{"id":37618,"date":"2026-07-01T04:51:01","date_gmt":"2026-07-01T02:51:01","guid":{"rendered":"https:\/\/xmau.com\/notiziole\/?p=37618"},"modified":"2026-06-28T22:54:09","modified_gmt":"2026-06-28T20:54:09","slug":"come-completare-un-album-di-figurine","status":"publish","type":"post","link":"https:\/\/xmau.com\/notiziole\/2026\/07\/01\/come-completare-un-album-di-figurine\/","title":{"rendered":"Come completare un album di figurine"},"content":{"rendered":"<p>Vi ricordate quando da bambini cercavate di completare la raccolta di figurine, e continuavate a trovare dei doppioni? Avete mai pensato che ci fosse sotto qualche complotto, come tra le due guerre per la figurina del Feroce Saladino nel concorso abbinato alla trasmissione radiofonica\u00a0<em>I quattro moschettieri<\/em>? Non \u00e8 detto in effetti che sia necessariamente cos\u00ec. Il punto \u00e8 che, pur assumendo che le figurine siano distribuite in modo assolutamente casuale, \u00e8 ovvio che in una collezione da 100 pezzi se ne abbiamo solo 10 \u00e8 probabile che la prossima che troviamo ci manchi, ma se ne abbiamo gi\u00e0 90 troveremo il solito doppione (o triplone, o quadruplone&#8230;). Fin qui l&#8217;analisi qualitativa. Ma se volessimo avere un&#8217;idea quantitativa?<\/p>\n<p>Io sono pigro, e quindi vi mando a leggere quanto scritto nel 2012 da Roberto Zanasi <a href=\"https:\/\/proooof.blogspot.com\/2012\/09\/una-misteriosa-costante-matematica-1.html\">qui<\/a> e <a href=\"https:\/\/proooof.blogspot.com\/2012\/09\/una-misteriosa-costante-matematica-2.html\">qui<\/a>. Se siete ancora pi\u00f9 pigri di me, vi svelo la risposta: se le figurine sono\u00a0<em>N<\/em>, il valore atteso del numero di figurine da comprare \u00e8 dell&#8217;ordine di <em>N<\/em> ln(<em>N<\/em>), dove ln() \u00e8 il logaritmo naturale. Quindi con un album di 100 figurine dobbiamo comprarne in media 460. Ma c&#8217;\u00e8 un ma! Adam Kucharski <a href=\"https:\/\/kucharski.substack.com\/p\/three-bits-of-maths-every-parent\">racconta<\/a> che in un <a href=\"https:\/\/www.jstor.org\/stable\/2308930\">articolo del 1960<\/a> di Donald Newman e Lawrence Shepp si dimostra che se si \u00e8 in tanti amici tutti disposti a scambiarsi tra loro i doppioni il numero medio di figurine da comprare per ciascuno scende all&#8217;ordine di <em>N<\/em> ln(ln(<em>N<\/em>)), nel nostro caso circa 153. 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<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_lmt_disableupdate":"","_lmt_disable":"","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":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"set","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 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