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391 392<div id="skinPosition" class="corpo"> 393 <div id="MediaBody" > <!-- style="padding-top:90px" --> 394 395 <div class="Content"> 396 <div id="fj-skin-ref" class="Page"> 397 <div class="PageBody"> 398 399 400 401 402 403 404 405 <a href="https://connect.mondadori.it/registration?area=MS&applicazione=FOCUSSCUOLA&layout=default&urlRitorno=https://www.focus-scuola.it" class="box_camp2033 box-strip-scuola"> 406 407 </a> 408 409 410 411 412 413<div id="PagePart0" class="PageContent "> 414 415 <div id="BPSItem20227_13435" > 416 <!-- SPECIAL_HEAD--><a name="content"></a> 417 418 <h1 class="ATitle">Matematica: gli Inca facevano i conti con nodi e chicchi di mais</h1> 419 420 <div class="Clear"></div> 421 422 <div onclick="return true;" class="ASAT ASleft"> 423 <div class="addthis_inline_share_toolbox"></div> 424 </div> 425 426 <div onclick="window.print();" class="BtIco ASright"><span class="Ico Print"></span>Stampa</div> 427 428 <div class="Clear"></div> 429 430 431<div id="top-gallery" class="gallery-article-content gallery-state-pop"> 432 433 434<div class="gallery-article-content"> 435 <div class="fullgallery-detail"> 436 437 438 439 <div class="gallery detail-gallery gallery-state-pop" id="main-gallery" > 440 441 442 <div class="slide-wrapper first-slide" > 443 444 <a class="GZLens" data-gallery="detailTopGallery1791352000" data-aut="" data-name="Matematica: gli Inca facevano i conti con nodi e chicchi di mais" href="javascript:void(0);" data-slide="0" > </a> 445 <figure> 446 <img src="https://www.focusjunior.it/content/uploads/sites/2/2026/10/1.jpg" alt="" > 447 </figure> 448 449 <div class="caption caption-detail"> 450 451 452 <div class="padd"> 453 <div class="row clearfix"> 454 <div class="col-sm-3 col-xs-12 pull-right counter"> 455 <div class="slide-count-wrap"><span class="current">1</span>/<span class="total">8</span></div> 456 </div> 457 458 459 <div class="col-sm-9 col-xs-12 pull-left dida"> 460 <div class="row"> 461 462 <div class="col-xs-12 text-dida"> 463 464 465 <div class="prev-dida"></div> 466 467 468 </div> 469 470 471 472 </div> 473 474 </div> 475 476 </div> 477 </div> 478 </div> 479 480 </div> 481 482 <div class="slide-wrapper" > 483 484 <a class="GZLens" data-gallery="detailTopGallery1791352000" data-aut="" data-name="Matematica: gli Inca facevano i conti con nodi e chicchi di mais" href="javascript:void(0);" data-slide="1" > </a> 485 <figure> 486 <img src="https://www.focusjunior.it/content/uploads/sites/2/2026/10/2.jpg" alt="" > 487 </figure> 488 489 <div class="caption caption-detail"> 490 491 492 <div class="padd"> 493 <div class="row clearfix"> 494 <div class="col-sm-3 col-xs-12 pull-right counter"> 495 <div class="slide-count-wrap"><span class="current">1</span>/<span class="total">8</span></div> 496 </div> 497 498 499 <div class="col-sm-9 col-xs-12 pull-left dida"> 500 <div class="row"> 501 502 <div class="col-xs-12 text-dida"> 503 504 505 <div class="prev-dida"></div> 506 507 508 </div> 509 510 511 512 </div> 513 514 </div> 515 516 </div> 517 </div> 518 </div> 519 520 </div> 521 522 <div class="slide-wrapper" > 523 524 <a class="GZLens" data-gallery="detailTopGallery1791352000" data-aut="" data-name="Matematica: gli Inca facevano i conti con nodi e chicchi di mais" href="javascript:void(0);" data-slide="2" > </a> 525 <figure> 526 <img src="https://www.focusjunior.it/content/uploads/sites/2/2026/10/3.jpg" alt="" > 527 </figure> 528 529 <div class="caption caption-detail"> 530 531 532 <div class="padd"> 533 <div class="row clearfix"> 534 <div class="col-sm-3 col-xs-12 pull-right counter"> 535 <div class="slide-count-wrap"><span class="current">1</span>/<span class="total">8</span></div> 536 </div> 537 538 539 <div class="col-sm-9 col-xs-12 pull-left dida"> 540 <div class="row"> 541 542 <div class="col-xs-12 text-dida"> 543 544 545 <div class="prev-dida"></div> 546 547 548 </div> 549 550 551 552 </div> 553 554 </div> 555 556 </div> 557 </div> 558 </div> 559
560 </div> 561 562 <div class="slide-wrapper" > 563 564 <a class="GZLens" data-gallery="detailTopGallery1791352000" data-aut="" data-name="Matematica: gli Inca facevano i conti con nodi e chicchi di mais" href="javascript:void(0);" data-slide="3" > </a> 565 <figure> 566 <img src="https://www.focusjunior.it/content/uploads/sites/2/2026/10/4.jpg" alt="" > 567 </figure> 568 569 <div class="caption caption-detail"> 570 571 572 <div class="padd"> 573 <div class="row clearfix"> 574 <div class="col-sm-3 col-xs-12 pull-right counter"> 575 <div class="slide-count-wrap"><span class="current">1</span>/<span class="total">8</span></div> 576 </div> 577 578 579 <div class="col-sm-9 col-xs-12 pull-left dida"> 580 <div class="row"> 581 582 <div class="col-xs-12 text-dida"> 583 584 585 <div class="prev-dida"></div> 586 587 588 </div> 589 590 591 592 </div> 593 594 </div> 595 596 </div> 597 </div> 598 </div> 599 600 </div> 601 602 <div class="slide-wrapper" > 603 604 <a class="GZLens" data-gallery="detailTopGallery1791352000" data-aut="" data-name="Matematica: gli Inca facevano i conti con nodi e chicchi di mais" href="javascript:void(0);" data-slide="4" > </a> 605 <figure> 606 <img src="https://www.focusjunior.it/content/uploads/sites/2/2026/10/5.jpg" alt="" > 607 </figure> 608 609 <div class="caption caption-detail"> 610 611 612 <div class="padd"> 613 <div class="row clearfix"> 614 <div class="col-sm-3 col-xs-12 pull-right counter"> 615 <div class="slide-count-wrap"><span class="current">1</span>/<span class="total">8</span></div> 616 </div> 617 618 619 <div class="col-sm-9 col-xs-12 pull-left dida"> 620 <div class="row"> 621 622 <div class="col-xs-12 text-dida"> 623 624 625 <div class="prev-dida"></div> 626 627 628 </div> 629 630 631 632 </div> 633 634 </div> 635 636 </div> 637 </div> 638 </div> 639 640 </div> 641 642 <div class="slide-wrapper" > 643 644 <a class="GZLens" data-gallery="detailTopGallery1791352000" data-aut="" data-name="Matematica: gli Inca facevano i conti con nodi e chicchi di mais" href="javascript:void(0);" data-slide="5" > </a> 645 <figure> 646 <img src="https://www.focusjunior.it/content/uploads/sites/2/2026/10/6.jpg" alt="" > 647 </figure> 648 649 <div class="caption caption-detail"> 650 651 652 <div class="padd"> 653 <div class="row clearfix"> 654 <div class="col-sm-3 col-xs-12 pull-right counter"> 655 <div class="slide-count-wrap"><span class="current">1</span>/<span class="total">8</span></div> 656 </div> 657 658 659 <div class="col-sm-9 col-xs-12 pull-left dida"> 660 <div class="row"> 661 662 <div class="col-xs-12 text-dida"> 663 664 665 <div class="prev-dida"></div> 666 667 668 </div> 669 670 671 672 </div> 673 674 </div> 675 676 </div> 677 </div> 678 </div> 679 680 </div> 681 682 <div class="slide-wrapper" > 683 684 <a class="GZLens" data-gallery="detailTopGallery1791352000" data-aut="" data-name="Matematica: gli Inca facevano i conti con nodi e chicchi di mais" href="javascript:void(0);" data-slide="6" > </a> 685 <figure> 686 <img src="https://www.focusjunior.it/content/uploads/sites/2/2026/10/7.jpg" alt="" > 687 </figure> 688 689 <div class="caption caption-detail"> 690 691 692 <div class="padd"> 693 <div class="row clearfix"> 694 <div class="col-sm-3 col-xs-12 pull-right counter"> 695 <div class="slide-count-wrap"><span class="current">1</span>/<span class="total">8</span></div> 696 </div> 697 698 699 <div class="col-sm-9 col-xs-12 pull-left dida"> 700 <div class="row"> 701 702 <div class="col-xs-12 text-dida"> 703 704 705 <div class="prev-dida"></div> 706 707 708 </div> 709 710 711 712 </div> 713 714 </div> 715 716 </div> 717 </div> 718 </div> 719
720 </div> 721 722 <div class="slide-wrapper" > 723 724 <a class="GZLens" data-gallery="detailTopGallery1791352000" data-aut="" data-name="Matematica: gli Inca facevano i conti con nodi e chicchi di mais" href="javascript:void(0);" data-slide="7" > </a> 725 <figure> 726 <img src="https://www.focusjunior.it/content/uploads/sites/2/2026/10/GettyImages-90774314-1.jpg" alt="inca" > 727 </figure> 728 729 <div class="caption caption-detail"> 730 731 732 <div class="padd"> 733 <div class="row clearfix"> 734 <div class="col-sm-3 col-xs-12 pull-right counter"> 735 <div class="slide-count-wrap"><span class="current">1</span>/<span class="total">8</span></div> 736 </div> 737 738 739 <div class="col-sm-9 col-xs-12 pull-left dida"> 740 <div class="row"> 741 742 <div class="col-xs-12 text-dida"> 743 744 <div class="prev-dida">Credits: Getty Images</div> 745 746 <div class="prev-dida">PERU - JANUARY 08: Replica made in 1974 from an original held at the Museum of Natural History, New York. Quipus were used by the Incas during the 15th and early 16th centuries as records of all types of accounts. It was discovered in the early 20th century that the knots represent numbers on a base 10 system; the long knots being units and the short ones tens, hundreds or thousands depending on their position. (Photo by SSPL/Getty Images)</div> 747 748 749 </div> 750 751 752 753 </div> 754 755 </div> 756 757 </div> 758 </div> 759 </div> 760 761 </div> 762 763 </div> 764 </div> 765</div> 766 767</div> 768
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771 772 773 774 775 776 777 <div class="fj-google-share-container"> 778 <a href="https://www.google.com/preferences/source?q=focusjunior.it" target="_blank" rel="noopener noreferrer" class="fj-google-share"> 779 <span class="fj-icon-google"> 780 <svg viewBox="0 0 24 24" aria-hidden="true"> 781 <path fill="#4285F4" d="M22.56 12.25c0-.78-.07-1.53-.2-2.25H12v4.26h5.92c-.26 1.37-1.04 2.53-2.21 3.31v2.77h3.57c2.08-1.92 3.28-4.74 3.28-8.09z"/> 782 <path fill="#34A853" d="M12 23c2.97 0 5.46-.98 7.28-2.66l-3.57-2.77c-.98.66-2.23 1.06-3.71 1.06-2.86 0-5.29-1.93-6.16-4.53H2.18v2.84C3.99 20.53 7.7 23 12 23z"/> 783 <path fill="#FBBC05" d="M5.84 14.09c-.22-.66-.35-1.36-.35-2.09s.13-1.43.35-2.09V7.07H2.18C1.43 8.55 1 10.22 1 12s.43 3.45 1.18 4.93l2.85-2.22.81-.62z"/> 784 <path fill="#EA4335" d="M12 5.38c1.62 0 3.06.56 4.21 1.64l3.15-3.15C17.45 2.09 14.97 1 12 1 7.7 1 3.99 3.47 2.18 7.07l3.66 2.84c.87-2.6 3.3-4.53 6.16-4.53z"/> 785 </svg> 786 </span> 787 Scegli Focus Junior su Google 788 </a> 789 <a href="https://whatsapp.com/channel/0029VaksRBV6mYPDjS78et1c" target="_blank" rel="noopener noreferrer" class="fj-google-share"> 790 <span class="fj-icon-google"> 791 <svg viewBox="0 0 32 32" aria-hidden="true"> 792 <path fill="#25D366" d="M16.003 0h-.006C7.164 0 0 7.164 0 16c0 3.5 1.128 6.746 3.046 9.383L1.05 31.324l6.145-1.965A15.9 15.9 0 0 0 16.003 32C24.836 32 32 24.836 32 16S24.836 0 16.003 0z"/> 793 <path fill="#fff" d="M25.314 22.593c-.386 1.09-1.918 1.994-3.14 2.258-.836.178-1.928.32-5.604-1.203-4.702-1.948-7.729-6.726-7.965-7.036-.226-.31-1.9-2.529-1.9-4.824s1.166-3.413 1.636-3.893c.386-.394.99-.573 1.57-.573.188 0 .356.01.508.017.47.02.706.048 1.016.79.386.93 1.326 3.225 1.438 3.461.114.236.228.556.068.866-.15.32-.282.462-.518.734-.236.272-.46.48-.696.772-.216.254-.46.526-.188.996.272.46 1.21 1.994 2.592 3.225 1.784 1.588 3.23 2.08 3.748 2.296.386.16.846.122 1.128-.188.358-.396.8-1.052 1.25-1.698.32-.462.724-.52 1.148-.36.432.15 2.716 1.28 3.186 1.514.47.236.78.35.894.548.112.198.112 1.14-.274 2.23z"/> 794 </svg> 795 </span> 796 Segui Focus Junior su Whatsapp 797 </a> 798 </div> 799 <h2 class="ASommario"> 800 Censimenti, bestiame e calcoli difficili, senza carta né penna: come i contabili dell'impero inca stupirono i conquistatori spagnoli. E perché la loro yupana si usa ancora nelle scuole del Perù </h2> 801 802 <div class="text-center visible-xs"> 803 804<div class="padd clearfix "> 805 806 <div class="amePlaceholderBox"> 807 808 809 810 <div 811 id="adv-gpt-box-mobile-container1" 812 class="adv_concessionaria adv-mobile" 813 ></div> 814 815 816 817 818 819 820 821 </div> 822 823</div> </div> 824 825 826 <div class="Clear"></div> 827 828 <div id="AContent" class="AText" > 829 <p>Dopo un'esplorazione della <a href="https://www.focus-scuola.it/con-i-numeri-dargilla-dei-sumeri-in-quarta-primaria-la-matematica-diventa-unavventura/" target="_blank" rel="noopener">matematica in Mesopotamia</a> e una piccola incursione nella <a href="https://www.focus-scuola.it/lalgoritmo-segreto-della-moltiplicazione-nascosto-in-una-filastrocca/" target="_blank" rel="noopener">matematica egizia</a>, questa volta cambiamo latitudine, continuando a proiettarci indietro di qualche secolo. In particolare, ci concentreremo su due artefatti della <strong>tradizione Inca: quipu e yupana</strong>.</p> 830<h2><strong>Il quipu: numeri fatti di nodi</strong></h2> 831<p dir="ltr">I conquistatori spagnoli sbarcarono nell'America del Sud subito dopo la "scoperta" di Colombo del 1492. Qui la civiltà inca, che occupava i territori dell'attuale Bolivia, del Perù e dell'Ecuador, li lasciò certamente meravigliati. Pur ignorando la ruota, la trazione animale e una scrittura paragonabile a quella europea, <strong>gli Incas erano ingegnosi</strong>. Per archiviare dati si servivano di un <strong>sistema molto elaborato di cordicelle a nodi (quipu)</strong>.</p> 832<p dir="ltr">Il quipu (nella lingua degli Incas significa "nodo") consisteva in una funicella da cui pendevano tante cordicelle lunghe una cinquantina di centimetri. Su ogni cordicella si rappresentavano i numeri secondo il principio della base decimale, con una sequenza di nodi a livelli diversi. Il <strong>livello più basso serviva per le unità </strong> (cinque nodi indicavano 5 unità ). Il livello successivo, andando <strong>verso l'alto, era quello delle decine</strong> (tre nodi a questo livello indicavano 3 decine), e così via procedendo verso l'alto.</p> 833<p><img class="size-medium wp-image-242063 aligncenter" src="https://www.focus-scuola.it/content/uploads/sites/2/2026/10/1-300x204.jpg" alt="" width="300" height="204" /></p> 834<p><em>[Fig. 1 Rappresentazione su una cordicella di un quipu inca del numero 4235]</em></p> 835<h2><strong>I guardiani dei nodi</strong></h2> 836<p dir="ltr">In ogni città o villaggio dell'impero degli Incas vi erano funzionari, detti quipucamayoes (guardiani dei nodi). Il loro compito era registrare su quipu le nascite, i matrimoni, i decessi e i giovani idonei alle armi. Registravano anche l'inventario delle risorse e altri dati utili all'amministrazione locale. Erano funzionari di governo importanti e godevano di uno status sociale elevato.</p> 837<p dir="ltr">Il peruviano Guanam Poma de Ayala dedicò ai quipucamayoes sette disegni. Si trovano in una lettera di 1179 pagine che l'autore spedì al re di Spagna attorno al 1600. La scritta in alto di uno di questi disegni (Fig. 2) indica che la persona con il quipu in mano è addirittura il Segretario dell'Inca e del suo Consiglio.</p> 838<p><img class="alignnone size-medium wp-image-242064 aligncenter" src="https://www.focus-scuola.it/content/uploads/sites/2/2026/10/2-300x139.jpg" alt="" width="300" height="139" /></p> 839<p><em>[Fig. 2 Un quipucamayu inca alle prese con un quipu]</em></p> 840<p><strong>Il colore delle cordicelle</strong> di uno stesso quipu variava a seconda del tipo di informazione. Il <strong>bianco</strong> serviva per l'inventario degli ovini o caprini, il <strong>verde</strong> per i bovini e così via. La prima cordicella verde a destra indicava il numero di tori, la seconda il numero di vacche da latte. Seguivano le vacche sterili e infine i vitelli. I pastori degli altipiani del Perù o della Bolivia praticavano questa classificazione ancora nel XIX secolo.</p> 841<h2><strong>Dal quipu al chimpu</strong></h2> 842<p>Un'evoluzione del quipu, tuttora in uso presso gli indios della Bolivia e del Perù, è il chimpu. Al posto delle singole cordicelle del quipu c'è un fascio di cordicelle sottili. Tre nodi su una sola cordicella del fascio indicano 3 unità , tre nodi su due cordicelle simboleggiano invece 3 decine. Cinque nodi su tre cordicelle rappresentano 5 centinaia, e così via. I vari nodi si trovano a diversi livelli, come nel quipu. Il numero di cordicelle sulle quali si eseguono i nodi, però, mostra con maggiore chiarezza l'ordine decimale corrispondente (fig. 3).</p> 843<p><img class="size-medium wp-image-242065 aligncenter" src="https://www.focus-scuola.it/content/uploads/sites/2/2026/10/3-300x130.jpg" alt="" width="300" height="130" /></p> 844<p><em>[Fig. 3 Il chimpu]</em></p> 845<h2><strong>Cordicelle a nodi in tutto il mondo</strong></h2> 846<p dir="ltr">La numerazione con l'impiego di cordicelle a nodi non è una esclusiva degli Incas. Anche gli esattori palestinesi, i pubblicani, utilizzavano sistemi analoghi nel 2° secolo d. C. Lo stesso facevano gli arabi, i cinesi già nel 500 a. C., i siberiani, gli africani della Nigeria, gli indiani d'America. Ancora alla fine del secolo scorso i mugnai tedeschi si servivano di cordicelle a nodi. Così registravano i commerci di grano con i contadini o di farina con i fornai.</p> 847<p dir="ltr">In alcuni villaggi dell'India abitati da analfabeti, per il censimento della popolazione del 1872 si distribuirono a ogni famiglia quattro cordicelle di colori diversi. Sulla cordicella nera si facevano tanti nodi quanti erano gli adulti maschi della famiglia. Su una rossa si registravano le donne adulte, su una bianca i ragazzi e su una gialla le ragazze. Il sistema delle cordicelle a nodi era quindi un metodo popolare ben noto a coloro che non sapevano scrivere.</p> 848<h2><strong>Uno strumento di calcolo inca: la yupana</strong></h2> 849<p>Sulla corda principale di un quipu si trovavano spesso corde che rappresentavano una somma, come mostra la fig. 4. In questo modo potevano registrare il numero complessivo dei bovini o degli ovini o altro.<
849/p> 850<p><img class="size-medium wp-image-242066 aligncenter" src="https://www.focus-scuola.it/content/uploads/sites/2/2026/10/4-300x163.jpg" alt="" width="300" height="163" /></p> 851<p><em>[Fig. 4 Rappresentazione su un quipu della somma (32+327+50+322=731)]</em></p> 852<p>Ma dove si eseguiva l'addizione? E come? A queste curiosità risponde un passo di un libro di padre José de Acosta, un sacerdote spagnolo vissuto in Perù dal 1571 al 1586:</p> 853<p>"<em>Vederli usare un'altra specie di quipu, con chicchi di granoturco, è perfetta letizia. Allo scopo di eseguire calcoli molto difficili per i quali un contabile capace avrebbe bisogno di carta e penna, questi indiani fanno uso delle loro granaglie. Ne mettono una qua, tre in un altro posto, e otto non so dove. Muovono qua e là un chicco e la realtà è che sono capaci di completare i loro calcoli senza fare il più piccolo errore. In verità , nell'esercizio della matematica sono migliori di noi che usiamo carta e inchiostro. Se questo non è ingegno e queste popolazioni sono animali selvaggi, lasciate che lo giudichi chi vuole! Quello che io reputo certo è che in quello che si impegnano a fare sono superiori a no</em>i".</p> 854<p><img class="size-medium wp-image-242067 aligncenter" src="https://www.focus-scuola.it/content/uploads/sites/2/2026/10/5-246x300.jpg" alt="" width="246" height="300" /></p> 855<p><em>[Fig. 5 Tratta da Nueva Cronica y Buen Gobierno di Felipe Guanam Poma de Ayala]</em></p> 856<h2><strong>La yupana nelle scuole di oggi</strong></h2> 857<p>L'altra specie di quipu di cui parla José de Acosta è la yupana: la scacchiera raffigurata in basso a sinistra di fig. 5. Felipe Guanam Poma de Ayala non fornisce spiegazioni sull'uso della yupana, perciò gli studiosi ne hanno elaborato diverse interpretazioni. Non è mia intenzione alimentare la discussione sui vari modelli interpretativi della yupana. Faccio riferimento solo all'uso che oggi se ne fa nelle scuole di alcuni Paesi dell'America Meridionale. Qui la yupana si disegna su un cartoncino, come in fig. 6.</p> 858<p><img class="size-medium wp-image-242068 aligncenter" src="https://www.focus-scuola.it/content/uploads/sites/2/2026/10/6-300x231.jpg" alt="" width="300" height="231" /></p> 859<p><em>[Fig. 6 Una yupana utilizzata oggi nella scuola primaria del Perù.]</em></p> 860<p dir="ltr">Sulla colonna a destra si sistemano le unità , collocando chicchi di mais nei dieci fori. Quando questa colonna è piena si tolgono tutti i chicchi e se ne colloca uno nella colonna adiacente a sinistra. Lì si sistemano le decine, e così via. Rappresentare un numero sulla yupana è molto semplice e calcolare somme o differenze è banale. La moltiplicazione e la divisione si considerano come addizioni e sottrazioni ripetute.</p> 861<p dir="ltr">Per comprendere la meraviglia di José de Acosta nel vedere all'opera i contabili Incas, si può vedere qualche filmato su YouTube. Mostrano bambini o maestre peruviane intente a eseguire calcoli con la loro yupana.</p> 862<h2><strong>Una possibile interpretazione dell'antica yupana</strong></h2> 863<p dir="ltr">Sulla yupana raffigurata in fig. 5 gli studiosi hanno avanzato diverse interpretazioni. Probabilmente il disegnatore inca autore del disegno per conto di Felipe Guanam Poma de Ayala ha volutamente nascosto qualche particolare. Alcuni studiosi sostengono questa ipotesi. Se la accettiamo, forse gli Incas utilizzavano la scacchiera ruotandola di 90° in verso antiorario, come avviene oggi nelle scuole peruviane (fig. 6).</p> 864<p dir="ltr">L'interpretazione che avanzo, e che probabilmente altri hanno già proposto, si basa su un atto di fede. Gli antichi incas avevano una intelligenza vivace e cercavano di economizzare gli sforzi, come usano fare i matematici. Mi spiego. Se su ogni colonna della scacchiera avessero praticato 1, 2, 4, 8 incavi, avrebbero realizzato qualcosa di simile al mini-computer di George Papy. Posizionando un gettone nella casella con un incavo e uno in quella con quattro incavi si ottiene il numero 5. Con tre gettoni, nelle caselle con uno, due e quattro incavi, si ha il numero 7, e così vi<span style="font-size: 1rem">a.</span></p> 865<h2 dir="ltr"><strong>Il trucco degli Incas: 1, 2, 3, 5</strong></h2> 866<p dir="ltr">Gli Incas sono stati ancora più attenti a minimizzare il numero di incavi: hanno praticato su ogni colonna 1, 2, 3, 5 incavi. In questo modo un chicco di mais nella prima casella in alto vale 1, nella seconda vale 2. Nella terza vale 3, nella quarta in basso vale 5. Pertanto, per rappresentare il numero 7 non occorrono sette chicchi ma solo due. Uno va nella casella che vale 2 e uno in quella che vale 5. Il numero 9 non necessita di nove chicchi ma solo di tre. Uno va nella casella che vale 5, uno in quella che vale 3 e uno in quella che vale 1. à una bella economia e, ad esempio, per rappresentare il numero 12869 (fig. 7) occorrono nove chicchi e non ventisei.</p> 867<p>.</p> 868<p><img class="size-medium wp-image-242069 aligncenter" src="https://www.focus-scuola.it/content/uploads/sites/2/2026/10/7-300x204.jpg" alt="" width="300" height="204" /></p> 869<p><em>[Fig. 7 Rappresentazione sulla yupana del numero 12869]</em></p> 870 <div class="Clear"></div> 871 872 </div> 873 874 <div class="Clear"></div> 875 876 877 <div class="AFirma"> 878 879 880 <a href="https://www.focus-scuola.it/autori/bruno-jannamorelli/" > 881 di Bruno Jannamorelli </a> 882 883 884 885 </div> 886 887 <div class="ADates"> 888 <time datetime="2026-10-06 7:23" class="time"> 889 06 ottobre 2026 </time> 890 </div> 891 892 <div class="Clear"></div> 893 894 <div class="ATags SStack BackNRL"> 895 896 <a href="https://www.focus-scuola.it/category/didattica/"><span>#</span>Didattica</a> 897 <a href="https://www.focus-scuola.it/tag/matematica-inca/"><span>#</span>matematica inca</a> 898 <a href="https://www.focus-scuola.it/tag/quipu/"><span>#</span>quipu</a> 899 <a href="https://www.focus-scuola.it/tag/sistema-decimale/"><span>#</span>sistema decimale</a> 900 901 </div> 902 903 904 905 906 907 908 909 910 911 <div id="adv_BoxBottom" class="adv_concessionaria"></div> 912 913 914 915 916 917 918 919 <div class="ARelatedA"> 920 <div class="TitleRedLabel SStack"> 921 ARTICOLI <span>CORRELATI</span> 922 </div> 923 <div class="Clear"></div> 924 925 926 <div class="ARBox"> 927 928 929 <a href="https://www.focus-scuola.it/con-i-numeri-dargilla-dei-sumeri-in-quarta-primaria-la-matematica-diventa-unavventura/" class="ARABImg" > 930 931 <img src="https://www.focusjunior.it/content/uploads/sites/2/2026/09/AdobeStock_199601054-1-810x540.jpeg" alt="Con i numeri d’argilla dei Sumeri: in quarta primaria la matematica diventa un’avventura" title="Con i numeri d’argilla dei Sumeri: in quarta primaria la matematica diventa un’avventura" > 932 </a> 933 934 <a href="https://www.focus-scuola.it/con-i-numeri-dargilla-dei-sumeri-in-quarta-primaria-la-matematica-diventa-unavventura/" class="ARABTitle LinkU" > 935 Con i numeri d’argilla dei Sumeri: in quarta primaria la matematica diventa un’avventura </a> 936 937</div> 938<div class="ARBox"> 939 940 941 <a href="https://www.focus-scuola.it/educazione-affettiva-a-scuola-il-ruolo-degli-insegnanti/" class="ARABImg" > 942 943 <img src="https://www.focusjunior.it/content/uploads/sites/2/2025/12/GettyImages-1465474772.jpg" alt="Educazione affettiva a scuola: il ruolo degli insegnanti" title="Educazione affettiva a scuola: il ruolo degli insegnanti" > 944 </a> 945 946 <a href="https://www.focus-scuola.it/educazione-affettiva-a-scuola-il-ruolo-degli-insegnanti/" class="ARABTitle LinkU" > 947 Educazione affettiva a scuola: il ruolo degli insegnanti </a> 948 949</div> 950<div class="ARBox"> 951 952 953 <a href="https://www.focus-scuola.it/i-messaggi-segreti-e-la-crittografia-di-giulio-cesare/" class="ARABImg" > 954 955 <img src="https://www.focusjunior.it/content/uploads/sites/2/2026/09/GettyImages-1142133247-1-810x540.jpg" alt="I messaggi segreti e la crittografia di Giulio Cesare" title="I messaggi segreti e la crittografia di Giulio Cesare" > 956 </a> 957 958 <a href="https://www.focus-scuola.it/i-messaggi-segreti-e-la-crittografia-di-giulio-cesare/" class="ARABTitle LinkU" > 959 I messaggi segreti e la crittografia di Giulio Cesare </a> 960 961</div> 962<div class="ARBox"> 963 964 965 <a href="https://www.focus-scuola.it/19-marzo-festa-di-san-giuseppe-e-del-papa/" class="ARABImg" > 966 967 <img src="https://www.focusjunior.it/content/uploads/sites/2/2024/03/GettyImages-1350791754.jpg" alt="19 marzo, festa di San Giuseppe e del papà " title="19 marzo, festa di San Giuseppe e del papà " > 968 </a> 969 970 <a href="https://www.focus-scuola.it/19-marzo-festa-di-san-giuseppe-e-del-papa/" class="ARABTitle LinkU" > 971 19 marzo, festa di San Giuseppe e del papà </a> 972 973</div> 974 975 <div class="Clear"></div> 976 </div> 977 978 979 980 <div class="ARelatedN"> 981 <div class="TitleRedLabel SStack">ULTIME <span>NEWS</span></div> 982 <div class="Clear"></div> 983 <div class="HList"> 984 985 986 987 988<div class="AList "> 989 990 991 992 993 <a href="https://www.focus-scuola.it/ia-in-classe-5-strumenti-gratuiti-di-magicschool-da-provare/" class="AListTitle LinkU">
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1698<script> 1699 async function isConsentGiven (siteId,cookiePolicyId){ 1700 var cs = document.cookie.split(';'); 1701 for (var i = 0; i < cs.length; i++) { 1702 while (cs[i].charAt(0) == ' ') cs[i] = cs[i].substring(1); 1703 await yieldToMain(); 1704 if(cs[i].indexOf('_iub_cs-s'+ siteId) == 0||cs[i].indexOf('_iub_cs-'+ cookiePolicyId) == 0) { 1705 return true; 1706 } 1707 } 1708 return false; 1709 } 1710 1711 /*postTcfReady*/ 1712 async function postTcfReady(cb) { 1713 if(typeof tcfIsReady !== 'undefined') { 1714 console.log('[Ame consent] cb by variable:',cb.name); 1715 await yieldToMain(); 1716 cb(); 1717 1718 } else { 1719 window.addEventListener('tcf2Ready', async function() { 1720 console.log('[Ame consent] cb by listener:',cb.name); 1721 await yieldToMain(); 1722 cb(); 1723 }) 1724 } 1725 } 1726 1727 /*postTcfRejected*/ 1728 async function postConsentRejected(cb) { 1729 if (typeof window.ameConsentGiven !== 'undefined' && window.ameConsentGiven === false) { 1730 console.log('[Ame consent rejected] cb by variable:', cb.name); 1731 await yieldToMain(); 1732 cb(); 1733 } else { 1734 window.addEventListener('consentRejected', async function () { 1735 console.log('[Ame consent rejected] cb by listener:', cb.name); 1736 await yieldToMain(); 1737 cb(); 1738 }); 1739 } 1740 } 1741 1742 /*MM LOADER*/ 1743 function mmLoader(objAttr, chainId = null, elementType = "script", target = document.body) { 1744 return new Promise(async function (resolve, reject) { 1745 let element = document.createElement(elementType); 1746 1747 for (const property in objAttr) { 1748 element.setAttribute(property, objAttr[property]); 1749 } 1750 let path = objAttr.src || objAttr.href; 1751 element.onload = async () => { 1752 await yieldToMain(); 1753 resolve(element); 1754 console.log(`[mmLoader] ${path} caricato!`, "chainId_" + chainId + " Time: " + performance.now()); 1755 }; 1756 element.onerror = e => { 1757 reject( 1758 new Error(`[mmLoader] Errore sul caricamento di ${path}`) 1759 ); 1760 console.log(e); 1761 }; 1762 await yieldToMain(); 1763 target.appendChild(element); 1764 1765 }); 1766 } 1767 1768 function wait(ms) { 1769 return new Promise(resolve => setTimeout(resolve, ms)); 1770 } 1771 1772 function loadJsbyIO (src, targetSelector, rootMargin) { 1773 let options = { 1774 root: null, 1775 rootMargin: rootMargin || "0px", 1776 threshold: 1.0, 1777 }; 1778 1779 const callback = (entries, observer) => { 1780 entries.forEach((entry) => { 1781 if (entry.isIntersecting) { 1782 console.log(`[loadJsbyIO] loading ${src} by intersection of ${targetSelector}`); 1783 mmLoader({ 1784 src: src, 1785 async: true 1786 }); 1787 obs.disconnect(); 1788 } 1789 }); 1790 }; 1791 1792 let obs = new IntersectionObserver(callback, options); 1793 let target = document.querySelector(targetSelector); 1794 obs.observe(target); 1795 }; 1796 1797 async function yieldToMain () { 1798 if ('scheduler' in window && 'yield' in scheduler) { 1799 return scheduler.yield(); 1800 } 1801 1802 return new Promise(resolve => { 1803 setTimeout(resolve, 0); 1804 }); 1805 } 1806 /*END MM LOADER*/ 1807</script>
1807 1808 1809<!-- SCRIPTS CON MM LOADER -->
1810<script type="text/javascript"> 1811 mmLoader({ 1812 src: "https://dafne.sirio.stbm.it/utility-fe/prod/web-components/ame-mh-piemme_v1.min.js", 1813 defer: true 1814 }); 1815</script>
1815 1816
1817<script> 1818 function startIasPet() { 1819 mmLoader({ 1820 src: "https://static.adsafeprotected.com/iasPET.1.js", 1821 async: true, 1822 }) 1823 } 1824 postTcfReady(startIasPet); 1825 1826 //OTTIMIZZAZIONE IAS --- TUTTO DEVE AVERE SCOPE GLOBALE NON WRAPPARE 1827 var globalAdRequestParams; 1828 var slotAdRequestParamsMap; 1829 var responseIas = {}; 1830 // Risolta quando il targeting IAS e' pronto (o e' fallito): il player la attende 1831 // prima di costruire la VAST, altrimenti cust_params parte senza le key value IAS. 1832 var iasTargetingResolve; 1833 var iasTargetingReady = new Promise(function (resolve) { 1834 iasTargetingResolve = resolve; 1835 }); 1836 var iasDFPUtilites = (function () { 1837 const equal = "%3D"; 1838 const ampsersand = "%26"; 1839 const comma = "%2C"; 1840 var adSlotDataObj; 1841 var parseIASResponseData = function (adSlotData) { 1842 adSlotDataObj = JSON.parse(adSlotData); 1843 } 1844 var getIASPageTargetingAsQueryString = function () { 1845 var iasPageTargeting = ""; 1846 iasPageTargeting = appendRequestParam( 1847 iasPageTargeting, "fr", adSlotDataObj.fr); 1848 if (adSlotDataObj.custom && adSlotDataObj.custom['ias-kw']) { 1849 var iasKw = adSlotDataObj.custom['ias-kw']; 1850 if (Array.isArray(iasKw)) { 1851 iasKw = iasKw.join(comma); 1852 } 1853 iasPageTargeting = appendRequestParam( 1854 iasPageTargeting, "ias-kw", iasKw); 1855 } 1856 for (const k in adSlotDataObj.brandSafety) { 1857 iasPageTargeting = appendRequestParam( 1858 iasPageTargeting, k, adSlotDataObj.brandSafety[k]); 1859 } 1860 return iasPageTargeting; 1861 } 1862 var getIASSlotTargetingAsQueryString = function () { 1863 var iasSlotTargeting = {}; 1864 for (const slotId in adSlotDataObj.slots) { 1865 const slotIdValues = adSlotDataObj.slots[slotId]; 1866 var slotParams = ""; 1867 for (const key in slotIdValues) { 1868 var segments = slotIdValues[key]; 1869 if (Array.isArray(segments)) { 1870 slotParams = slotParams.concat(ampsersand, key, equal); 1871 const last = segments.length - 1; 1872 for (var i = 0, len = segments.length; i < len; i++) { 1873 var separator = comma; 1874 if(i === last) { 1875 separator = ""; 1876 } 1877 slotParams = slotParams.concat(segments[i], separator); 1878 } 1879 } else { 1880 slotParams = appendRequestParam(slotParams, key, segments); 1881 } 1882 } 1883 iasSlotTargeting[slotId] = slotParams; 1884 } 1885 return iasSlotTargeting; 1886 } 1887 var appendRequestParam = function (query, key, value) { 1888 return query.concat(ampsersand, key, equal, value); 1889 } 1890 return { 1891 parseIASResponseData: parseIASResponseData, 1892 getIASPageTargetingAsQueryString: getIASPageTargetingAsQueryString, 1893 getIASSlotTargetingAsQueryString: getIASSlotTargetingAsQueryString 1894 }; 1895 }()); 1896 var iasDataHandler; 1897 var __iasPET = __iasPET || {}; 1898 __iasPET.queue = __iasPET.queue || []; 1899 __iasPET.pubId = '931714'; //your account manager provides this ID 1900 iasDataHandler = function (adSlotData) { 1901 try { 1902 console.log("Callback function"); 1903 iasDFPUtilites.parseIASResponseData(adSlotData); 1904 globalAdRequestParams = iasDFPUtilites.getIASPageTargetingAsQueryString(); 1905 slotAdRequestParamsMap = iasDFPUtilites.getIASSlotTargetingAsQueryString(); 1906 var slotParams = slotAdRequestParamsMap['ad-1'] || ""; 1907 responseIas['slot'] = globalAdRequestParams.substr(3) + slotParams; 1908 console.log('&cust_params=' + responseIas['slot']); 1909 } catch (e) { 1910 console.warn('[IAS] targeting non applicato', e); 1911 } finally { 1912 // Sempre, anche in errore: il player non deve restare bloccato ad aspettare. 1913 iasTargetingResolve(); 1914 const iasReady = new Event("iasReady"); 1915 document.dispatchEvent(iasReady); 1916 } 1917 } 1918 var iasPETSlots = []; 1919 var adSlots = ['ad-1']; 1920 for (var i = 0; i < adSlots.length; i++) { 1921 iasPETSlots.push({ 1922 adSlotId: adSlots[i], 1923 size: [640, 360], 1924 adUnitPath:"38681514,22676954050", 1925 type: "video" 1926 }); } 1927 __iasPET.queue.push({ 1928 adSlots: iasPETSlots, 1929 dataHandler: iasDataHandler 1930 }); 1931</script>
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1932<script> 1933var startPageTimes = {}; 1934 1935function startAdvChain2022() { 1936 let startTime = performance.now(); 1937 1938 const startAdmantx = function () { 1939 1940 /* ADMANTX CONF */ 1941 let admantxOptions = `{"tag": "focusjunior.it","key": "c7ce35aef2897252b6d542f0b2b2f5cbf2d2d93120f21e66933b2e56aac6a928","method": "descriptor","filter": "default","decorator": "template.focusjunior","type": "URL","mode": "async","body": "${escape(document.location.href)}"}`; 1942 let decodedAdmantx = 'https://euasync01.admantx.com/admantx/service?request='+admantxOptions; 1943 let urlAdmantx = encodeURI(decodedAdmantx); 1944 1945 return mmLoader({ 1946 src: urlAdmantx, 1947 async: true 1948 },"advChain"); 1949 } 1950 1951 const promises = [startAdmantx()]; 1952 1953 Promise.allSettled(promises). 1954 then((results) => { 1955 console.log('[startAdvChain2022] admantx e neodata elaborati', performance.now() - startTime); 1956 console.log('[startAdvChain2022]',results); 1957 1958 mmLoader({ 1959 src: "//securepubads.g.doubleclick.net/tag/js/gpt.js?cb=1", 1960 async: true 1961 },"advChain").then( () => window.dispatchEvent(new Event("introCanStart") )) 1962 .then((results) => { 1963 console.log('[startAdvChain2022] gpt caricato', performance.now() - startTime); 1964 mmLoader({ 1965 src: "https://www.focusjunior.it/content/themes/FocusJunior/assets/js/piemme2.js?cb=1", 1966 async: true, 1967 "data-hpSez": "Didattica", 1968 "data-subSez": "Didattica", 1969 "data-isArticle": "1", 1970 },"advChain") 1971 }).then(e => { 1972 console.log('[startAdvChain2022] piemme caricato', performance.now() - startTime); 1973 const advChainEvent = new Event('advChainLoaded'); 1974 window.dispatchEvent(advChainEvent); 1975 }); 1976 }); 1977} 1978postTcfReady(startAdvChain2022); 1979 1980(function () { 1981 1982 function injectAudioSentinel() { 1983 return new Promise((resolve, reject)=>{ 1984 const videoSentinel = window.top.document.createElement('video'); 1985 videoSentinel.src = "https://www.focusjunior.it/content/themes/FocusJunior/assets/video-sentinel/sentinel.mp4" 1986 videoSentinel.controls = true; 1987 videoSentinel.muted = false; 1988 videoSentinel.playsInline = true; 1989 videoSentinel.volume = 0.001; 1990 videoSentinel.setAttribute("style", "position:fixed;bottom:-200px;z-index:-1;"); 1991 window.top.document.body.appendChild(videoSentinel); 1992 console.log('[Check AudioOn] Video sentinella caricato'); 1993 resolve(checkSentinelResponse(videoSentinel)); 1994 }); 1995 } 1996 function checkSentinelResponse(elem){ 1997 let video = elem; 1998 return new Promise((resolve, reject) => { 1999 let interrogateSentinel = video.play(); 2000 if (interrogateSentinel !== undefined){ 2001 interrogateSentinel.then(function () { 2002 video.pause(); 2003 console.log('[Check AudioOn]',video) 2004 resolve(audioModeOnSentinel = true); 2005 console.log('[Check AudioOn] AudioOn permesso!', 'Valore audioModeOnSentinel:',audioModeOnSentinel); 2006 }).catch(function (error) { 2007 resolve(); // Non modifico audioModeOnSentinel. à false di default 2008 console.log('[Check AudioOn]', error) 2009 }) 2010 } 2011 }) 2012 } 2013 2014 /** pushdown **/ 2015 const getClock = () => { 2016 const today = new Date(); 2017 return today.getHours() +":"+ today.getMinutes() +":"+ today.getSeconds(); 2018 }; 2019 2020 let pushObjConf = { 2021 adServer: "ima", 2022 AudicomTracker: true, 2023 closeFlyingAfter: 7000, 2024 flyMode: "fade", 2025 targetElementId, 2026 audioModeOn: audioModeOnSentinel, 2027 iasMonitoring:{enabled:true,id:'931714'}, 2028 type: "flyfirst", 2029 advFallbacks: false, 2030 website, 2031 }; 2032 2033 let pushFrequencyCap = { 2034 mobile: null, // Impostare il valore in GIORNI x 1000 (negli altri è settato a ORE, ma qui esisteva già un set_cookie) 2035 desktop: null, //Impostare null se non utilizzato 2036 }
2037 let checkCap = isMobile ? getCookie('pushDownCapMobile') : getCookie('pushDownCapDesktop'); 2038 console.log(`%c[Push-diretta] Il valore di pushFrequencyCap ${isMobile ? 'Mobile' : 'Desktop'} risulta settato a: ${isMobile ? pushFrequencyCap.mobile : pushFrequencyCap.desktop }`,'background-color: #55FFFF;padding:5px;color:black;'); 2039 2040 2041 function initPushdown() { 2042 // Senza guard, decodeURIComponent(undefined) restituisce la stringa "undefined", 2043 // che finisce dentro cust_params. Se il targeting manca, il parametro va omesso. 2044 const iasSlotParams = (typeof responseIas !== 'undefined' && responseIas.slot) ? responseIas.slot : false; 2045 pushObjConf['adRequestCustomParams'] = iasSlotParams ? decodeURIComponent(iasSlotParams) : false; 2046 console.log('IAS', iasSlotParams); 2047 //Le variabili, website, targetElementId, showPushDown e mobile sono inizializzate in site-footer.tpl 2048 //PushConfObj è l'oggetto che contiene tutti i parametri con i quali andremo a inizializzare la PUSH 2049 const pushConfObj = { 2050 ...pushObjConf, 2051 eventListener: (ptpEvent) => { 2052 if (ptpEvent === 'preroll_started'){ 2053 if (isMobile && typeof pushFrequencyCap.mobile == "number") { 2054 console.log(`%c[Push-diretta] ${getClock()} Il preroll è stato erogato setto il cookie pushDownCapMobile.`, 'background-color: #FFFF55;padding:5px;color:black;'); 2055 set_cookie('pushDownCapMobile','enabled', pushFrequencyCap.mobile); 2056 } else if (!isMobile && typeof pushFrequencyCap.desktop == "number") { 2057 console.log(`%c[Push-diretta] ${getClock()} Il preroll è stato erogato setto il cookie pushDownCapDesktop.`, 'background-color: #FFFF55;padding:5px;color:black;'); 2058 set_cookie('pushDownCapDesktop','enabled', pushFrequencyCap.desktop); 2059 } else { 2060 console.log(`%c[Push-diretta] ${getClock()} Il preroll è stato erogato, ma non ho settato il cookie ${isMobile ? 'Mobile' : 'Desktop'}.`, 'background-color: #FFFF55;padding:5px;color:black;'); 2061 } 2062 } else if (ptpEvent === 'flight_closed' || ptpEvent === 'flight_auto_closed' || ptpEvent === 'preroll_error'){ 2063 const PiemmeDataEvent = new CustomEvent("callAncorAd"); 2064 2065 window.dispatchEvent(PiemmeDataEvent); 2066 } 2067 } 2068 }; 2069 2070 //Facciamo partire la chiamata a PTP per il caricamento di tutte le risorse del player 2071 (function (a,l,t,e,r) { 2072 a[e] = a[e] || function(s) { (a[e].run = a[e].run || []).push(s)}; 2073 let g,z = l.getElementsByTagName(t)[0]; 2074 if (l.getElementById(e)){return;} 2075 g = l.createElement(t); g.id = e; g.src = r; g.async = 1; 2076 z.parentNode.insertBefore(g,z); 2077 }(window, document, 'script', 'AVPushLoader', "https://ptp.stbm.it/pushdown/loader/av/pushdown-loader.js")); 2078 2079 console.log("[Push-diretta] Parametri di Configurazione:", pushConfObj); 2080 //Avviamo la Pushdown! 2081 AVPushLoader(pushConfObj); 2082 console.log("%c[Push-diretta] Push inizializzata.", 'background-color: #55FF55;padding:5px;color:black;'); 2083 } 2084 2085 2086 function pushChainStarter(){ 2087 injectAudioSentinel().then(function () { 2088 if (showPushDown && (typeof checkCap == null || checkCap === null || checkCap === '')) { 2089 initPushdown(); 2090 console.log(`%c[Push-diretta] Controllo showPushDown: ${showPushDown} | siamo su ${isMobile ? 'Mobile' : 'Desktop'} e il cookie pushFrequencyCap NON è ancora stato salvato nel browser. Possiamo erogare!`, 'background-color: #55FF55;padding:5px;color:black;'); 2091 } else { 2092 console.log(`%c[Push-diretta] Controllo showPushDown: ${showPushDown}. Valore cookie: ${checkCap || 'Disabled'}. Non possiamo erogare!`,'background-color: #FF5555;padding:5px;color:black;'); 2093 } 2094 }).then(function () { 2095 if (audioModeOnSentinel){ 2096 window.addEventListener("preroll_started", function() { 2097 console.log('[Check AudioOn] preroll_started'); 2098 setTimeout(function () { 2099 AVPushRunningInstances[0].api.setVolume(0.05); 2100 console.log('[Check AudioOn] Siamo su mobile o è in esecuzione un video content. Imposto audio on'); 2101 },200) 2102 }); 2103 } 2104 }) 2105 } 2106 // Il targeting IAS arriva da una callback asincrona (iasDataHandler in iasSlot.php). 2107 // Senza attesa il player costruisce la VAST prima che responseIas.slot esista e 2108 // cust_params parte senza le key value IAS. Timeout di sicurezza a 2s, allineato 2109 // alla soglia pet_longreq usata da IAS nel suo diagnostico: se IAS non risponde 2110 // il player parte comunque, senza il targeting. 2111 // Il timeout parte dal consenso, non dal caricamento pagina: iasPET.1.js viene 2112 // caricato solo in postTcfReady(startIasPet), quindi prima del consenso IAS non 2113 // puo' rispondere. Con il timer avviato al load, un consenso dato dopo 2s faceva 2114 // partire il player subito, senza IAS. 2115 const IAS_TARGETING_TIMEOUT = 2000; 2116 function waitForIasTargeting() { 2117 if (typeof iasTargetingReady === 'undefined') return Promise.resolve(); 2118 return Promise.race([ 2119 iasTargetingReady, 2120 new Promise(resolve => setTimeout(resolve, IAS_TARGETING_TIMEOUT)) 2121 ]); 2122 } 2123 2124 // Sentinella contro il doppio avvio del player se tcf2Ready arrivasse piu' volte. 2125 let pushChainStarted = false;
2126 function startPushChainOnce() { 2127 if (pushChainStarted) return; 2128 pushChainStarted = true; 2129 pushChainStarter(); 2130 } 2131 function pushChainAfterIasTargeting() { 2132 waitForIasTargeting().then(startPushChainOnce); 2133 } 2134 postTcfReady(pushChainAfterIasTargeting); 2135 /*********** No consent ***********/ 2136 let trackAnalytics = false; 2137 2138 function startPushNoConsent() { 2139 window.initStartPushNoConsent = 1; 2140 console.log('[Push-diretta - NoConsent] track init'); 2141 if (typeof gtag === "function" && trackAnalytics == true) { 2142 gtag("event", 'init', { 2143 event_category: 'pushNoConsentV1', 2144 event_label: document.location.href, 2145 non_interaction: true 2146 }); 2147 } 2148 2149 window.GlobalPusTimerStart = new Date().getTime(); 2150 2151 let obj = { 2152 ...pushObjConf, 2153 eventListener: (eventName, eventData) => { 2154 if(eventName === 'preroll_started'){ 2155 console.log('[Push-diretta - NoConsent]', 'track preroll started'); 2156 if (typeof gtag === "function" && trackAnalytics == true) { 2157 gtag("event", 'preroll_started', { 2158 event_category: 'pushNoConsentV1', 2159 event_label: document.location.href, 2160 non_interaction: true 2161 }); 2162 } 2163 } 2164 console.log('[Push-diretta - NoConsent] evento:', eventName); 2165 } 2166 }; 2167 2168 (function (a, l, t, e, r) { 2169 a[e] = a[e] || function (s) { (a[e].run = a[e].run || []).push(s) }; 2170 let g, z = l.getElementsByTagName(t)[0]; 2171 if (l.getElementById(e)) { return; } 2172 g = l.createElement(t); g.id = e; g.src = r; g.async = 1; 2173 z.parentNode.insertBefore(g, z); 2174 }(window, document, 'script', 'AVPushLoader', "https://ptp.stbm.it/pushdown/loader/av/pushdown-loader.js")); 2175 2176 AVPushLoader(obj); 2177 } 2178 postConsentRejected(startPushNoConsent); 2179 /***************************************** FINE pushdown */ 2180 2181})();/***************************************** FINE configurazioni intro */ 2182 2183/* ============================================================================ 2184 INTRO PIEMME-FIRST + FALLBACK ADKAORA 2185 Piemme (piemme2.js) definisce e refresha da solo lo slot out-of-page 2186 'adv_IntropageOvl'. Qui si ascolta solo lo slotRenderEnded dello slot: 2187 - slot erogato -> incremento cap 2188 - slot empty -> fallback AdKaora (interstitial) 2189 Cap/frequency su cookie introCap. 2190 ============================================================================ */ 2191 2192/* device canonico (nessun global sul sito): da innerWidth. Soglia 1000 = isMobile */ 2193var device = window.innerWidth < 1000 ? 'smartphone' : 'desktop'; 2194 2195/* --- Config cap/frequency e gating --- */ 2196window.INTRO_CAP_CONFIG = { 2197 enabled: true, // false = cap disattivato (config mantenuta) 2198 frequencyHours: 0.25, // finestra cookie introCap in ore (0.25 = 15 min) 2199 limit: 1, // massimo erogazioni nella finestra 2200 cookieDomain: '.focusjunior.it' 2201}; 2202 2203window.INTRO_GATE_CONFIG = { 2204 introDevices: null, // device ammessi all'intro Piemme; null = tutti 2205 adkFallbackDevices: null // device ammessi al fallback AdK su Piemme empty; null = tutti 2206}; 2207 2208function getSecondLevelDomain() { 2209 const parts = location.hostname.split('.'); 2210 return '.' + (parts.length >= 2 ? parts.slice(-2).join('.') : location.hostname); 2211} 2212 2213const isIntroDeviceAllowed = (list) => { 2214 if (!Array.isArray(list) || list.length === 0) return true; 2215 if (typeof device === 'undefined') return false; 2216 return list.includes(device); 2217}; 2218 2219/* Incremento cookie introCap: max-age corretto (frequencyHours -> secondi). 2220 NB: non uso set_cookie() del sito perché tratta 'expires' come giorni*1000. */ 2221window.incrementIntroCap = () => { 2222 if (!window.INTRO_CAP_CONFIG.enabled) return; 2223 const next = (Number(getCookie('introCap')) || 0) + 1; 2224 const maxAge = Math.round(window.INTRO_CAP_CONFIG.frequencyHours * 3600); 2225 const domain = typeof getSecondLevelDomain === 'function' ? getSecondLevelDomain() : window.INTRO_CAP_CONFIG.cookieDomain; 2226 document.cookie = 'introCap=' + next + ';path=/;domain=' + domain + ';max-age=' + maxAge; 2227}; 2228 2229/* --- Config AdKaora (namespace da creative.html: piemme/generic) --- */ 2230const INTRO_CONFIG = { 2231 adkQueueSrc: 'https://cdn.adkaora.space/library/dev/feat/onDemand-delivery-hardening/adk-ondemand-queue.js', 2232 adkInitSrc: 'https://cdn.adkaora.space/piemme/generic/prod/adk-init.js', 2233 adkInterstitial: { id: 'adk_interstitial', bannerType: 'interstitial-adk' } 2234}; 2235 2236const ADK_QUEUE_SRC = INTRO_CONFIG.adkQueueSrc; 2237const ADK_INIT_SRC = INTRO_CONFIG.adkInitSrc; 2238 2239function dispatchAdKaoraChainReady() { 2240 window.__ameMhAdKaoraChainReady = true; 2241 if (!window.__ameMhAdKaoraChainEventDispatched) { 2242 window.__ameMhAdKaoraChainEventDispatched = true; 2243 window.dispatchEvent(new CustomEvent("adkaora:chain-ready", { 2244 detail: { timestamp: Date.now() } 2245 })); 2246 } 2247} 2248 2249function loadAdKaoraScriptForIntro() { 2250 if (window.__ameMhAdKaoraChainReady && window.AdKaora && typeof window.AdKaora.requestAdv === "function") { 2251 return Promise.resolve(); 2252 }
2253 if (window.__ameMhAdKaoraChainPromise) { 2254 return window.__ameMhAdKaoraChainPromise; 2255 } 2256 2257 const loadStep = function (src, marker, srcFragment, isReadyCheck) { 2258 const existing = 2259 document.querySelector('script[data-ame-adkaora="' + marker + '"]') || 2260 document.querySelector('script[src*="' + srcFragment + '"]'); 2261 2262 if (existing) { 2263 if (isReadyCheck()) { 2264 return Promise.resolve(); 2265 } 2266 return new Promise(function (resolve, reject) { 2267 existing.addEventListener("load", function () { resolve(); }, { once: true }); 2268 existing.addEventListener("error", function () { 2269 reject(new Error("adkaora_script_error:" + marker)); 2270 }, { once: true }); 2271 }); 2272 } 2273 2274 return mmLoader({ 2275 src: src, 2276 async: true, 2277 "data-ame-adkaora": marker 2278 }, "AdkIntroChain"); 2279 }; 2280 2281 const queueReady = function () { 2282 return window.AdKaora && window.AdKaora.cmd && Array.isArray(window.AdKaora.cmd.loadAdv); 2283 }; 2284 const initReady = function () { 2285 return window.AdKaora && typeof window.AdKaora.requestAdv === "function"; 2286 }; 2287 2288 window.__ameMhAdKaoraChainPromise = 2289 loadStep(ADK_QUEUE_SRC, "ondemand-queue", "adk-ondemand-queue.js", queueReady) 2290 .then(function () { 2291 return loadStep(ADK_INIT_SRC, "adk-init", "adk-init.js", initReady); 2292 }) 2293 .then(dispatchAdKaoraChainReady); 2294 2295 window.__ameMhAdKaoraScriptPromise = window.__ameMhAdKaoraChainPromise; 2296 2297 return window.__ameMhAdKaoraChainPromise; 2298} 2299 2300function requestAdkInterstitialIntro() { 2301 if (window.__ameAdkInterstitialRequested) return; 2302 if (!window.AdKaora || typeof window.AdKaora.requestAdv !== "function") { 2303 console.warn("[requestAdkInterstitialIntro] AdKaora.requestAdv non disponibile"); 2304 return; 2305 } 2306 AdKaora.requestAdv({ 2307 id: INTRO_CONFIG.adkInterstitial.id, 2308 bannerType: INTRO_CONFIG.adkInterstitial.bannerType 2309 }); 2310 window.__ameAdkInterstitialRequested = true; 2311} 2312 2313function attachAdkInterstitialFallbackListener() { 2314 if (window.__ameAdkInterstitialListenerAttached) return; 2315 window.__ameAdkInterstitialListenerAttached = true; 2316 2317 const onAdkInteractions = function (event) { 2318 if ( 2319 (event.detail.id === "adk_interstitial_mondadori" || event.detail.id === INTRO_CONFIG.adkInterstitial.id) && 2320 (event.detail.isEmpty === false || event.detail.canBeDelivered === true) 2321 ) { 2322 window.__ameAdkIntroDelivered = true; 2323 window.incrementIntroCap(); 2324 window.removeEventListener("adkInteractionsEvents", onAdkInteractions); 2325 return; 2326 } 2327 if ( 2328 (event.detail.id === "adk_interstitial_mondadori" || event.detail.id === INTRO_CONFIG.adkInterstitial.id) && 2329 (event.detail.isEmpty === true || event.detail.canBeDelivered === false) 2330 ) { 2331 window.removeEventListener("adkInteractionsEvents", onAdkInteractions); 2332 } 2333 }; 2334 2335 window.addEventListener("adkInteractionsEvents", onAdkInteractions); 2336} 2337 2338function startAdkIntro() { 2339 if (window.__ameAdkIntroStarted) return; 2340 window.__ameAdkIntroStarted = true; 2341 2342 if (typeof device === "undefined") { 2343 return; 2344 } 2345 2346 attachAdkInterstitialFallbackListener(); 2347 2348 loadAdKaoraScriptForIntro() 2349 .then(function () { 2350 requestAdkInterstitialIntro(); 2351 }) 2352 .catch(function (err) { 2353 console.warn("[startAdkIntro] AdKaora script load failed", err); 2354 }); 2355} 2356window.startAdkIntro = startAdkIntro; 2357 2358/* --- Orchestrazione Piemme: registra il listener slotRenderEnded (NO initIntro) --- */ 2359const INTRO_PM_SLOT_ID = 'adv_IntropageOvl'; 2360 2361window.startIntro = function startIntro() { 2362 if (window.__ameAdkIntroDelivered || window.__amePmIntroStarted) return; 2363 2364 const introCheckCap = Number(getCookie('introCap')) || 0; 2365 const introCapLimit = window.INTRO_CAP_CONFIG.limit; 2366 if (window.INTRO_CAP_CONFIG.enabled && introCheckCap >= introCapLimit) { 2367 console.log(`%c[Load Intro] introCap: ${introCheckCap}, limite: ${introCapLimit}. Cap raggiunto, intro non erogata.`, 'background-color: #FF5555;padding:5px;color:black;'); 2368 return; 2369 } 2370 if (!isIntroDeviceAllowed(window.INTRO_GATE_CONFIG.introDevices)) { 2371 console.log(`%c[Load Intro] Intro non prevista per device: ${typeof device !== 'undefined' ? device : 'undefined'}.`, 'background-color: #FF5555;padding:5px;color:black;'); 2372 return; 2373 } 2374 window.__amePmIntroStarted = true; 2375 2376 window.googletag = window.googletag || {}; 2377 googletag.cmd = googletag.cmd || []; 2378 /* FIFO: eseguito dopo define+refresh di piemme2.js, ma il listener è registrato 2379 prima dell'evento slotRenderEnded (async sul render). NIENTE initIntro. */ 2380 googletag.cmd.push(function () { 2381 console.log(`%c[Load Intro] introCap: ${introCheckCap}, limite: ${introCapLimit}. Registro listener intro Piemme.`, 'background-color: #55FF55;padding:5px;color:black;'); 2382 googletag.pubads().addEventListener('slotRenderEnded', function (event) { 2383 if (event.slot.getSlotElementId() !== INTRO_PM_SLOT_ID) return; 2384 2385 /* Slot intro Piemme VUOTO -> fallback AdKaora */ 2386 if (event.isEmpty === true) { 2387 if (window.__amePmEmptyHandled || window.__ameAdkIntroStarted || window.__ameAdkIntroDelivered) return; 2388 window.__amePmEmptyHandled = true; 2389 if (!isIntroDeviceAllowed(window.INTRO_GATE_CONFIG.adkFallbackDevices)) { 2390 console.log(`%c[Load Intro] Fallback AdK non previsto per device: ${typeof device !== 'undefined' ? device : 'undefined'}.`, 'background-color: #FF5555;padding:5px;color:black;'); 2391 return; 2392 } 2393 console.log(`%c[Load Intro] Intro Piemme vuota. Avvio fallback AdKaora.`, 'background-color: #55FFFF;padding:5px;color:black;'); 2394 if (typeof window.startAdkIntro === 'function') window.startAdkIntro(); 2395 return; 2396 } 2397 2398 /* Slot intro Piemme EROGATO (out-of-page: nessun vincolo size [1,1]) */ 2399 if (window.INTRO_CAP_CONFIG.enabled) { 2400 window.incrementIntroCap(); 2401 console.log(`%c[Load Intro] Intro Piemme erogata. Incremento il cookie introCap.`, 'background-color: #FFFF55;padding:5px;color:black;'); 2402 } else { 2403 console.log(`%c[Load Intro] Intro Piemme erogata (cap disabilitato).`, 'background-color: #FFFF55;padding:5px;color:black;'); 2404 } 2405 }); 2406 }); 2407}; 2408 2409/* Listener sull'evento introCanStart già dispatchato dalla adv chain (adv-chain.php:52) */ 2410window.addEventListener('introCanStart', function () { 2411 if (window.__ameIntroCanStartHandled) return; 2412 window.__ameIntroCanStartHandled = true; 2413 postTcfReady(window.startIntro); 2414}); 2415 2416</script>
2416 2417 2418 2419 2420<!-- Webtrekk 4, (c) www.webtrekk.com -->
2421<script> 2422 function getContentIdByURL(){ 2423 var url = document.location.href; 2424 if(url && url !== null) { 2425 return url.split("?")[0].toLowerCase(); 2426 } 2427 return "no_content"; 2428 }; 2429 function getRefresh() { 2430 if (RegExp('[?&]' + 'refresh_cens$').exec(window.location.search)) return 'refresh_cens' 2431 else if(RegExp('[?&]' + 'refresh_ce$').exec(window.location.search)) return 'refresh_ce' 2432 else if(RegExp('[?&]' + 'refresh_ce-awe$').exec(window.location.search)) return 'refresh_ce-awe' 2433 else return 'no-refresh'; 2434 }; 2435 function getMMsezioneTag(){ 2436 if (typeof(MMsezioneTag) == 'undefined' || typeof(MMsezioneTag) == 'undefined' || MMsezioneTag == null || MMsezioneTag == '') 2437 return 'undefined'; 2438 else 2439 return MMsezioneTag; 2440 } 2441 var pageConfig = { 2442 linkTrack : "", // Attivare la rilevazione dei LINK ["link" o "standard"] 2443 heatmap : "0", // Attivare la rilevazione della HEATMAP ["1" = on | "0" = off] 2444 form : "", // Attivare la rilevazione dei FORM ["1" = on | "0" = off] 2445 contentId : getContentIdByURL() // Popolare con il NOME della pagina 2446 }; 2447 mmLoader({ 2448 src: "https://www.focusjunior.it/content/themes/FocusJunior/assets/js/webtrekk_v4.min.js?ts=123123424", 2449 defer: true 2450 }, "wtChain").then( 2451 element => { 2452 var wt = new webtrekkV3(pageConfig); 2453 var refresh; 2454 var wt_tagPfx = getMMsezioneTag(); 2455 wt.ignorePrerendering = true; 2456 wt.contentGroup = { 1:"Aggregato Mondadori", 2:"Aggregato Mondadori - web", 3:"Aggregato Mondadori - web - Donnamoderna", 4:"Aggregato Mondadori - web - Donnamoderna - www.focusjunior.it", 5: "Aggregato Mondadori - web - Donnamoderna - www.focusjunior.it - ", 8: "mondadori", 11: "web"}; 2457 2458 var wt_refresh = getRefresh(); 2459 2460 wt.customParameter = { 1: wt_refresh, 2: document.title, 10: wt_tagPfx}; 2461 wt.sendinfo(); 2462 } 2463 ); 2464</script>
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Line numbers count LF bytes from the start of the resource, as the search results do. Vendor segments are library code the classifier recognised; they are stored but not indexed. Bytes are shown as Latin1 characters, one per byte.