// Numbas version: finer_feedback_settings
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$\\var{number1}=\\left(\\var{bases[0]}+1\\right)^3=\\left(\\var{bases[0]}^3+3\\cdot\\var{bases[0]}^2+3\\cdot\\var{bases[0]}^1+1\\cdot\\var{bases[0]}^0\\right)=\\left(1,3,3,1\\right)_\\var{bases[0]}$</p>\n<p>b) $\\var{number2}=\\left(\\var{bases[1]}+1\\right)^3=\\left(\\var{bases[1]}^3+3\\cdot\\var{bases[1]}^2+3\\cdot\\var{bases[1]}^1+1\\cdot\\var{bases[1]}^0\\right)=\\left(1,3,3,1\\right)_\\var{bases[1]}$</p>\n<p>c) $\\var{number3}=\\left(\\var{bases[2]}+1\\right)^3=\\left(\\var{bases[2]}^3+3\\cdot\\var{bases[2]}^2+3\\cdot\\var{bases[2]}^1+1\\cdot\\var{bases[2]}^0\\right)=\\left(1,3,3,1\\right)_\\var{bases[2]}$</p>", "rulesets": {}, "extensions": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random([5,6,7,8,9,11,12,13,14,15])", "description": "", "templateType": "anything"}, "b1": {"name": "b1", "group": "Ungrouped variables", "definition": "random([4,5,6,7,8,9,11,12,13,14,15])", "description": "", "templateType": "anything"}, "c1": {"name": "c1", "group": "Ungrouped variables", "definition": "random([5,6,7,8,9,11,12,13,14])", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "if(a=b1,15,b1)", "description": "", "templateType": "anything"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "if(a=c1,4,if(b=c1,4,c1))\n", "description": "", "templateType": "anything"}, "bases": {"name": "bases", "group": "Ungrouped variables", "definition": "shuffle([a,b,c])", "description": "", "templateType": "anything"}, "number1": {"name": "number1", "group": "Ungrouped variables", "definition": "(bases[0]+1)^3", "description": "", "templateType": "anything"}, "number2": {"name": "number2", "group": "Ungrouped variables", "definition": "(bases[1]+1)^3", "description": "", "templateType": "anything"}, "number3": {"name": "number3", "group": "Ungrouped variables", "definition": "(bases[2]+1)^3", "description": "", "templateType": "anything"}, "digits1a": {"name": 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"showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Stellen Sie die&nbsp;Dezimalzahl $\\var{number1}$ im Stellenwertsystem zur Basis $\\var{bases[0]}$ dar.&nbsp;</p>\n<p><strong>L&ouml;sung: </strong>$\\Bigg($[[0]]$,$[[1]]$,$[[2]]$,$[[3]]$\\Bigg)_\\var{bases[0]}$</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "z4", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "1", "maxValue": "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"}, {"type": "numberentry", "useCustomName": true, "customName": "z3", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "3", "maxValue": "3", "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": "z2", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "3", "maxValue": "3", "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": "z1", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "1", "maxValue": "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>Stellen Sie die&nbsp;Dezimalzahl $\\var{number2}$ im Stellenwertsystem zur Basis $\\var{bases[1]}$ dar.&nbsp;</p>\n<p><strong>L&ouml;sung: </strong>$\\Bigg($[[0]]$,$[[1]]$,$[[2]]$,$[[3]]$\\Bigg)_\\var{bases[1]}$</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "z4", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "1", "maxValue": "1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": 0, 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"extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "1", "maxValue": "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>Stellen Sie die&nbsp;Dezimalzahl $\\var{number3}$ im Stellenwertsystem zur Basis $\\var{bases[2]}$ dar.&nbsp;</p>\n<p><strong>L&ouml;sung: </strong>$\\Bigg($[[0]]$,$[[1]]$,$[[2]]$,$[[3]]$\\Bigg)_\\var{bases[2]}$</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "z4", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "1", "maxValue": "1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": 0, "precisionPartialCredit": 0, 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"variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<h4 style=\"padding-left: 30px;\">d)</h4>\n<p style=\"padding-left: 30px;\">Was stellen Sie beim Vergleich der Ergebnisse fest? Woran liegt das?</p>\n<p style=\"padding-left: 30px; text-align: right;\"><em>Nur zum &Uuml;berlegen, wird nicht bewertet!</em></p>"}], "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/"}], "resources": []}]}], "contributors": [{"name": "Andreas Vohns", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3622/"}]}