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{"name": "\u00dcbungen (Lektion 3)", "metadata": {"description": "<p>&Uuml;bungen zur Ethnomathematik</p>", "licence": "Creative Commons Attribution 4.0 International"}, "duration": 0, "percentPass": "5", "showQuestionGroupNames": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", ""], "questions": [{"name": "Quipu (Inka)", "extensions": [], "custom_part_types": [], "resources": [["question-resources/quipud00.jpg", "/srv/numbas/media/question-resources/quipud00.jpg"], ["question-resources/quipud01.jpg", "/srv/numbas/media/question-resources/quipud01.jpg"], ["question-resources/quipud03.jpg", "/srv/numbas/media/question-resources/quipud03.jpg"], ["question-resources/quipud04.jpg", "/srv/numbas/media/question-resources/quipud04.jpg"], ["question-resources/quipud05.jpg", "/srv/numbas/media/question-resources/quipud05.jpg"], ["question-resources/quipud06.jpg", "/srv/numbas/media/question-resources/quipud06.jpg"], ["question-resources/quipud07.jpg", "/srv/numbas/media/question-resources/quipud07.jpg"], ["question-resources/quipud08.jpg", "/srv/numbas/media/question-resources/quipud08.jpg"], ["question-resources/quipud09.jpg", "/srv/numbas/media/question-resources/quipud09.jpg"], ["question-resources/quipud10.jpg", "/srv/numbas/media/question-resources/quipud10.jpg"], ["question-resources/quipud11.jpg", "/srv/numbas/media/question-resources/quipud11.jpg"], ["question-resources/quipud12.jpg", "/srv/numbas/media/question-resources/quipud12.jpg"], ["question-resources/quipud13.jpg", "/srv/numbas/media/question-resources/quipud13.jpg"], ["question-resources/quipud14.jpg", "/srv/numbas/media/question-resources/quipud14.jpg"], ["question-resources/quipud15.jpg", "/srv/numbas/media/question-resources/quipud15.jpg"], ["question-resources/quipud16.jpg", "/srv/numbas/media/question-resources/quipud16.jpg"], ["question-resources/quipud17.jpg", "/srv/numbas/media/question-resources/quipud17.jpg"], ["question-resources/quipud18.jpg", "/srv/numbas/media/question-resources/quipud18.jpg"], ["question-resources/quipud19.jpg", "/srv/numbas/media/question-resources/quipud19.jpg"], ["question-resources/quipuds.jpg", "/srv/numbas/media/question-resources/quipuds.jpg"], ["question-resources/quipudm.jpg", "/srv/numbas/media/question-resources/quipudm.jpg"], ["question-resources/quipud02.jpg", "/srv/numbas/media/question-resources/quipud02.jpg"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Andreas Vohns", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3622/"}], "tags": [], "metadata": {"description": "<p>Dechiffrierung einer einfachen Zahlenschnur</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Unten ist ein Ausschnitt aus einem Quipu, einer Zahlenschnur der Inka, dargestellt. Der obere Teil mit dem Ergebnis fehlt.</p>\n<table style=\"border-collapse: collapse;\">\n<tbody>\n<tr style=\"padding: 0px; margin: 0px; border: none;\">\n<td style=\"padding: 0px; margin: 0px; border: none; line-height: 0;\">\n<div style=\"position: relative; left: 3px;\"><img src=\"resources/question-resources/quipuds.jpg\"/></div>\n</td>\n<td style=\"padding: 0px; margin: 0px; border: none; line-height: 0;\"><img src=\"resources/question-resources/quipudm.jpg\"/></td>\n<td style=\"padding: 0px; margin: 0px; border: none; line-height: 0;\">\n<div style=\"position: relative; left: -3px;\"><img src=\"resources/question-resources/quipuds.jpg\"/></div>\n</td>\n</tr>\n<tr style=\"padding: 0px; margin: 0px; border: none;\">\n<td style=\"padding: 0px; margin: 0px; border: none; line-height: 0;\">\n<div style=\"position: relative; left: 3px;\">{image('resources/question-resources/'+tens[H[0]])}</div>\n</td>\n<td style=\"padding: 0px; margin: 0px; border: none; line-height: 0;\">\n<div style=\"position: relative; left: 0px;\">{image('resources/question-resources/'+tens[H[1]])}</div>\n</td>\n<td style=\"padding: 0px; margin: 0px; border: none; line-height: 0;\">\n<div style=\"position: relative; left: -3px;\">{image('resources/question-resources/'+tens[H[2]])}</div>\n</td>\n</tr>\n<tr style=\"padding: 0px; margin: 0px; border: none;\">\n<td style=\"padding: 0px; margin: 0px; border: none; line-height: 0;\">\n<div style=\"position: relative; left: 3px;\">{image('resources/question-resources/'+tens[T[0]])}</div>\n</td>\n<td style=\"padding: 0px; margin: 0px; border: none; line-height: 0;\">\n<div style=\"position: relative; left: 0px;\">{image('resources/question-resources/'+tens[T[1]])}</div>\n</td>\n<td style=\"padding: 0px; margin: 0px; border: none; line-height: 0;\">\n<div style=\"position: relative; left: -3px;\">{image('resources/question-resources/'+tens[T[2]])}</div>\n</td>\n</tr>\n<tr style=\"padding: 0px; margin: 0px; border: none;\">\n<td style=\"padding: 0px; margin: 0px; border: none; line-height: 0;\">\n<div style=\"position: relative; left: 3px;\">{image('resources/question-resources/'+ones[O[0]])}</div>\n</td>\n<td style=\"padding: 0px; margin: 0px; border: none; line-height: 0;\">\n<div style=\"position: relative; left: 0px;\">{image('resources/question-resources/'+ones[O[1]])}</div>\n</td>\n<td style=\"padding: 0px; margin: 0px; border: none; line-height: 0;\">\n<div style=\"position: relative; left: -3px;\">{image('resources/question-resources/'+ones[O[2]])}</div>\n</td>\n</tr>\n</tbody>\n</table>", "advice": "<p>Man liest die Schn&uuml;re von au&szlig;en nach innen (also unten nach oben f&uuml;r die unteren Schn&uuml;re), jede Schnur stellt (in diesem Fall eine dreistellige) Zahl dar:</p>\n<ol>\n<li><strong>Links:</strong> {einer[O[0]]} meint {O[0]},&nbsp;{zehner[T[0]]} meint {T[0]*10},&nbsp;{zehner[H[0]]}&nbsp;meint {H[0]*100}, ergibt {a}.</li>\n<li><strong>Mitte:</strong> {einer[O[1]]} meint {O[1]},&nbsp;{zehner[T[1]]} meint {T[1]*10},&nbsp;{zehner[H[1]]}&nbsp;meint {H[1]*100}, ergibt {b}.</li>\n<li><strong>Rechts:</strong> {einer[O[2]]} meint {O[2]},&nbsp;{zehner[T[2]]} meint {T[2]*10},&nbsp;{zehner[H[2]]}&nbsp;meint {H[2]*100}, ergibt {c}.</li>\n</ol>\n<p>Als&nbsp;<strong>L&ouml;sung</strong> (dargestellt auf der fehlenden oberen Schnur) ergibt sich $\\var{a}+\\var{b}+\\var{c}=\\var{a+b+c}$.</p>", "rulesets": {}, "variables": {"ones": {"name": "ones", "group": "Ungrouped variables", "definition": "['quipud00.jpg','quipud01.jpg','quipud02.jpg','quipud03.jpg','quipud04.jpg',\n  'quipud05.jpg','quipud06.jpg','quipud07.jpg','quipud08.jpg','quipud09.jpg']", "description": "", "templateType": "anything"}, "tens": {"name": "tens", "group": "Ungrouped variables", "definition": "['quipud10.jpg','quipud11.jpg','quipud12.jpg','quipud13.jpg','quipud14.jpg',\n  'quipud15.jpg','quipud16.jpg','quipud17.jpg','quipud18.jpg','quipud19.jpg']", "description": "", "templateType": "anything"}, "H": {"name": "H", "group": "Ungrouped variables", "definition": "shuffle([random(0..9),random(6..9),random(1..5)])", "description": "", "templateType": "anything"}, "T": {"name": "T", "group": "Ungrouped variables", "definition": "shuffle([random(1..3),random(3..6),random(6..9)])", "description": "", "templateType": "anything"}, "O": {"name": "O", "group": "Ungrouped variables", "definition": "shuffle([1,random(2..9),0])", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "100*H[0]+10*T[0]+O[0]", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "100*H[1]+10*T[1]+O[1]", "description": "", "templateType": "anything"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "100*H[2]+10*T[2]+O[2]", "description": "", "templateType": "anything"}, "einer": {"name": "einer", "group": "Ungrouped variables", "definition": "['kein Knoten','geknotete Acht','Doppelknoten','Dreifachknoten','Vierfachknoten','F\u00fcnffachknoten',\n'Sechsfachknoten','Siebenfachknoten','Achtfachknoten','Neunfachknoten']", "description": "", "templateType": "anything"}, "zehner": {"name": "zehner", "group": "Ungrouped variables", "definition": "['kein Knoten','ein Einzelknoten','zwei Einzelknoten','drei Einzelknoten','vier Einzelknoten','f\u00fcnf Einzelknoten',\n'sechs Einzelknoten','sieben Einzelknoten','acht Einzelknoten','neun Einzelknoten']", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["ones", "tens", "H", "T", "O", "a", "b", "c", "einer", "zehner"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": "tr, img  { padding: 0px; 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"/srv/numbas/media/question-resources/mayand15.png"], ["question-resources/mayand16.png", "/srv/numbas/media/question-resources/mayand16.png"], ["question-resources/mayand17.png", "/srv/numbas/media/question-resources/mayand17.png"], ["question-resources/mayand18.png", "/srv/numbas/media/question-resources/mayand18.png"], ["question-resources/mayand19.png", "/srv/numbas/media/question-resources/mayand19.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Andreas Vohns", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3622/"}], "tags": [], "metadata": {"description": "<p>Dechiffrierung von Maya-Zahlen</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Unten sei ein Auszug aus einem Codex der Maya dargestellt, auf dem drei Zahlenangaben zu finden sind.</p>\n<table style=\"border-collapse: collapse;\">\n<tbody>\n<tr style=\"padding: 0px; margin: 0px; border: none;\">\n<td style=\"padding: 0px; margin: 0px; border: none; line-height: 0;\">\n<div style=\"position: relative; left: 0px;\">{image('resources/question-resources/'+digits[H[0]])}</div>\n</td>\n<td>&nbsp;</td>\n<td style=\"padding: 0px; margin: 0px; border: none; line-height: 0;\">\n<div style=\"position: relative; left: 0px;\">{image('resources/question-resources/'+digits[H[1]])}</div>\n</td>\n<td>&nbsp;</td>\n<td style=\"padding: 0px; margin: 0px; border: none; line-height: 0;\">\n<div style=\"position: relative; left: 0x;\">{image('resources/question-resources/'+digits[Hc])}</div>\n</td>\n</tr>\n<tr style=\"padding: 0px; margin: 0px; border: none;\">\n<td style=\"padding: 0px; margin: 0px; border: none; line-height: 0;\">\n<div style=\"position: relative; top: -30px;\">{image('resources/question-resources/'+digits[T[0]])}</div>\n</td>\n<td>&nbsp;</td>\n<td style=\"padding: 0px; margin: 0px; border: none; line-height: 0;\">\n<div style=\"position: relative; top: -30px;\">{image('resources/question-resources/'+digits[T[1]])}</div>\n</td>\n<td>&nbsp;</td>\n<td style=\"padding: 0px; margin: 0px; border: none; line-height: 0;\">\n<div style=\"position: relative; top: -30px;\">{image('resources/question-resources/'+digits[Tc])}</div>\n</td>\n</tr>\n<tr style=\"padding: 0px; margin: 0px; border: none;\">\n<td style=\"padding: 0px; margin: 0px; border: none; line-height: 0;\">\n<div style=\"position: relative; top: -40px;\">{image('resources/question-resources/'+digits[O[0]])}</div>\n</td>\n<td>&nbsp;</td>\n<td style=\"padding: 0px; margin: 0px; border: none; line-height: 0;\">\n<div style=\"position: relative; top: -40px;\">{image('resources/question-resources/'+digits[O[1]])}</div>\n</td>\n<td>&nbsp;</td>\n<td style=\"padding: 0px; margin: 0px; border: none; line-height: 0;\">\n<div style=\"position: relative; top: -40px;\">{image('resources/question-resources/'+digits[Oc])}</div>\n</td>\n</tr>\n</tbody>\n</table>", "advice": "<p>a) Die Zahlen werden von links nach rechts und unten nach oben gelesen. Die Stellenwerte sind Einer (Unten), 20er (Mitte) und 360er (Oben).</p>\n<p><strong>Erste Zahl (Links):</strong> $\\qquad\\var{H[0]}\\cdot 360+\\var{T[0]}\\cdot 20+\\var{O[0]}=\\var{a}$</p>\n<p><strong>Zweite Zahl (Mitte):</strong> $\\quad\\var{H[1]}\\cdot 360+\\var{T[1]}\\cdot 20+\\var{O[1]}=\\var{b}$</p>\n<p><strong>Dritte&nbsp;Zahl (Rechts):</strong> $\\quad\\var{Hc}\\cdot 360+\\var{Tc}\\cdot 20+\\var{Oc}=\\var{c}$</p>\n<hr/>\n<p>b) Es gilt {bop[switch]}, es liegt also eine <strong>{cstring[switch]}-Aufgabe</strong> vor.</p>", "rulesets": {}, "variables": {"H": {"name": "H", "group": "Ungrouped variables", "definition": "[random(8..11),random(3..6)]", "description": "", "templateType": "anything"}, "T": {"name": "T", "group": "Ungrouped variables", "definition": "[random(0..5),random(6..8)]\n", "description": "", "templateType": "anything"}, "O": {"name": "O", "group": "Ungrouped variables", "definition": "[random(0..19),random(1..19)]", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "H[0]*360+20*T[0]+O[0]", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "H[1]*360+20*T[1]+O[1]", "description": "", "templateType": "anything"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "if(switch=1,a-b,a+b)", "description": "", "templateType": "anything"}, "Hc": {"name": "Hc", "group": "Ungrouped variables", "definition": "floor(c/360)", "description": "", "templateType": "anything"}, "Tc": {"name": "Tc", "group": "Ungrouped variables", "definition": "floor((c-Hc*360)/20)", "description": "", "templateType": "anything"}, "Oc": {"name": "Oc", "group": "Ungrouped variables", "definition": "c-Hc*360-Tc*20", "description": "", "templateType": "anything"}, "Test": {"name": "Test", "group": "Ungrouped variables", "definition": "Hc*360+Tc*20+Oc", "description": "", "templateType": "anything"}, "switch": {"name": "switch", "group": "Ungrouped variables", "definition": "random(0..1)", "description": "", "templateType": "anything"}, "digits": {"name": "digits", "group": "Ungrouped variables", "definition": "['mayand00.png','mayand01.png','mayand02.png','mayand03.png','mayand04.png','mayand05.png',\n  'mayand06.png','mayand07.png','mayand08.png','mayand09.png','mayand10.png',\n  'mayand11.png','mayand12.png','mayand13.png','mayand14.png','mayand15.png',\n  'mayand16.png','mayand17.png','mayand18.png','mayand19.png']", "description": "", "templateType": "anything"}, "bstring": {"name": "bstring", "group": "Ungrouped variables", "definition": "['addi','subtra']", "description": "", "templateType": "anything"}, "cstring": {"name": "cstring", "group": "Ungrouped variables", "definition": "['Additions','Subtraktions']", "description": "", "templateType": "anything"}, "dstring": {"name": "dstring", "group": "Ungrouped variables", "definition": "['plus','minus']", "description": "", "templateType": "anything"}, "bop": {"name": "bop", "group": "Ungrouped variables", "definition": "['$'+a+'+'+b+'='+c+'$','$'+a+'-'+b+'='+c+'$']", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["H", "T", "O", "a", "b", "c", "Hc", "Tc", "Oc", "Test", "switch", "digits", "bstring", "cstring", "dstring", "bop"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Welche drei Zahlen sind hier dargestellt?</p>\n<p>1. Zahl: [[0]] 2. Zahl: [[1]] 3. Zahl:&nbsp;[[2]]</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "a", "marks": "1.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{a}", "maxValue": "{a}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": 0, "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["eu", "plain-eu"], "correctAnswerStyle": "plain-eu"}, {"type": "numberentry", "useCustomName": true, "customName": "b", "marks": "1.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{b}", "maxValue": "{b}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": 0, "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["eu", "plain-eu"], "correctAnswerStyle": "plain-eu"}, {"type": "numberentry", "useCustomName": true, "customName": "c", "marks": "1.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{c}", "maxValue": "{c}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": 0, "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["eu", "plain-eu"], "correctAnswerStyle": "plain-eu"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Bei der Rechnung handelt es sich um eine [[0]]-Aufgabe.</p>", "gaps": [{"type": "patternmatch", "useCustomName": true, "customName": "Op", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{bstring[switch]}.*|{dstring[switch]}.*", "displayAnswer": "{cstring[switch]}", "matchMode": "regex"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Maya-Kalender", "extensions": [], "custom_part_types": [], "resources": [["question-resources/10Ajaw_sm.gif", "/srv/numbas/media/question-resources/10Ajaw_sm.gif"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Andreas Vohns", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3622/"}], "tags": [], "metadata": {"description": "<p>Einige Berechnungen am spirituellen Maya-Kalender (Modulo-Rechnungen/Kongruenzen).</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Der spirituelle Kalender der Maya hie&szlig; \"Tzolk'in\" und verwendet die Tageszahlen 1 - 13 alternierend mit 20 Tagesnamen,&nbsp;so dass sich dieselben Kombinationen (Datumsangaben) nach $13&nbsp;\\cdot 20 = 260$ Tagen ($\\approx$ ein Mondjahr) wiederholen (s. Tabelle unten f&uuml;r die ersten 20 Tage im Jahr).</p>\n<table border=\"1\" align=\"center\" width=\"100%\">\n<tbody>\n<tr>\n<th class=\"text-bold-left\" colspan=\"2\">Erste 20 Datumsangaben im Tzolk'in</th>\n<th rowspan=\"11\"><img src=\"resources/question-resources/10Ajaw_sm.gif\" width=\"200px\" alt=\"maja\"/></th>\n</tr>\n<tr>\n<td class=\"block-center\" style=\"text-align: left;\">1 Imix</td>\n<td class=\"block-center\" style=\"text-align: left;\">11 Chuwen</td>\n</tr>\n<tr>\n<td class=\"block-center\" style=\"text-align: left;\">2 Ik'</td>\n<td class=\"block-center\" style=\"text-align: left;\">12 Eb'</td>\n</tr>\n<tr>\n<td class=\"block-center\" style=\"text-align: left;\">3 Ak'bal</td>\n<td class=\"block-center\" style=\"text-align: left;\">13 Ben</td>\n</tr>\n<tr>\n<td class=\"block-center\" style=\"text-align: left;\">4 K'an</td>\n<td class=\"block-center\" style=\"text-align: left;\">1 Ix</td>\n</tr>\n<tr>\n<td class=\"block-center\" style=\"text-align: left;\">5 Chikchan</td>\n<td class=\"block-center\" style=\"text-align: left;\">2 Men</td>\n</tr>\n<tr>\n<td class=\"block-center\" style=\"text-align: left;\">6 Kimi'</td>\n<td class=\"block-center\" style=\"text-align: left;\">3 Kib'</td>\n</tr>\n<tr>\n<td class=\"block-center\" style=\"text-align: left;\">7 Manik'</td>\n<td class=\"block-center\" style=\"text-align: left;\">4 Kab'an</td>\n</tr>\n<tr>\n<td class=\"block-center\" style=\"text-align: left;\">8 Lamat</td>\n<td class=\"block-center\" style=\"text-align: left;\">5 Etz'nab'</td>\n</tr>\n<tr>\n<td class=\"block-center\" style=\"text-align: left;\">9 Muluk</td>\n<td class=\"block-center\" style=\"text-align: left;\">6 Kawak</td>\n</tr>\n<tr>\n<td class=\"block-center\" style=\"text-align: left;\">10 Ok</td>\n<td class=\"block-center\" style=\"text-align: left;\">7 Ajaw</td>\n</tr>\n</tbody>\n</table>\n<p><em><strong>Hinweis:</strong> F&uuml;r diese Aufgabe sollten Sie etwas Modulo-Rechnung beherrschen.</em></p>", "advice": "<p>a) Da&nbsp;dies der 260. Tag ist, liegt sowohl ein ganzzahliges Vielfaches von 20, als auch von 13 vor. Der Tag ist also der 13 Ajaw.</p>\n<hr/>\n<p>b) Alle Tage, f&uuml;r die sich die Datumszahl <strong>{maya_date(forb)}</strong> ergibt, liegen in der Restklasse $\\var{mod(maya_date(forb),13)}\\pmod{13}$. Alle, f&uuml;r die sich der Monat <strong>{maya_name(forb)}</strong>&nbsp;ergibt, liegen in der Restklasse $\\var{mod(forb+1,20)}\\pmod{20}$. F&uuml;r den gesuchten Tag muss gelten:</p>\n<p>\\[13\\cdot x+\\var{mod(maya_date(forb),13)}=20\\cdot y+\\var{mod(forb+1,20)}\\Leftrightarrow13\\cdot x-20\\cdot y= \\var{mod(forb+1,20)-maya_date(forb)}\\] Diese Gleichung kann man mit dem erweiterten Euklidischen Algorithmus (oder durch geschicktes Probieren) l&ouml;sen und erh&auml;lt $x=\\var{(forb-mod(maya_date(forb),13)+1)/13},y=\\var{(forb-mod(forb,20))/20}$, also den $13\\cdot\\var{(forb-mod(maya_date(forb),13)+1)/13}+\\var{mod(maya_date(forb),13)}=20\\cdot\\var{(forb-mod(forb,20))/20}+\\var{mod(forb+1,20)}=\\var{forb+1}$-ten Tag des Maya-Kalenders.</p>\n<hr/>\n<p>c) Es ist&nbsp;$40\\pmod{20}=0$ und $40\\pmod{13}=1$ (weil $3\\cdot 13=39$&nbsp;), d. h. alle 40 Tage &auml;ndert sich der Datumsname nicht, die Datumszahl r&uuml;ckt genau eins weiter. Im Beispiel r&uuml;ckt die Datumszahl genau $\\var{maya_date(forc3)-maya_date(forc1)}$ weiter, also sind $\\var{maya_date(forc3)-maya_date(forc1)}\\cdot 40=\\var{forc4}$ Tage vergangen. Alternativ bestimmt man nach der Methode aus b)&nbsp;das gr&ouml;&szlig;ere der beiden Daten und zieht das kleinere Datum (das eh in der Tabelle steht)&nbsp;davon ab ($\\var{forc3+1}-\\var{forc1+1}=\\var{forc4}$).</p>", "rulesets": {}, "variables": {"daynames": {"name": "daynames", "group": "Ungrouped variables", "definition": "['Imix',\n'Ik\\'',\n'Ak\\'bal',\n'K\\'an',\n'Chikchan',\n'Kimi\\'',\n'Manik\\'',\n'Lamat',\n'Muluk',\n'Ok',\n'Chuwen',\n'Eb\\'',\n'Ben',\n'Ix',\n'Men',\n'Kib\\'',\n'Kab\\'an',\t\n'Etz\\'nab\\'',\n'Kawak',\t\n'Ajaw']", "description": "", "templateType": "anything"}, "dates": {"name": "dates", "group": "Ungrouped variables", "definition": "[1,2,3,4,5,6,7,8,9,10,11,12,13]", "description": "", "templateType": "anything"}, "randomday": {"name": "randomday", "group": "Ungrouped variables", "definition": "20", "description": "", "templateType": "anything"}, "randomdate": {"name": "randomdate", "group": "Ungrouped variables", "definition": "maya_date(randomday)", "description": "", "templateType": "anything"}, "randomname": {"name": "randomname", "group": "Ungrouped variables", "definition": "maya_name(randomday)", "description": "", "templateType": "anything"}, "forb": {"name": "forb", "group": "Ungrouped variables", "definition": "random(110..141)", "description": "", "templateType": "anything"}, "forc1": {"name": "forc1", "group": "Ungrouped variables", "definition": "random(1..6)", "description": "", "templateType": "anything"}, "forc2": {"name": "forc2", "group": "Ungrouped variables", "definition": "random(2..4)", "description": "", "templateType": "anything"}, "forc3": {"name": "forc3", "group": "Ungrouped variables", "definition": "forc1+40*forc2", "description": "", "templateType": "anything"}, "forc4": {"name": "forc4", "group": "Ungrouped variables", "definition": "forc3-forc1", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["daynames", "dates", "randomday", "randomdate", "randomname", "forb", "forc1", "forc2", "forc3", "forc4"], "variable_groups": [], "functions": {"maya_date": {"parameters": [["raw", "number"]], "type": "anything", "language": "jme", "definition": "dates[mod(raw,13)]"}, "maya_name": {"parameters": [["raw2", "number"]], "type": "anything", "language": "jme", "definition": "daynames[mod(raw2,20)]"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Der letzte Tag des Jahres hat die Datumsangabe (erste L&uuml;cke: Zahl, zweite L&uuml;cke: Name):&nbsp;[[0]]&nbsp;[[1]]</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Nr", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{maya_date(259)}", "maxValue": "{maya_date(259)}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": 0, "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["eu", "plain-eu"], "correctAnswerStyle": "eu"}, {"type": "patternmatch", "useCustomName": true, "customName": "Name", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{maya_name(259)}", "displayAnswer": "", "matchMode": "exact"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Der Tag {maya_date(forb)} {maya_name(forb)} ist der [[0]]-te&nbsp;Tag des Maya-Kalenders.</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "b", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{forb+1}", "maxValue": "{forb+1}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": 0, "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["eu", "plain-eu"], "correctAnswerStyle": "plain-eu"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Der Tag {maya_date(forc3)} {maya_name(forc3)}&nbsp;ist der [[0]]-te Tag nach&nbsp;dem Tag {maya_date(forc1)} {maya_name(forc1)}.</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Tag", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{forc4}", "maxValue": "{forc4}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": 0, "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["eu", "plain-eu"], "correctAnswerStyle": "eu"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Kolam", "extensions": ["geogebra"], "custom_part_types": [], "resources": [["question-resources/kolam-00.png", "/srv/numbas/media/question-resources/kolam-00.png"], ["question-resources/bin1.png", "/srv/numbas/media/question-resources/bin1.png"], ["question-resources/reset1.png", "/srv/numbas/media/question-resources/reset1.png"], ["question-resources/line1_5BSfqfY.png", "/srv/numbas/media/question-resources/line1_5BSfqfY.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Andreas Vohns", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3622/"}], "tags": [], "metadata": {"description": "<p>Aktivit&auml;t zum Erstellen eines Kolam</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Ein Kolam ist eine in einem einzigen Linienzug durchf<span class=\"pl-cce\">&uuml;</span>hrbare, regelgeleitet erstellte Kreidezeichnung, wie sie sich noch heute bei den s<span class=\"pl-cce\">&uuml;</span>dindischen Tamilen als ethnomathematische Praxis auffinden l<span class=\"pl-cce\">&auml;</span>sst.<br/>Eine vereinfachte Variante f&uuml;r 8 Arme mit 5 Punkten sieht etwa so aus:</p>\n<p style=\"text-align: center;\"><img src=\"resources/question-resources/kolam-00.png\" alt=\"kolam-demo\"/></p>\n<p>Unten&nbsp;ist ein Punktmuster zur Erstellung eines&nbsp;solchen Kolam mit&nbsp;4 Armen zu je 3 Punkten abgebildet (bitte etwas Geduld, bis das Applet l&auml;dt).</p>", "advice": "<p>a) Es ergibt sich:</p>\n<p>{geogebra_applet('https://www.geogebra.org/m/fwc7k2nw',defs)}</p>\n<p>b)&nbsp;Angenommen, ein Kolam hat $a$ Arme mit je $b$ Punkten.</p>\n<p>i) F&uuml;r $a,b$&nbsp;muss dann zwingend $\\operatorname{ggT}(a,b)=1$ gelten, damit wir einen Eulergraphen haben.</p>\n<p>ii) Der Graph hat dann genau $a\\cdot b$ Kanten.</p>\n<p></p>\n<p><span style=\"margin: 0px auto; border: 2px dotted #000000; position: absolute; z-index: 2147483647; visibility: hidden; left: 36px; width: 0px; top: 60px; height: 0px;\"></span><span style=\"z-index: 2147483647; position: absolute; visibility: hidden; left: 21px; width: 50px; top: 45px; height: 20px; font-size: 10px; color: black;\"></span></p>", "rulesets": {}, "variables": {"f_correct": {"name": "f_correct", "group": "Lines", "definition": "\"Strecke A\"+kolam[0]+\", B\"+kolam[1]", "description": "", "templateType": "anything"}, "app": {"name": "app", "group": "initial setup", "definition": "geogebra_applet('https://www.geogebra.org/m/xyhpupec')", "description": "", "templateType": "anything"}, "kolam": {"name": "kolam", "group": "initial setup", "definition": "shuffle(1..3)", "description": "", "templateType": "anything"}, "kolam_string": {"name": "kolam_string", "group": "initial setup", "definition": "\"<\"+kolam[0]+\", \"+kolam[1]+\", \"+kolam[2]+\">\"", "description": "", "templateType": "anything"}, "g_correct": {"name": "g_correct", "group": "Lines", "definition": "\"Strecke B\"+kolam[1]+\", C\"+kolam[2]", "description": "", "templateType": "anything"}, "h_correct": {"name": "h_correct", "group": "Lines", "definition": "\"Strecke C\"+kolam[2]+\", D\"+kolam[0]", "description": "", "templateType": "anything"}, "i_correct": {"name": "i_correct", "group": "Lines", "definition": "\"Strecke D\"+kolam[0]+\", A\"+kolam[1]", "description": "", "templateType": "anything"}, "j_correct": {"name": "j_correct", "group": "Lines", "definition": "\"Strecke A\"+kolam[1]+\", B\"+kolam[2]", "description": "", "templateType": "anything"}, "k_correct": {"name": "k_correct", "group": "Lines", "definition": "\"Strecke B\"+kolam[2]+\", C\"+kolam[0]", "description": "", "templateType": "anything"}, "l_correct": {"name": 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Linie fehlt\"));\n  if(exists(app,\"r\")=true,if(definition_string(app,\"r\")=r_correct,add_credit(1/12,\"12. Linie ok. \"),negative_feedback(\"12. Linie falsch\")),negative_feedback(\"12. Linie fehlt\"))\n  \ninterpreted_answer:\n  f", "extendBaseMarkingAlgorithm": false, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p style=\"text-align: center;\">{app}</p>\n<p>Erstellen Sie ein Kolam gem&auml;&szlig; der Punktfolge {kolam_string}.&nbsp;Beginnen Sie dabei mit dem Z<span class=\"pl-cce\">&auml;</span>hlen der Punkte beim innersten Punkt des nach oben zeigenden Arms (der gemeinsame Punkt aller vier Arme in der Mitte sei 0) und schreiten Sie im Uhrzeigersinn (rechts herum) fort.</p>\n<p><em>Sie k&ouml;nnen das Icon <img src=\"resources/question-resources/line1_5BSfqfY.png\" alt=\"line\" style=\"vertical-align: middle;\"/> zum Zeichnen von Linien verwenden, das Icon <img src=\"resources/question-resources/bin1.png\" alt=\"bin\" style=\"vertical-align: middle;\"/> um fehlerhafte Linien wieder zu l&ouml;schen. Mit <img src=\"resources/question-resources/reset1.png\" alt=\"reset\" style=\"vertical-align: middle;\"/> k&ouml;nnen Sie die ganze Zeichnung wieder zur&uuml;cksetzen, mit den beiden Pfeilen oben rechts einen Schritt r&uuml;ckg&auml;ngig machen bzw. wiederholen.</em></p>"}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Angenommen, ein Kolam hat $a$ Arme mit je $b$ Punkten.</p>\n<p>i) F&uuml;r $a,b$&nbsp;muss dann zwingend $\\operatorname{ggT}(a,b)=$[[0]] gelten, damit wir einen Eulergraphen haben.</p>\n<p>ii) Der Graph hat dann genau [[1]] Kanten.</p>\n<p></p>", "gaps": [{"type": "numberentry", "useCustomName": true, 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