// Numbas version: finer_feedback_settings
{"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}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Maya-Kalender", "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": {}, "extensions": [], "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", "type": "question", "contributors": [{"name": "Andreas Vohns", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3622/"}]}]}], "contributors": [{"name": "Andreas Vohns", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3622/"}]}