{"showTitleScreen":true,"titleScreen":{"titleScreenIntroduction":"

Ein langer, harter Winter<\/strong><\/em><\/span><\/p>\n\n

Es ist dunkel und kalt in Modularien.
\nNicht die freundlichste Umgebung - und dann rechnen die hier noch so seltsam!
\nWenigstens kennst du dich mit diesem modulo-Rechnen inzwischen gut aus.
\nL\u00f6se alle Aufgaben ohne Taschenrechner.<\/span><\/p>\n","titleScreenMedium":{"params":{"decorative":true,"contentName":"Bild","file":{"path":"images\/image-enP47U8c.jpg","mime":"image\/jpeg","copyright":{"license":"U"},"width":2048,"height":1536},"title":"Es ist dunkel und kalt und Modularien. Bring mit deinen Rechenfertigkeiten Licht ins Dunkel!","expandImage":"Bild vergr\u00f6\u00dfern","minimizeImage":"Bild verkleinern"},"library":"H5P.Image 1.1","metadata":{"contentType":"Image","license":"CC BY-SA","title":"Ein langer harter Winter","authors":[{"name":"Seferos","role":"Author"}],"licenseVersion":"4.0","source":"https:\/\/apps.zum.de\/apps\/29605","yearFrom":2024},"subContentId":"64e0cf07-8c1e-4003-ae52-8d2550640799"}},"gamemapSteps":{"backgroundImageSettings":{"backgroundImage":{"path":"images\/image-Vl39Fb0f.jpg","mime":"image\/jpeg","copyright":{"license":"CC BY-SA","author":"Seferos","source":"https:\/\/apps.zum.de\/apps\/29605","version":"4.0","year":"2024","title":"Ein langer, harter Winter"},"width":4096,"height":2100}},"gamemap":{"elements":[{"id":"de05c207-b260-4aae-a5c1-6ad2a7e5c02b","label":"Flaggschiff","telemetry":{"x":"26.499302649930264","y":"21.739130434782606","width":"4.375","height":"8.533599800149888"},"neighbors":["1"],"canBeStartStage":true,"time":{},"accessRestrictions":{"openOnScoreSufficient":false},"contentType":{"params":{"text":"

Die Winter sind hart in Modularien...<\/strong><\/p>\n\n

Starte am Schiff und erkunde die ganze Karte. Du startest mit 6 Leben und hast 25 Minuten Zeit.<\/p>\n"},"library":"H5P.AdvancedText 1.1","metadata":{"contentType":"Text","license":"U","title":"Unbenannt: Text"},"subContentId":"62ea4b39-7598-42c5-9643-8ad59e4fc4ae"},"specialStageExtraLives":1,"specialStageExtraTime":1},{"id":"1bfc0139-9da8-488c-bd09-ed333d60f96d","label":"Anlegestelle","telemetry":{"x":"29.41176470588236","y":"35.320088300220746","width":"4.375","height":"8.533599800149888"},"neighbors":["0","2","3","6"],"canBeStartStage":false,"time":{},"accessRestrictions":{"openOnScoreSufficient":false},"contentType":{"params":{"cards":[{"image":{"path":"images\/image-v2L8WhK2.png","mime":"image\/png","copyright":{"license":"CC BY-SA","author":"Seferos","year":"2024","source":"https:\/\/apps.zum.de\/apps\/29605","version":"4.0","title":"37 mod 13"},"width":200,"height":200},"match":{"path":"images\/image-LCxVDIKy.png","mime":"image\/png","copyright":{"license":"CC BY-SA","author":"Seferos","year":"2024","source":"https:\/\/apps.zum.de\/apps\/29605","version":"4.0","title":"11"},"width":200,"height":200},"imageAlt":"37 mod 13","matchAlt":"11"},{"image":{"path":"images\/image-HoIH9HV4.png","mime":"image\/png","copyright":{"license":"CC BY-SA","author":"Seferos","year":"2024","source":"https:\/\/apps.zum.de\/apps\/29605","version":"4.0","title":"37 mod 11"},"width":200,"height":200},"match":{"path":"images\/image-OWIingUf.png","mime":"image\/png","copyright":{"license":"CC BY-SA","author":"Seferos","year":"2024","source":"https:\/\/apps.zum.de\/apps\/29605","version":"4.0","title":"4"},"width":200,"height":200},"imageAlt":"37 mod 11","matchAlt":"4"},{"image":{"path":"images\/image-OhNHYDPN.png","mime":"image\/png","copyright":{"license":"CC BY-SA","author":"Seferos","source":"https:\/\/apps.zum.de\/apps\/29605","year":"2024","version":"4.0","title":"11 mod 4"},"width":200,"height":200},"match":{"path":"images\/image-IfLdCpZm.png","mime":"image\/png","copyright":{"license":"CC BY-SA","author":"Seferos","year":"2024","source":"https:\/\/apps.zum.de\/apps\/29605","version":"4.0","title":"3"},"width":200,"height":200},"imageAlt":"11 mod 4","matchAlt":"3"},{"image":{"path":"images\/image-FZWXW7mJ.png","mime":"image\/png","copyright":{"license":"CC BY-SA","author":"Seferos","year":"2024","source":"https:\/\/apps.zum.de\/apps\/29605","version":"4.0","title":"11 mod 3"},"width":200,"height":200},"match":{"path":"images\/image-c55XmNfv.png","mime":"image\/png","copyright":{"license":"CC BY-SA","author":"Seferos","year":"2024","source":"https:\/\/apps.zum.de\/apps\/29605","version":"4.0","title":"2"},"width":200,"height":200},"imageAlt":"11 mod 3","matchAlt":"2"},{"image":{"path":"images\/image-AlNCtDNn.png","mime":"image\/png","copyright":{"license":"CC BY-SA","author":"Seferos","year":"2024","source":"https:\/\/apps.zum.de\/apps\/29605","version":"4.0","title":"13 mod 3"},"width":200,"height":200},"match":{"path":"images\/image-7T3docES.png","mime":"image\/png","copyright":{"license":"CC BY-SA","author":"Seferos","year":"2024","source":"https:\/\/apps.zum.de\/apps\/29605","version":"4.0","title":"1"},"width":200,"height":200},"imageAlt":"13 mod 3","matchAlt":"1"},{"image":{"path":"images\/image-cxpCCC8l.png","mime":"image\/png","copyright":{"license":"CC BY-SA","author":"Seferos","year":"2024","source":"https:\/\/apps.zum.de\/apps\/29605","version":"4.0","title":"13 mod 37"},"width":200,"height":200},"match":{"path":"images\/image-TpUWBmPU.png","mime":"image\/png","copyright":{"license":"CC BY-SA","author":"Seferos","year":"2024","source":"https:\/\/apps.zum.de\/apps\/29605","version":"4.0","title":"13"},"width":200,"height":200},"imageAlt":"13 mod 37","matchAlt":"13"}],"behaviour":{"useGrid":true,"allowRetry":true},"lookNFeel":{"themeColor":"#707070","cardBack":{"path":"images\/image-LXUef24c.jpg","mime":"image\/jpeg","copyright":{"license":"CC BY-SA","author":"Seferos","year":"2024","source":"https:\/\/apps.zum.de\/apps\/29605","version":"4.0","title":"Ein langer, harter Winter"},"width":4096,"height":2100}},"l10n":{"cardTurns":"Z\u00fcge","timeSpent":"Ben\u00f6tigte Zeit","feedback":"Gut gemacht!","tryAgain":"Nochmal spielen?","closeLabel":"Schlie\u00dfen","label":"Memory - Finde die Kartenpaare!","done":"Du hast alle Kartenpaare gefunden!","cardPrefix":"Karte %num von %total:","cardUnturned":"Zugedeckt. Click to turn.","cardTurned":"Umgedreht.","cardMatched":"Paar gefunden.","cardMatchedA11y":"Die Karten passen zueinander!","cardNotMatchedA11y":"Die Karten passen nicht zueinander. Drehe andere Karten um, um es weiter zu versuchen."}},"library":"H5P.MemoryGame 1.3","metadata":{"contentType":"Memory Game","license":"U","title":"Unbenannt: Memory-Spiel (Memory Game)"},"subContentId":"86d6828c-3bf0-4bb7-8257-04382a4dd5a2"},"specialStageExtraLives":1,"specialStageExtraTime":1},{"id":"36dab63e-a835-4984-b436-2039e8fc8b34","label":"Einsamer Wanderer","telemetry":{"x":"25.104602510460246","y":"48.91304347826087","width":"4.375","height":"8.533599800149888"},"neighbors":["1","8"],"canBeStartStage":false,"time":{},"accessRestrictions":{"openOnScoreSufficient":false},"contentType":{"params":{"scoreShow":"\u00dcberpr\u00fcfen","submit":"\u00dcbermitteln","tryAgain":"Wiederholen","scoreExplanation":"Richtige Antworten geben +1 Punkte. Bei falschen Antworten gibt es -1 Punkt. Die kleinstm\u00f6gliche Punktzahl ist 0.","question":{"settings":{"size":{"width":620,"height":310},"background":{"path":"images\/image-OwsW9rA7.jpg","mime":"image\/jpeg","copyright":{"license":"CC BY-SA","author":"Seferos","year":"2024","source":"https:\/\/apps.zum.de\/apps\/29605","version":"4.0","title":"Ein langer, harter Winter"},"width":2048,"height":1536}},"task":{"elements":[{"x":67.74193548387096,"y":83.87096774193549,"width":5.525,"height":1.275,"dropZones":["0","1","2","3"],"type":{"library":"H5P.AdvancedText 1.1","params":{"text":"

211 mod 17<\/strong><\/span><\/p>\n"},"metadata":{"contentType":"Text","license":"U","title":"Unbenannt: Text"},"subContentId":"1f5d1e5a-cec4-4fbe-a5f1-2c1317a1eaf6"},"backgroundOpacity":50,"multiple":false},{"x":46.774193548387096,"y":51.61290322580645,"width":5.4625,"height":1.275,"dropZones":["0","1","2","3"],"type":{"library":"H5P.AdvancedText 1.1","params":{"text":"

46 mod 17<\/strong><\/span><\/p>\n"},"metadata":{"contentType":"Text","license":"U","title":"Unbenannt: Text"},"subContentId":"24fb0327-4c6e-4b70-9a78-12727e32024e"},"backgroundOpacity":50,"multiple":false},{"x":67.74193548387096,"y":51.61290322580645,"width":5.4625,"height":1.275,"dropZones":["0","1","2","3"],"type":{"library":"H5P.AdvancedText 1.1","params":{"text":"

319 mod 29<\/strong><\/span><\/p>\n"},"metadata":{"contentType":"Text","license":"U","title":"Unbenannt: Text"},"subContentId":"c4bf1fdf-51e2-4bab-b8fc-a26c05cf574e"},"backgroundOpacity":50,"multiple":false},{"x":46.774193548387096,"y":83.87096774193549,"width":5.525,"height":1.275,"dropZones":["0","1","2","3"],"type":{"library":"H5P.AdvancedText 1.1","params":{"text":"

232 mod 29<\/strong><\/span><\/p>\n"},"metadata":{"contentType":"Text","license":"U","title":"Unbenannt: Text"},"subContentId":"8a01ad49-4913-4c2c-bd22-ced7687b8f49"},"backgroundOpacity":50,"multiple":false},{"x":67.74193548387096,"y":67.74193548387096,"width":5.4625,"height":1.275,"dropZones":["0","1","2","3"],"type":{"library":"H5P.AdvancedText 1.1","params":{"text":"

165 mod 17<\/strong><\/span><\/p>\n"},"metadata":{"contentType":"Text","license":"U","title":"Unbenannt: Text"},"subContentId":"6ca3b43c-2f40-46bf-995c-9498f7b6938f"},"backgroundOpacity":50,"multiple":false},{"x":46.774193548387096,"y":67.74193548387096,"width":5.4625,"height":1.275,"dropZones":["0","1","2","3"],"type":{"library":"H5P.AdvancedText 1.1","params":{"text":"

227 mod 29<\/strong><\/span><\/p>\n"},"metadata":{"contentType":"Text","license":"U","title":"Unbenannt: Text"},"subContentId":"fa063b61-97e8-4e76-a518-d83522251b2e"},"backgroundOpacity":50,"multiple":false}],"dropZones":[{"x":79.03225806451613,"y":9.67741935483871,"width":6.875,"height":6.25,"correctElements":["5"],"showLabel":true,"backgroundOpacity":50,"tipsAndFeedback":{"tip":""},"single":false,"autoAlign":true,"label":"

24<\/strong><\/div>\n"},{"x":58.064516129032256,"y":9.67741935483871,"width":6.875,"height":6.25,"correctElements":["4","1"],"showLabel":true,"backgroundOpacity":50,"tipsAndFeedback":{"tip":""},"single":false,"autoAlign":true,"label":"
12<\/strong><\/div>\n"},{"x":37.096774193548384,"y":9.67741935483871,"width":6.875,"height":6.25,"correctElements":["3","2"],"showLabel":true,"backgroundOpacity":50,"tipsAndFeedback":{"tip":""},"single":false,"autoAlign":true,"label":"
0<\/strong><\/div>\n"},{"x":4.838709677419355,"y":19.35483870967742,"width":10.125,"height":2.5,"correctElements":["0"],"showLabel":true,"backgroundOpacity":50,"tipsAndFeedback":{"tip":""},"single":false,"autoAlign":true,"label":"
anderes Ergebnis<\/strong><\/div>\n"}]}},"overallFeedback":[{"from":0,"to":100}],"behaviour":{"enableRetry":true,"enableCheckButton":true,"singlePoint":true,"applyPenalties":false,"enableScoreExplanation":true,"dropZoneHighlighting":"dragging","autoAlignSpacing":2,"enableFullScreen":false,"showScorePoints":true,"showTitle":false},"grabbablePrefix":"Ziehbares Element {num} von {total}.","grabbableSuffix":"Abgelegt in Ablagezone {num}.","dropzonePrefix":"Ablagezone {num} von {total}.","noDropzone":"Keine Ablagezone.","tipLabel":"Hinweis zeigen","tipAvailable":"Hinweis verf\u00fcgbar","correctAnswer":"Richtige Antwort","wrongAnswer":"Falsche Antwort","feedbackHeader":"R\u00fcckmeldung","scoreBarLabel":"Du hast :num von :total Punkten erreicht.","scoreExplanationButtonLabel":"Zeige Erkl\u00e4rung der Punktevergabe","a11yCheck":"Die Antworten \u00fcberpr\u00fcfen. Die Eingaben werden als richtig, falsch oder unbeantwortet markiert.","a11yRetry":"Die Aufgabe wiederholen. Alle Versuche werden zur\u00fcckgesetzt und die Aufgabe wird erneut gestartet.","localize":{"fullscreen":"Vollbild","exitFullscreen":"Vollbild beenden"}},"library":"H5P.DragQuestion 1.14","metadata":{"contentType":"Drag and Drop","license":"U","title":"Der einsame Wanderer"},"subContentId":"890a4274-f475-4828-aabc-35d581894697"},"specialStageExtraLives":1,"specialStageExtraTime":1},{"id":"a99722aa-a769-45e2-9adb-6ffabbf34e50","label":"Die Furt","telemetry":{"x":"64.15620641562064","y":"29.891304347826082","width":"4.375","height":"8.533599800149888"},"neighbors":["1","4","9"],"canBeStartStage":false,"time":{},"accessRestrictions":{"openOnScoreSufficient":false},"contentType":{"params":{"media":{"disableImageZooming":false},"text":"
Gib des Ergebnis als kleinstm\u00f6gliche nat\u00fcrliche Zahl an.<\/p>\n\n
<\/p>\n","overallFeedback":[{"from":0,"to":50,"feedback":"T\u00fcren sind keine Fenster!"},{"from":51,"to":100}],"showSolutions":"L\u00f6sung anzeigen","tryAgain":"Wiederholen","checkAnswer":"\u00dcberpr\u00fcfen","submitAnswer":"Absenden","notFilledOut":"Bitte f\u00fclle alle L\u00fccken aus, um die L\u00f6sung ansehen zu k\u00f6nnen","answerIsCorrect":"':ans' ist korrekt","answerIsWrong":"':ans' ist falsch","answeredCorrectly":"Korrekt beantwortet","answeredIncorrectly":"Falsch beantwortet","solutionLabel":"Korrekte Antwort:","inputLabel":"L\u00fccke @num von @total","inputHasTipLabel":"Tipp verf\u00fcgbar","tipLabel":"Tipp","behaviour":{"enableRetry":true,"enableSolutionsButton":false,"enableCheckButton":true,"autoCheck":false,"caseSensitive":false,"showSolutionsRequiresInput":true,"separateLines":false,"confirmCheckDialog":false,"confirmRetryDialog":false,"acceptSpellingErrors":false},"scoreBarLabel":"Du hast :num von :total Punkten erreicht.","a11yCheck":"Die Antworten \u00fcberpr\u00fcfen. Die Eingaben werden als richtig, falsch oder unbeantwortet markiert.","a11yShowSolution":"Die L\u00f6sung anzeigen. Die richtigen L\u00f6sungen werden in der Aufgabe angezeigt.","a11yRetry":"Die Aufgabe wiederholen. Alle Eingaben werden zur\u00fcckgesetzt und die Aufgabe wird erneut gestartet.","a11yCheckingModeHeader":"\u00dcberpr\u00fcfen-Modus aktiv","confirmCheck":{"header":"Beenden?","body":"Ganz sicher beenden?","cancelLabel":"Abbrechen","confirmLabel":"Beenden"},"confirmRetry":{"header":"Wiederholen?","body":"Ganz sicher wiederholen?","cancelLabel":"Abbrechen","confirmLabel":"Best\u00e4tigen"},"questions":["
Berechne zuerst:<\/p>\n\n
Anzahl der Personen am Feuer<\/strong> mal Anzahl der Reiter<\/strong> mal Anzahl der beleuchteten Fenster in der Siedlung<\/strong><\/p>\n\n
Anschlie\u00dfend dieses Ergebnis <\/strong>modulo Anzahl aller Segel am Flaggschiff<\/strong> => *4*<\/p>\n"]},"library":"H5P.Blanks 1.14","metadata":{"contentType":"Fill in the Blanks","license":"U","title":"Unbenannt: L\u00fcckentext (Fill in the Blanks)"},"subContentId":"aa498d4e-4d40-4f05-a1e2-cf37024e554b"},"specialStageExtraLives":1,"specialStageExtraTime":1},{"id":"e0d24769-a46a-4af8-b401-1e2693ee79c7","label":"Am Feuer","telemetry":{"x":"87.8661087866109","y":"46.19565217391303","width":"4.375","height":"8.533599800149888"},"neighbors":["3","5","10"],"canBeStartStage":false,"time":{},"accessRestrictions":{"openOnScoreSufficient":false},"contentType":{"params":{"text":"
W\u00e4rm dich hier kurz auf und zieh dann weiter ins Gebirge.<\/span><\/p>\n"},"library":"H5P.AdvancedText 1.1","metadata":{"contentType":"Text","license":"U","title":"Unbenannt: Text"},"subContentId":"cb7b390b-a894-49ac-9604-01489c6a68d6"},"specialStageExtraLives":1,"specialStageExtraTime":1},{"id":"b81db7e8-87f6-45d7-830b-6bc8941af4fe","label":"Die dunkle H\u00f6hle","telemetry":{"x":"72.52440725244072","y":"78.804347826087","width":"4.375","height":"8.533599800149888"},"neighbors":["4","6","10"],"canBeStartStage":false,"time":{},"accessRestrictions":{"openOnScoreSufficient":false},"contentType":{"params":{"media":{"disableImageZooming":false},"correct":"false","behaviour":{"enableRetry":true,"enableSolutionsButton":true,"enableCheckButton":true,"confirmCheckDialog":false,"confirmRetryDialog":false,"autoCheck":false},"l10n":{"trueText":"Wahr","falseText":"Falsch","score":"Du hast @score von @total Punkten erreicht.","checkAnswer":"\u00dcberpr\u00fcfen","submitAnswer":"Submit","showSolutionButton":"L\u00f6sung anzeigen","tryAgain":"Wiederholen","wrongAnswerMessage":"Falsche Antwort","correctAnswerMessage":"Richtige Antwort","scoreBarLabel":"Du hast :num von :total Punkten erreicht.","a11yCheck":"Die Antworten \u00fcberpr\u00fcfen. Die Antwort wird als richtig, falsch oder unbeantwortet markiert.","a11yShowSolution":"Die L\u00f6sung anzeigen. Die richtige L\u00f6sung wird in der Aufgabe angezeigt.","a11yRetry":"Die Aufgabe wiederholen. Alle Versuche werden zur\u00fcckgesetzt und die Aufgabe wird erneut gestartet."},"confirmCheck":{"header":"Beenden?","body":"Ganz sicher beenden?","cancelLabel":"Abbrechen","confirmLabel":"Beenden"},"confirmRetry":{"header":"Wiederholen?","body":"Ganz sicher wiederholen?","cancelLabel":"Abbrechen","confirmLabel":"Best\u00e4tigen"},"question":"
Das Inverse von 13 modulo 7 und das Inverse von 7 modulo 13 stimmen \u00fcberein.<\/p>\n"},"library":"H5P.TrueFalse 1.8","metadata":{"contentType":"True\/False Question","license":"U","title":"Unbenannt: Richtig\/Falsch-Frage (True\/False Question)"},"subContentId":"7e70019f-ada8-4726-b73e-fc7ca7518e91"},"specialStageExtraLives":1,"specialStageExtraTime":1},{"id":"3c50a3f2-4e9a-4b69-830c-a9b93ba894f2","label":"Die geheimnisvollen Reiter","telemetry":{"x":"61.36680613668061","y":"70.65217391304346","width":"4.375","height":"8.533599800149888"},"neighbors":["5","7","1","10"],"canBeStartStage":false,"time":{},"accessRestrictions":{"openOnScoreSufficient":false},"contentType":{"params":{"media":{"disableImageZooming":false},"taskDescription":"Ziehe die W\u00f6rter in die richtigen Felder!","overallFeedback":[{"from":0,"to":80,"feedback":"Da stimmt etwas noch nicht"},{"from":81,"to":100,"feedback":"Prima"}],"checkAnswer":"\u00dcberpr\u00fcfen","submitAnswer":"Absenden","tryAgain":"Wiederholen","showSolution":"L\u00f6sung anzeigen","dropZoneIndex":"Ablagefeld @index.","empty":"Ablagefeld @index ist leer.","contains":"Ablagefeld @index enth\u00e4lt ziehbaren Text @draggable.","ariaDraggableIndex":"@index von @count ziehbaren Texten.","tipLabel":"Tipp anzeigen","correctText":"Richtig!","incorrectText":"Falsch!","resetDropTitle":"Ablagefelder zur\u00fccksetzen","resetDropDescription":"Bist du sicher, dass du dieses Ablagefeld zur\u00fccksetzen m\u00f6chtest?","grabbed":"Ziehbarer Text wurde aufgenommen.","cancelledDragging":"Ziehen abgebrochen.","correctAnswer":"Korrekte Antwort:","feedbackHeader":"R\u00fcckmeldung","behaviour":{"enableRetry":true,"enableSolutionsButton":true,"enableCheckButton":true,"instantFeedback":false},"scoreBarLabel":"Du hast :num von :total Punkten erreicht.","a11yCheck":"Die Antworten \u00fcberpr\u00fcfen. Die Eingaben werden als richtig, falsch oder unbeantwortet markiert.","a11yShowSolution":"Die L\u00f6sung anzeigen. Die richtigen L\u00f6sungen werden in der Aufgabe angezeigt.","a11yRetry":"Die Aufgabe wiederholen. Alle Eingaben werden zur\u00fcckgesetzt und die Aufgabe wird erneut gestartet.","textField":"In der modernen Kryptographie ist das Rechnen mit Rest unverzichtbar. Der Fachbegriff hierf\u00fcr lautet *modulares* Rechnen.\n\nBeim *RSA*-Verfahren spielt das *Inverse* bez\u00fcglich der modularen Multiplikation eine wichtige Rolle. \n\nZwei nat\u00fcrliche Zahlen *a* und *b* hei\u00dfen *modular invers* zueinander bez\u00fcglich *n* genau dann, wenn gilt: [a\u2022b] mod n = *1*.\n\nDas *modulare Inverse* bez\u00fcglich n zu einer Zahl a ungleich Null existiert genau dann, wenn gilt: *ggT(a, n) = 1*."},"library":"H5P.DragText 1.10","metadata":{"contentType":"Drag the Words","license":"U","title":"Unbenannt: Drag the Words"},"subContentId":"d9f1ac8b-7d33-4c93-a63b-9719dc73f5b0"},"specialStageExtraLives":1,"specialStageExtraTime":1},{"id":"c99f6706-7c0d-4b16-a8b9-e270d4d2e259","label":"Der Schmied","telemetry":{"x":"36.199095022624434","y":"79.43179787255163","width":"4.375","height":"8.533599800149888"},"neighbors":["6","8"],"canBeStartStage":false,"time":{},"accessRestrictions":{"openOnScoreSufficient":false},"contentType":{"params":{"media":{"disableImageZooming":false},"correct":"true","behaviour":{"enableRetry":true,"enableSolutionsButton":true,"enableCheckButton":true,"confirmCheckDialog":false,"confirmRetryDialog":false,"autoCheck":false},"l10n":{"trueText":"Wahr","falseText":"Falsch","score":"Du hast @score von @total Punkten erreicht.","checkAnswer":"\u00dcberpr\u00fcfen","submitAnswer":"Submit","showSolutionButton":"L\u00f6sung anzeigen","tryAgain":"Wiederholen","wrongAnswerMessage":"Falsche Antwort","correctAnswerMessage":"Richtige Antwort","scoreBarLabel":"Du hast :num von :total Punkten erreicht.","a11yCheck":"Die Antworten \u00fcberpr\u00fcfen. Die Antwort wird als richtig, falsch oder unbeantwortet markiert.","a11yShowSolution":"Die L\u00f6sung anzeigen. Die richtige L\u00f6sung wird in der Aufgabe angezeigt.","a11yRetry":"Die Aufgabe wiederholen. Alle Versuche werden zur\u00fcckgesetzt und die Aufgabe wird erneut gestartet."},"confirmCheck":{"header":"Beenden?","body":"Ganz sicher beenden?","cancelLabel":"Abbrechen","confirmLabel":"Beenden"},"confirmRetry":{"header":"Wiederholen?","body":"Ganz sicher wiederholen?","cancelLabel":"Abbrechen","confirmLabel":"Best\u00e4tigen"},"question":"
7^{7<\/sup>mod 7 = 0<\/p>\n"},"library":"H5P.TrueFalse 1.8","metadata":{"contentType":"True\/False Question","license":"U","title":"Unbenannt: True\/False Question"},"subContentId":"dfc550a8-d0b1-460c-af93-ac819f269323"},"specialStageExtraLives":1,"specialStageExtraTime":1},{"id":"7e100744-32a3-4a72-8926-910218c9530e","label":"Der verschneite Pfad","telemetry":{"x":"29.288702928870304","y":"62.5","width":"4.375","height":"8.533599800149888"},"neighbors":["2","7"],"canBeStartStage":false,"time":{},"accessRestrictions":{"openOnScoreSufficient":false},"contentType":{"params":{"media":{"disableImageZooming":false},"answers":[{"correct":false,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"}
2<\/div>\n"},{"correct":true,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"
3<\/div>\n"},{"correct":false,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"
4<\/div>\n"},{"correct":false,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"
5<\/div>\n"},{"correct":false,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"
6<\/div>\n"},{"correct":false,"tipsAndFeedback":{"tip":"","chosenFeedback":"","notChosenFeedback":""},"text":"
alle<\/div>\n"}],"overallFeedback":[{"from":0,"to":50,"feedback":"Das stimmt leider nicht. Die Teilbarkeitsregeln k\u00f6nnen helfen!"},{"from":51,"to":100,"feedback":"Super, das ist korrekt."}],"behaviour":{"enableRetry":true,"enableSolutionsButton":false,"enableCheckButton":true,"type":"auto","singlePoint":true,"randomAnswers":false,"showSolutionsRequiresInput":false,"confirmCheckDialog":false,"confirmRetryDialog":true,"autoCheck":false,"passPercentage":100,"showScorePoints":true},"UI":{"checkAnswerButton":"\u00dcberpr\u00fcfen","submitAnswerButton":"Absenden","showSolutionButton":"L\u00f6sung anzeigen","tryAgainButton":"Wiederholen","tipsLabel":"Hinweis anzeigen","scoreBarLabel":"Du hast :num von :total Punkten erreicht.","tipAvailable":"Hinweis verf\u00fcgbar","feedbackAvailable":"R\u00fcckmeldung verf\u00fcgbar","readFeedback":"R\u00fcckmeldung vorlesen","wrongAnswer":"Falsche Antwort","correctAnswer":"Richtige Antwort","shouldCheck":"H\u00e4tte gew\u00e4hlt werden m\u00fcssen","shouldNotCheck":"H\u00e4tte nicht gew\u00e4hlt werden sollen","noInput":"Bitte antworte, bevor du die L\u00f6sung ansiehst","a11yCheck":"Die Antworten \u00fcberpr\u00fcfen. Die Auswahlen werden als richtig, falsch oder fehlend markiert.","a11yShowSolution":"Die L\u00f6sung anzeigen. Die richtigen L\u00f6sungen werden in der Aufgabe angezeigt.","a11yRetry":"Die Aufgabe wiederholen. Alle Versuche werden zur\u00fcckgesetzt und die Aufgabe wird erneut gestartet."},"confirmCheck":{"header":"Beenden?","body":"Ganz sicher beenden?","cancelLabel":"Abbrechen","confirmLabel":"Beenden"},"confirmRetry":{"header":"Wiederholen?","body":"Ganz sicher wiederholen?","cancelLabel":"Abbrechen","confirmLabel":"Best\u00e4tigen"},"question":"
Betrachte die Gleichung [54 444 = 44 445] mod n<\/p>\n\n
F\u00fcr welche der Zahlen n = 2, 3, 4, 5, 6 ist die Gleichung korrekt?<\/p>\n"},"library":"H5P.MultiChoice 1.16","metadata":{"contentType":"Multiple Choice","license":"U","title":"Unbenannt: Multiple Choice"},"subContentId":"79f89696-3660-4da5-b8c5-787b13db538e"},"specialStageExtraLives":1,"specialStageExtraTime":1},{"id":"b68af572-bd6f-4ed5-b3e6-15847af01e31","label":"Gipfelkreuz","telemetry":{"x":"72.39819004524887","y":"12.066365007541481","width":"4.375","height":"8.533599800149888"},"neighbors":["3"],"canBeStartStage":false,"time":{},"accessRestrictions":{"openOnScoreSufficient":false},"contentType":{"params":{"media":{"disableImageZooming":false},"text":"
Von allem etwas<\/h2>\n\n
Berechne jeweils!<\/p>\n","overallFeedback":[{"from":0,"to":80,"feedback":"Da stimmt etwas noch nicht."},{"from":81,"to":100,"feedback":"Gut gemacht!"}],"showSolutions":"L\u00f6sung anzeigen","tryAgain":"Wiederholen","checkAnswer":"\u00dcberpr\u00fcfen","submitAnswer":"Absenden","notFilledOut":"Bitte f\u00fclle alle L\u00fccken aus, um die L\u00f6sung ansehen zu k\u00f6nnen","answerIsCorrect":"':ans' ist korrekt","answerIsWrong":"':ans' ist falsch","answeredCorrectly":"Korrekt beantwortet","answeredIncorrectly":"Falsch beantwortet","solutionLabel":"Korrekte Antwort:","inputLabel":"L\u00fccke @num von @total","inputHasTipLabel":"Tipp verf\u00fcgbar","tipLabel":"Tipp","behaviour":{"enableRetry":true,"enableSolutionsButton":true,"enableCheckButton":true,"autoCheck":false,"caseSensitive":true,"showSolutionsRequiresInput":true,"separateLines":false,"confirmCheckDialog":false,"confirmRetryDialog":false,"acceptSpellingErrors":false},"scoreBarLabel":"Du hast :num von :total Punkten erreicht.","a11yCheck":"Die Antworten \u00fcberpr\u00fcfen. Die Eingaben werden als richtig, falsch oder unbeantwortet markiert.","a11yShowSolution":"Die L\u00f6sung anzeigen. Die richtigen L\u00f6sungen werden in der Aufgabe angezeigt.","a11yRetry":"Die Aufgabe wiederholen. Alle Eingaben werden zur\u00fcckgesetzt und die Aufgabe wird erneut gestartet.","a11yCheckingModeHeader":"\u00dcberpr\u00fcfen-Modus aktiv","confirmCheck":{"header":"Beenden?","body":"Ganz sicher beenden?","cancelLabel":"Abbrechen","confirmLabel":"Beenden"},"confirmRetry":{"header":"Wiederholen?","body":"Ganz sicher wiederholen?","cancelLabel":"Abbrechen","confirmLabel":"Best\u00e4tigen"},"questions":["
1) Die Gegenzahl zu 5 mod 17 lautet *12*<\/p>\n\n
2) (220 + 15) mod 7 = *4*<\/p>\n\n
3) (13 \u2022 15) mod 11 = *8*<\/p>\n\n
4) Das Inverse zu 7 mod 13 ist *2*<\/p>\n\n
5) 53 mod 3 =*2*<\/p>\n"]},"library":"H5P.Blanks 1.14","metadata":{"contentType":"Fill in the Blanks","license":"U","title":"Unbenannt: Fill in the Blanks"},"subContentId":"6ec706c0-a7aa-4ee0-8002-8dc5eb7335f2"},"specialStageExtraLives":1,"specialStageExtraTime":1},{"id":"cdb8b07c-2049-47cb-963e-57170ea7c754","label":"In der Wildnis","telemetry":{"x":"68.3403068340307","y":"57.06521739130434","width":"4.375","height":"8.533599800149888"},"neighbors":["5","6","4"],"canBeStartStage":false,"time":{},"accessRestrictions":{"openOnScoreSufficient":false},"contentType":{"params":{"media":{"disableImageZooming":false},"text":"
b hei\u00dft modular invers zu a bez\u00fcglich n, wenn gilt [a \u2022 b] mod n = 1<\/p>\n\n
Ermittle jeweils das modulare Inverse b zu a bzgl. n<\/p>\n","overallFeedback":[{"from":0,"to":100}],"showSolutions":"L\u00f6sung anzeigen","tryAgain":"Wiederholen","checkAnswer":"\u00dcberpr\u00fcfen","submitAnswer":"Absenden","notFilledOut":"Bitte f\u00fclle alle L\u00fccken aus, um die L\u00f6sung ansehen zu k\u00f6nnen","answerIsCorrect":"':ans' ist korrekt","answerIsWrong":"':ans' ist falsch","answeredCorrectly":"Korrekt beantwortet","answeredIncorrectly":"Falsch beantwortet","solutionLabel":"Korrekte Antwort:","inputLabel":"L\u00fccke @num von @total","inputHasTipLabel":"Tipp verf\u00fcgbar","tipLabel":"Tipp","behaviour":{"enableRetry":true,"enableSolutionsButton":false,"enableCheckButton":true,"autoCheck":false,"caseSensitive":false,"showSolutionsRequiresInput":false,"separateLines":false,"confirmCheckDialog":false,"confirmRetryDialog":true,"acceptSpellingErrors":false},"scoreBarLabel":"Du hast :num von :total Punkten erreicht.","a11yCheck":"Die Antworten \u00fcberpr\u00fcfen. Die Eingaben werden als richtig, falsch oder unbeantwortet markiert.","a11yShowSolution":"Die L\u00f6sung anzeigen. Die richtigen L\u00f6sungen werden in der Aufgabe angezeigt.","a11yRetry":"Die Aufgabe wiederholen. Alle Eingaben werden zur\u00fcckgesetzt und die Aufgabe wird erneut gestartet.","a11yCheckingModeHeader":"\u00dcberpr\u00fcfen-Modus aktiv","confirmCheck":{"header":"Beenden?","body":"Ganz sicher beenden?","cancelLabel":"Abbrechen","confirmLabel":"Beenden"},"confirmRetry":{"header":"Wiederholen?","body":"Ganz sicher wiederholen?","cancelLabel":"Abbrechen","confirmLabel":"Best\u00e4tigen"},"questions":["
1) a = 5; n = 7 => b = *3* ist modular invers zu a bzgl. n<\/p>\n\n
2) a = 7; n = 11 => b = *8* ist modular invers zu a bzgl. n<\/p>\n\n
<\/p>\n"]},"library":"H5P.Blanks 1.14","metadata":{"contentType":"Fill in the Blanks","license":"U","title":"Unbenannt: Fill in the Blanks"},"subContentId":"2fe9699a-dbae-4c8a-af7a-f00c6a989f68"},"specialStageExtraLives":1,"specialStageExtraTime":1}]}},"endScreen":{"noSuccess":{"endScreenTextNoSuccess":"
Das Abenteuer war dieses Mal zu gro\u00df f\u00fcr dich.<\/p>\n\n
Versuche es erneut!<\/p>\n","endScreenMediumNoSuccess":{"params":{"decorative":false,"contentName":"Bild","expandImage":"Bild vergr\u00f6\u00dfern","minimizeImage":"Bild verkleinern","file":{"path":"images\/file-65ef2f33a3992.jpg","mime":"image\/jpeg","copyright":{"license":"U"},"width":1280,"height":854},"alt":"Ein Paar Schuhe vor einem steinernen Drachen"},"library":"H5P.Image 1.1","metadata":{"contentType":"Image","license":"CC0 1.0","title":"Drache","authors":[{"name":"Silviarita","role":"Author"}],"yearFrom":2019,"source":"https:\/\/pixabay.com\/de\/photos\/drache-schuhe-socken-fl%C3%BCchten-4185954\/"},"subContentId":"1f79c7cd-d660-497a-a588-c0d9aa345b85"}},"success":{"endScreenTextSuccess":"
Prima - du hast das Abenteuer bravour\u00f6s gemeistert!<\/p>\n","endScreenMediumSuccess":{"params":{"decorative":false,"contentName":"Bild","expandImage":"Bild vergr\u00f6\u00dfern","minimizeImage":"Bild verkleinern","file":{"path":"images\/file-65ef2fcd605e9.jpg","mime":"image\/jpeg","copyright":{"license":"U"},"width":835,"height":1280}},"library":"H5P.Image 1.1","metadata":{"contentType":"Image","license":"CC0 1.0","title":"Lorbeerkranz","authors":[{"name":"wal_172619","role":"Author"}],"source":"https:\/\/pixabay.com\/de\/photos\/lorbeerkranz-gewinner-statue-sieg-6542984\/","yearFrom":2021},"subContentId":"b205f244-fc10-44d9-bcac-c7c983dd6de7"}},"overallFeedback":[{"from":0,"to":100}]},"visual":{"stages":{"colorStage":"rgba(250, 223, 10, 0.7)","colorStageLocked":"rgba(153, 0, 0, 0.7)","colorStageCleared":"rgba(0, 130, 0, 0.7)"},"paths":{"displayPaths":true,"style":{"colorPath":"rgba(0, 0, 0, 0.7)","colorPathCleared":"rgba(0, 130, 0, 0.7)","pathWidth":"0.2","pathStyle":"dotted"}},"misc":{"useAnimation":true}},"audio":{"backgroundMusic":{"muteDuringExercise":true},"ambient":{}},"behaviour":{"enableRetry":true,"enableSolutionsButton":true,"map":{"showLabels":true,"roaming":"complete","fog":"0"},"lives":6,"timeLimitGlobal":1500},"l10n":{"start":"Start","continue":"Fortfahren","restart":"Neustart","showSolutions":"Zeige L\u00f6sungen","completedMap":"Du hast die Karte abgeschlossen!","fullScoreButnoLivesLeft":"Du hast die volle Punktzahl erreicht, aber alle deine Leben verloren!","fullScoreButTimeout":"Du hast die volle Punktzahl erreicht, aber die verf\u00fcgbare Zeit \u00fcberschritten!","confirmFinishHeader":"Karte beenden?","confirmFinishDialog":"Wenn du jetzt aufh\u00f6rst, kannst du die Karte nicht weiter erkunden.","confirmFinishDialogSubmission":"Deine Punkte werden \u00fcbertragen.","confirmFinishDialogQuestion":"Willst du die Karte wirklich beenden?","confirmAccessDeniedHeader":"Etappe gesperrt","confirmAccessDeniedDialog":"Um diese Etappe zu \u00f6ffnen, musst du einige Voraussetzungen erf\u00fcllen.","confirmAccessDeniedMinScore":"Du brauchst eine Mindestpunktzahl: @minScore","yes":"Ja","no":"Nein","confirmGameOverHeader":"Game over!","confirmGameOverDialog":"Du hast alle deine Leben verloren. Versuche es noch einmal!","confirmGameOverDialogTimeout":"Dir ist die Zeit ausgegangen. Versuche es noch einmal!","confirmTimeoutHeader":"Zeit abgelaufen!","confirmTimeoutDialog":"Die Zeit f\u00fcr die Aufgabe ist abgelaufen.","confirmTimeoutDialogLostLife":"Die Zeit f\u00fcr die Aufgabe ist abgelaufen, und du hast ein Leben verloren.","confirmScoreIncompleteHeader":"Nicht volle Punktzahl!","confirmIncompleteScoreDialogLostLife":"Du hast nicht die volle Punktzahl erreicht und hast ein Leben verloren.","confirmFullScoreHeader":"Du hast die volle Punktzahl erreicht!","confirmFullScoreDialog":"Du hast den langen, harten Winter \u00fcberstanden und gen\u00fcgend Punkte gesammelt.","confirmFullScoreDialogLoseLivesAmendmend":"Gut gemacht!","ok":"OK","noBackground":"Es wurde f\u00fcr die Karte kein Hintergrundbild gesetzt.","noStages":"Es wurden keine g\u00fcltigen Etappen f\u00fcr die Karte gesetzt."},"a11y":{"buttonFinish":"Beenden","buttonAudioActive":"Ton ausschalten. Derzeit eingeschaltet.","buttonAudioInactive":"Ton einschalten. Derzeit ausgeschaltet.","close":"Schlie\u00dfen","yourResult":"Du hast @score von @total Punkten erreicht","mapWasOpened":"Die Karte wurde ge\u00f6ffnet.","mapSolutionsWasOpened":"Die Karte wurde im L\u00f6sungsmodus ge\u00f6ffnet.","startScreenWasOpened":"Der Titelbildschirm wurde ge\u00f6ffnet.","endScreenWasOpened":"Der Endbildschirm wurde ge\u00f6ffnet.","exerciseLabel":". \u00dcbung f\u00fcr @stagelabel","stageButtonLabel":"Etappe: @stagelabel","adjacentStageLabel":"Nachbaretappe von @stagelabelOrigin: @stagelabelNeighbor","locked":"Verschlossen","cleared":"Absolviert","applicationInstructions":"Benutze die Space-Taste oder die Eingabetaste, um die aktuelle Etappe zu aktivieren. Benutze die Pfeiltasten, um Nachbaretappen auszuw\u00e4hlen. Benutze die Space-Taste oder die Eingabetaste auf einer Nachbaretappe, um dorthin zu navigieren.","applicationDescription":"Karte","movedToStage":"Zu Etappe @stagelabel gegangen","stageUnlocked":"Etappe @stagelabel wurde freigeschaltet.","toolbarFallbackLabel":"Game Map","enterFullscreen":"Gehe in den Vollbildmodus","exitFullscreen":"Verlasse den Vollbildmodus"},"headline":"Moduares Rechnen"}