insieme di numeri interi in cui \u00e8 impossibile trovarne due o la cui somma o la cui differenza sia divisibile per 2021, ma che non pu\u00f2 essere ampliato mantenendo tale caratteristica. Quanto \u00e8 grande il mio insieme? 5. Cinque, sette, due<\/strong><\/p>\n Ho preso un numero intero e l’ho moltiplicato per 5. Il risultato \u00e8 un numero di 2021 cifre, che ha un “5”, 1010 “7” e 1010 “2”. Qual \u00e8 la somma delle cifre del numero di partenza? I cinque usuali problemini<\/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":[],"class_list":["post-1874","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/phh2yP-ue","jetpack-related-posts":[{"id":679,"url":"https:\/\/xmau.com\/ilpost\/2015\/12\/25\/problemini-per-natale-2015\/","url_meta":{"origin":1874,"position":0},"title":"Problemini per Natale 2015","author":".mau.","date":"25\/12\/2015","format":false,"excerpt":"Le tradizioni vanno rispettate, vero? Ecco i soliti cinque problemini, le cui soluzioni poster\u00f2 il 31 dicembre. Se state attenti, trovate anche gli aiutini! 1. 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":1459,"url":"https:\/\/xmau.com\/ilpost\/2019\/04\/21\/problemini-per-pasqua-2019\/","url_meta":{"origin":1874,"position":1},"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":744,"url":"https:\/\/xmau.com\/ilpost\/2016\/03\/27\/quizzini-pasqua-2016\/","url_meta":{"origin":1874,"position":2},"title":"Quizzini per Pasqua 2016","author":".mau.","date":"27\/03\/2016","format":false,"excerpt":"Come d'uso, ecco i quizzini pasquali","rel":"","context":"In \"quizzini\"","block_context":{"text":"quizzini","link":"https:\/\/xmau.com\/ilpost\/tag\/quizzini\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":483,"url":"https:\/\/xmau.com\/ilpost\/2014\/12\/31\/risposte-ai-problemini-di-natale-2014\/","url_meta":{"origin":1874,"position":3},"title":"Risposte ai problemini di Natale 2014","author":".mau.","date":"31\/12\/2014","format":false,"excerpt":"Le risposte... giusto prima di Capodanno","rel":"","context":"In \"problemi\"","block_context":{"text":"problemi","link":"https:\/\/xmau.com\/ilpost\/tag\/problemi\/"},"img":{"alt_text":"[fiammiferi 3d]","src":"https:\/\/i0.wp.com\/xmau.com\/wp\/ilpost\/wp-content\/uploads\/sites\/4\/2014\/12\/dic2014-angoli2.png?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":2468,"url":"https:\/\/xmau.com\/ilpost\/2011\/12\/31\/risposte-ai-problemini-natalizi-2011\/","url_meta":{"origin":1874,"position":4},"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":1468,"url":"https:\/\/xmau.com\/ilpost\/2019\/04\/28\/risposte-ai-problemini-per-pasqua-2019\/","url_meta":{"origin":1874,"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\/1874","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=1874"}],"version-history":[{"count":7,"href":"https:\/\/xmau.com\/ilpost\/wp-json\/wp\/v2\/posts\/1874\/revisions"}],"predecessor-version":[{"id":1890,"href":"https:\/\/xmau.com\/ilpost\/wp-json\/wp\/v2\/posts\/1874\/revisions\/1890"}],"wp:attachment":[{"href":"https:\/\/xmau.com\/ilpost\/wp-json\/wp\/v2\/media?parent=1874"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/xmau.com\/ilpost\/wp-json\/wp\/v2\/categories?post=1874"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/xmau.com\/ilpost\/wp-json\/wp\/v2\/tags?post=1874"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n
\n
\n![\"questa](\"https:\/\/i0.wp.com\/xmau.com\/wp\/ilpost\/wp-content\/uploads\/sites\/4\/2020\/12\/q491a.png?resize=467%2C77\")
<\/p>\n
\n
\n
\n![\"tanti](\"https:\/\/i0.wp.com\/xmau.com\/wp\/ilpost\/wp-content\/uploads\/sites\/4\/2020\/12\/q492a.png?resize=366%2C104\")
<\/p>\n
\n
\n
\n![\"settima](\"https:\/\/i0.wp.com\/xmau.com\/wp\/ilpost\/wp-content\/uploads\/sites\/4\/2020\/12\/q493a.png?resize=278%2C118\")
<\/p>\n
\n
\n
\n![\"la](\"https:\/\/i0.wp.com\/xmau.com\/wp\/ilpost\/wp-content\/uploads\/sites\/4\/2020\/12\/q494a.png?resize=506%2C106\")
<\/p>\n
\n
\n
\n![\"il](\"https:\/\/i0.wp.com\/xmau.com\/wp\/ilpost\/wp-content\/uploads\/sites\/4\/2020\/12\/q495a.png?resize=461%2C91\")
<\/p>\n","protected":false},"excerpt":{"rendered":"