// Numbas version: exam_results_page_options
{"name": "Weitere \u00dcbungen (Lektion 3)", "metadata": {"description": "<p>&Uuml;bungen zu&nbsp;Stellenwertsysteme, Euklidischer Algorithmus</p>", "licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", ""], "questions": [{"name": "Stellenwertdarstellungen", "extensions": [], "custom_part_types": [], "resources": [], "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>Zifferndarstellungen in b-adischen Systemen</p>", "licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International"}, "statement": "<p>Die folgenden Beispiele ergeben&nbsp;jeweils eine vierstellige Zahl in einem Stellenwertsystem zur Basis $b$, die einzelnen Stellenwerte sind jeweils durch Beistrich (,) getrennt.</p>", "advice": "<p>Aufgrund des binomischen Lehrsatzes ergibt sich stets dieselbe Zifferndarstellung:</p>\n<p>a) $\\var{number1}=\\left(\\var{bases[0]}+1\\right)^3=\\left(\\var{bases[0]}^3+3\\cdot\\var{bases[0]}^2+3\\cdot\\var{bases[0]}^1+1\\cdot\\var{bases[0]}^0\\right)=\\left(1,3,3,1\\right)_\\var{bases[0]}$</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": {}, "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": "digits1a", "group": "Ungrouped variables", "definition": "[floor(number1/bases[0]^3),floor(mod(number1,bases[0]^3)/bases[0]^2)]\n", "description": "", "templateType": "anything"}, "digits1b": {"name": "digits1b", "group": "Ungrouped variables", "definition": "[floor((number1-digits1a[0]*bases[0]^3-digits1a[1]*bases[0]^2)/bases[0]),mod(number1-digits1a[0]*bases[0]^3-digits1a[1]*bases[0]^2,bases[0])]", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b1", "c1", "b", "c", "bases", "number1", "number2", "number3", "digits1a", "digits1b"], "variable_groups": [], "functions": {"": {"parameters": [], "type": "anything", "language": "jme", "definition": ""}}, "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>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, "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 $\\var{number3}$ 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, "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": "information", "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": "<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"}, {"name": "Addition in anderen Stellenwertsystemen", "extensions": [], "custom_part_types": [], "resources": [], "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>Aufgabe zum schriftlichen Addieren in b-adischen Systemen</p>", "licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International"}, "statement": "<p>Wir wollen die Summe der Zahlen $\\left(\\var{z14},\\var{z13},\\var{z12},\\var{z11}\\right)_\\var{base}$ und&nbsp;$\\left(\\var{z24},\\var{z23},\\var{z22},\\var{z21}\\right)_\\var{base}$ ermitteln.</p>", "advice": "<p>a)</p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\">$\\Big($</td>\n<td style=\"text-align: right;\">{z14}</td>\n<td style=\"text-align: right;\">,</td>\n<td style=\"text-align: right;\">{z13}</td>\n<td style=\"text-align: right;\">,</td>\n<td style=\"text-align: right;\">{z12}</td>\n<td style=\"text-align: right;\">,</td>\n<td style=\"text-align: right;\">{z11}$\\Big)_\\var{base}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$+\\Big($</td>\n<td style=\"text-align: right;\">{z24 }</td>\n<td style=\"text-align: right;\">,</td>\n<td style=\"text-align: right;\">{z23}</td>\n<td style=\"text-align: right;\">,</td>\n<td style=\"text-align: right;\">{z22}</td>\n<td style=\"text-align: right;\">,</td>\n<td style=\"text-align: right;\">{z21}$\\Big)_\\var{base}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td style=\"text-align: right;\"></td>\n<td style=\"text-align: right;\">{u3}</td>\n<td style=\"text-align: right;\"></td>\n<td style=\"text-align: right;\">{u2}</td>\n<td style=\"text-align: right;\"></td>\n<td style=\"text-align: right;\">{u1}</td>\n<td style=\"text-align: right;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\Big($</td>\n<td style=\"text-align: right;\">{e4}</td>\n<td style=\"text-align: right;\">,</td>\n<td style=\"text-align: right;\">{e3}</td>\n<td style=\"text-align: right;\">,</td>\n<td style=\"text-align: right;\">{e2}</td>\n<td style=\"text-align: right;\">,</td>\n<td style=\"text-align: right;\">{e1}$\\Big)_\\var{base}$</td>\n</tr>\n</tbody>\n</table>\n<p>b)</p>\n<p>$\\left(\\var{z14},\\var{z13},\\var{z12},\\var{z11}\\right)_\\var{base}=\\var{z14}\\cdot\\var{base}^3+\\var{z13}\\cdot\\var{base}^2+\\var{z12}\\cdot\\var{base}^1+\\var{z11}\\cdot\\var{base}^0=\\var{a}$</p>\n<p>$\\left(\\var{z24},\\var{z23},\\var{z22},\\var{z21}\\right)_\\var{base}=\\var{z24}\\cdot\\var{base}^3+\\var{z23}\\cdot\\var{base}^2+\\var{z22}\\cdot\\var{base}^1+\\var{z21}\\cdot\\var{base}^0=\\var{b}$</p>\n<p>$\\var{a}+\\var{b}=\\var{sum}=\\var{e4}\\cdot\\var{base}^3+\\var{e3}\\cdot\\var{base}^2+\\var{e2}\\cdot\\var{base}^1+\\var{e1}\\cdot\\var{base}^0$</p>", "rulesets": {}, "variables": {"base": {"name": "base", "group": "Ungrouped variables", "definition": "random(11..18)", "description": "", "templateType": "anything"}, "choice": {"name": "choice", "group": "Ungrouped variables", "definition": "deal(base)", "description": "", "templateType": "anything"}, "z11": {"name": "z11", "group": "Ungrouped variables", "definition": "choice[0]", "description": "", "templateType": "anything"}, "z12": {"name": "z12", "group": "Ungrouped variables", "definition": "choice[1]", "description": "", "templateType": "anything"}, "z13": {"name": "z13", "group": "Ungrouped variables", "definition": "choice[2]", "description": "", "templateType": "anything"}, "z14": {"name": "z14", "group": "Ungrouped variables", "definition": "1", "description": "", "templateType": "anything"}, "z21": {"name": "z21", "group": "Ungrouped variables", "definition": "base-z11", "description": "", "templateType": "anything"}, "z22": {"name": "z22", "group": "Ungrouped variables", "definition": "base-1-z12", "description": "", "templateType": "anything"}, "z23": {"name": "z23", "group": "Ungrouped variables", "definition": "z13", "description": "", "templateType": "anything"}, "z24": {"name": "z24", "group": "Ungrouped variables", "definition": "base-3", "description": "", "templateType": "anything"}, "e1": {"name": "e1", "group": "Ungrouped variables", "definition": "mod(z11+z21,base)", "description": "", "templateType": "anything"}, "u1": {"name": "u1", "group": "Ungrouped variables", "definition": "floor((z11+z21)/base)", "description": "", "templateType": "anything"}, "e2": {"name": "e2", "group": "Ungrouped variables", "definition": "mod(z12+z22+u1,base)", "description": "", "templateType": "anything"}, "u2": {"name": "u2", "group": "Ungrouped variables", "definition": "floor((z12+z22+u1)/base)", "description": "", "templateType": "anything"}, "e3": {"name": "e3", "group": "Ungrouped variables", "definition": "mod(z13+z23+u2,base)", "description": "", "templateType": "anything"}, "u3": {"name": "u3", "group": "Ungrouped variables", "definition": "floor((z13+z23+u2)/base)", "description": "", "templateType": "anything"}, "e4": {"name": "e4", "group": "Ungrouped variables", "definition": "z14+z24+u3", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "z14*base^3+z13*base^2+z12*base+z11", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "z24*base^3+z23*base^2+z22*base+z21", "description": "", "templateType": "anything"}, "sum": {"name": "sum", "group": "Ungrouped variables", "definition": "a+b", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["base", "choice", "z11", "z12", "z13", "z14", "z21", "z22", "z23", "z24", "e1", "u1", "e2", "u2", "e3", "u3", "e4", "a", "b", "sum"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": "table {\n  border-collapse: collapse;\n}\ntable {\n  border-collapse: collapse;\n}\ntr:last-child { \n  border-top: solid;\n  border-width: 1px 0;\n}\n"}, "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>Ermitteln Sie die Summe schriftliche ohne vorherige Umwandlung in das Dezimalsystem!</p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\">$\\Big($</td>\n<td style=\"text-align: right;\">{z14}</td>\n<td style=\"text-align: center;\">,</td>\n<td style=\"text-align: right;\">{z13}</td>\n<td style=\"text-align: center;\">,</td>\n<td>{z12}</td>\n<td style=\"text-align: center;\">,</td>\n<td style=\"text-align: right;\">{z11}$\\Big)_\\var{base}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$+\\Big($</td>\n<td style=\"text-align: right;\">{z24}</td>\n<td style=\"text-align: center;\">,</td>\n<td style=\"text-align: right;\">{z23}</td>\n<td style=\"text-align: center;\">,</td>\n<td style=\"text-align: right;\">{z22}</td>\n<td style=\"text-align: center;\">,</td>\n<td style=\"text-align: right;\">{z21}$\\Big)_\\var{base}$</td>\n</tr>\n<tr>\n<td></td>\n<td></td>\n<td style=\"text-align: right;\">[[4]]</td>\n<td></td>\n<td style=\"text-align: right;\">[[5]]</td>\n<td></td>\n<td style=\"text-align: right;\">[[6]]</td>\n<td></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\Big($</td>\n<td style=\"padding-left: 30px;\">[[0]]</td>\n<td style=\"text-align: center;\">,</td>\n<td style=\"text-align: right;\">[[1]]</td>\n<td style=\"text-align: center;\">,</td>\n<td>[[2]]</td>\n<td style=\"text-align: center;\">,</td>\n<td style=\"text-align: right;\">[[3]]$\\Big)_\\var{base}$</td>\n</tr>\n</tbody>\n</table>\n<p><em>Hinweis: Tragen Sie f&uuml;hr fehlende &Uuml;bertr&auml;ge bitte eine $0$ ein!</em></p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "e4", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "e4", "maxValue": "e4", "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": ["plain-eu"], "correctAnswerStyle": "plain-eu"}, {"type": "numberentry", "useCustomName": true, "customName": "e3", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "e3", "maxValue": "e3", "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": ["plain-eu"], "correctAnswerStyle": "plain-eu"}, {"type": "numberentry", "useCustomName": true, "customName": "e2", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "e2", "maxValue": "e2", "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": ["plain-eu"], "correctAnswerStyle": "plain-eu"}, {"type": "numberentry", "useCustomName": true, "customName": "e1", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "e1", "maxValue": "e1", "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": ["plain-eu"], "correctAnswerStyle": "plain-eu"}, {"type": "numberentry", "useCustomName": true, "customName": "u3", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "u3", "maxValue": "u3", "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": ["plain-eu"], "correctAnswerStyle": "plain-eu"}, {"type": "numberentry", "useCustomName": true, "customName": "u2", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "u2", "maxValue": "u2", "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": ["plain-eu"], "correctAnswerStyle": "plain-eu"}, {"type": "numberentry", "useCustomName": true, "customName": "u1", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "u1", "maxValue": "u1", "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": ["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>Wandeln Sie die beiden Zahlen und deren Summe&nbsp;in das Dezimalsystem um!</p>\n<p>$\\left(\\var{z14},\\var{z13},\\var{z12},\\var{z11}\\right)_\\var{base}=$[[0]]</p>\n<p>$\\left(\\var{z24},\\var{z23},\\var{z22},\\var{z21}\\right)_\\var{base}=$[[1]]</p>\n<p>$\\left(\\var{z14},\\var{z13},\\var{z12},\\var{z11}\\right)_\\var{base}+\\left(\\var{z24},\\var{z23},\\var{z22},\\var{z21}\\right)_\\var{base}=$[[2]]&nbsp;</p>\n<p>&nbsp;</p>\n<p></p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "a", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "a", "maxValue": "a", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["eu", "plain-eu"], "correctAnswerStyle": "plain-eu"}, {"type": "numberentry", "useCustomName": true, "customName": "b", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "b", "maxValue": "b", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["eu", "plain-eu"], "correctAnswerStyle": "plain-eu"}, {"type": "numberentry", "useCustomName": true, "customName": "sum", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "sum", "maxValue": "sum", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["eu", "plain-eu"], "correctAnswerStyle": "plain-eu"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Euklidischer Algorithmus", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "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>Aufgabe zum einfachen und erweiterten euklidischen Algorithmus (mit \"sch&ouml;nen\" Zahlen)</p>", "licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International"}, "statement": "<p>&nbsp;In dieser Aufgabe geht es um den einfachen und den erweiterten Euklidischen Algorithmus.</p>", "advice": "<p>a) $\\operatorname{ggT}(\\var{a},\\var{b})=\\var{ergebnis[0]}$</p>\n<div id=\"ausg\">Rechenweg:<br/>{app}</div>\n<div>&nbsp;</div>\n<div>b)&nbsp;Durch R&uuml;ckeinsetzung in die Zeilen oben ermittelt man $r=\\var{ergebnis[1]},s=\\var{ergebnis[2]}$</div>\n<div><br/>Eine ausf&uuml;hrliche Rechenanleitung finden Sie zB <a href=\"https://www.arndt-bruenner.de/mathe/scripts/erweitertereuklid.htm\" target=\"_blank\" rel=\"noopener noreferrer\">hier</a>.</div>", "rulesets": {}, "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "chosen[0]", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "chosen[1]", "description": "", "templateType": "anything"}, "ergebnis": {"name": "ergebnis", "group": "Ungrouped variables", "definition": "euclid_gcd(a,b)", "description": "", "templateType": "anything"}, "defs": {"name": "defs", "group": "Ungrouped variables", "definition": "[['a',a],['b',b]]", "description": "", "templateType": "anything"}, "app": {"name": "app", "group": "Ungrouped variables", "definition": "geogebra_applet('https://www.geogebra.org/m/mzkxnpvm',defs)", "description": "", "templateType": "anything"}, "choice": {"name": "choice", "group": "Ungrouped variables", "definition": "[[3641,1243],[4303,1441],[4303,1469],[5627,1921],[6289,2147],[3707,1243],[4381,1469],[5729,1921],[6403,2147],[3817,1639],[3817,1963],[4511,1937],[5899,2533],[6593,2831],[3839,1243]]", "description": "", "templateType": "anything"}, "chosen": {"name": "chosen", "group": "Ungrouped variables", "definition": "random(choice)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "ergebnis", "defs", "app", "choice", "chosen"], "variable_groups": [], "functions": {"euclid_gcd": {"parameters": [["a", "number"], ["b", "number"]], "type": "anything", "language": "javascript", "definition": "  a = +a;\n  b = +b;\n  if (a !== a || b !== b) {\n    return [NaN, NaN, NaN];\n  }\n  \n  if (a === Infinity || a === -Infinity || b === Infinity || b === -Infinity) {\n    return [Infinity, Infinity, Infinity];\n  }\n  // Checks if a or b are decimals\n  if ((a % 1 !== 0) || (b % 1 !== 0)) {\n    return false;\n  }\n  var signX = (a < 0) ? -1 : 1,\n    signY = (b < 0) ? -1 : 1,\n    x = 0,\n    y = 1,\n    u = 1,\n    v = 0,\n    q, r, m, n;\n  a = Math.abs(a);\n  b = Math.abs(b);\n\n  while (a !== 0) {\n    q = Math.floor(b / a);\n    r = b % a;\n    m = x - u * q;\n    n = y - v * q;\n    b = a;\n    a = r;\n    x = u;\n    y = v;\n    u = m;\n    v = n;\n  }\n  return [b, signX * x, signY * y];"}}, "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>Ermitteln Sie mittels Euklidischem Algorithmus: $\\operatorname{ggT}(\\var{a},\\var{b})=$[[0]]</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "ggT", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "ergebnis[0]", "maxValue": "ergebnis[0]", "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>Ermitteln Sie mittels erweitertem Euklidischem Algorithmus Zahlen $r,s\\in\\mathbb{Z}$, f&uuml;r die gilt:</p>\n<p style=\"text-align: center;\">$r\\cdot \\var{a}+s\\cdot \\var{b}=\\operatorname{ggT}(\\var{a},\\var{b})$</p>\n<p>$r=$[[0]] , $s=$[[1]]</p>\n<p><span style=\"margin: 0px auto; border: 2px dotted #000000; position: absolute; z-index: 2147483647; visibility: hidden; left: 1265px; width: 0px; top: 35px; height: 0px;\"></span><span style=\"z-index: 2147483647; position: absolute; visibility: hidden; left: 1250px; width: 50px; top: 20px; height: 20px; font-size: 10px; color: black;\"></span></p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "r", "marks": "1.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "ergebnis[1]", "maxValue": "ergebnis[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": "s", "marks": "1.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "ergebnis[2]", "maxValue": "ergebnis[2]", "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}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}], "allowPrinting": true, "navigation": {"allowregen": false, "reverse": true, "browse": true, "allowsteps": true, "showfrontpage": false, "showresultspage": "oncompletion", "navigatemode": "menu", "onleave": {"action": "none", "message": ""}, "preventleave": true, "startpassword": ""}, "timing": {"allowPause": true, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "feedback": {"showactualmark": true, "showtotalmark": true, "showanswerstate": true, "allowrevealanswer": true, "advicethreshold": 0, "intro": "", "reviewshowscore": true, "reviewshowfeedback": true, "reviewshowexpectedanswer": true, "reviewshowadvice": true, "feedbackmessages": []}, "contributors": [{"name": "Andreas Vohns", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3622/"}], "extensions": ["geogebra"], "custom_part_types": [], "resources": []}