// Numbas version: exam_results_page_options
{"name": "SIT316 MH-Constraint Programming", "metadata": {"description": "<p>LP: Constraint Programming</p>", "licence": "None specified"}, "duration": 5400, "percentPass": "0", "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", ""], "variable_overrides": [[], [], [], []], "questions": [{"name": "SIT316-Constraint Programming - Q1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Musa Mammadov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4417/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a1": {"name": "a1", "group": "Ungrouped variables", "definition": "random(-10..20)", "description": "", "templateType": "anything", "can_override": false}, "a2": {"name": "a2", "group": "Ungrouped variables", "definition": "random(-10..20 except a1)", "description": "", "templateType": "anything", "can_override": false}, "a12": {"name": "a12", "group": "Ungrouped variables", "definition": "repeat(random(-15..45),5)", "description": "", "templateType": "anything", "can_override": false}, "sol0": {"name": "sol0", "group": "Ungrouped variables", "definition": "if(a12[0]>=a1 and a12[0]>a2, 1, 0)", "description": "", "templateType": "anything", "can_override": false}, "sol1": {"name": "sol1", "group": "Ungrouped variables", "definition": "if(a12[1]>=a1 and a12[1]>a2, 1, 0)", "description": "", "templateType": "anything", "can_override": false}, "sol2": {"name": "sol2", "group": "Ungrouped variables", "definition": "if(a12[2]>=a1 and a12[2]>a2, 1, 0)", "description": "", "templateType": "anything", "can_override": false}, "sol3": {"name": "sol3", "group": "Ungrouped variables", "definition": "if(a12[3]>=a1 and a12[3]>a2, 1, 0)", "description": "", "templateType": "anything", "can_override": false}, "sol4": {"name": "sol4", "group": "Ungrouped variables", "definition": "if(a12[4]>=a1 and a12[4]>a2, 1, 0)", "description": "", "templateType": "anything", "can_override": false}, "code1": {"name": "code1", "group": "Ungrouped variables", "definition": "abs(a12[4])", "description": "", "templateType": "anything", "can_override": false}, "code2": {"name": "code2", "group": "Ungrouped variables", "definition": "abs(a12[3])", "description": "", "templateType": "anything", "can_override": false}, "code3": {"name": "code3", "group": "Ungrouped variables", "definition": "abs(a12[2])", "description": "", "templateType": "anything", "can_override": false}, "code4": {"name": "code4", "group": "Ungrouped variables", "definition": "abs(a12[1])", "description": "", "templateType": "anything", "can_override": false}, "code5": {"name": "code5", "group": "Ungrouped variables", "definition": "abs(a12[0])", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a1", "a2", "a12", "sol0", "sol1", "sol2", "sol3", "sol4", "code1", "code2", "code3", "code4", "code5"], "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><strong>P-{code1}{code2}{code3}{code4}{code5}</strong>&nbsp;</p>\n<p>Which of the following values of $X$ statisfy the constraint ($X\u2004&ge;\u2004\\var{a1}$)\u2005$\\land$\u2005($X\u2004&gt;\u2004\\var{a2}$)?</p>\n<p>(<em>Put</em> $ 1$ <em>for</em> \"Yes\" <em>and&nbsp;</em> $ 0$ <em>for</em> \"No\")</p>\n<p>a) $X\u2004=\u2004\\var{a12[0]}$&nbsp; [[0]]</p>\n<p>b) $X\u2004=\u2004\\var{a12[1]}$&nbsp; [[1]]</p>\n<p>c) $X\u2004=\u2004\\var{a12[2]}$&nbsp; [[2]]</p>\n<p>d) $X\u2004=\u2004\\var{a12[3]}$&nbsp; [[3]]</p>\n<p>e) $X\u2004=\u2004\\var{a12[4]}$&nbsp; [[4]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "0.2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{sol0}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": "0.2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{sol1}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": "0.2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{sol2}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": "0.2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{sol3}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": "0.2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{sol4}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "SIT316-Constraint Programming - Q2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Musa Mammadov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4417/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a1": {"name": "a1", "group": "Ungrouped variables", "definition": "random(-10..40)", "description": "", "templateType": "anything", "can_override": false}, "a2": {"name": "a2", "group": "Ungrouped variables", "definition": "random(-10..10 except a1)", "description": "", "templateType": "anything", "can_override": false}, "a12": {"name": "a12", "group": "Ungrouped variables", "definition": "repeat(random(-15..15),5)", "description": "", "templateType": "anything", "can_override": false}, "sol0": {"name": "sol0", "group": "Ungrouped variables", "definition": "if(a12[0]>=a1 and a12[0]>a2, 1, 0)", "description": "", "templateType": "anything", "can_override": false}, "sol1": {"name": "sol1", "group": "Ungrouped variables", "definition": "if(a12[1]>=a1 and a12[1]>a2, 1, 0)", "description": "", "templateType": "anything", "can_override": false}, "sol2": {"name": "sol2", "group": "Ungrouped variables", "definition": "if(a12[2]>=a1 and a12[2]>a2, 1, 0)", "description": "", "templateType": "anything", "can_override": false}, "sol3": {"name": "sol3", "group": "Ungrouped variables", "definition": "if(a12[3]>=a1 and a12[3]>a2, 1, 0)", "description": "", "templateType": "anything", "can_override": false}, "sol4": {"name": "sol4", "group": "Ungrouped variables", "definition": "if(a12[4]>=a1 and a12[4]>a2, 1, 0)", "description": "", "templateType": "anything", "can_override": false}, "kx1": {"name": "kx1", "group": "Ungrouped variables", "definition": "random(-5..5 except 0)", "description": "", "templateType": "anything", "can_override": false}, "ky1": {"name": "ky1", "group": "Ungrouped variables", "definition": "random(-3..7 except 0)", "description": "", "templateType": "anything", "can_override": false}, "kx2": {"name": "kx2", "group": "Ungrouped variables", "definition": "random(-5..5 except 0)", "description": "", "templateType": "anything", "can_override": false}, "ky2": {"name": "ky2", "group": "Ungrouped variables", "definition": "random(-3..7 except kx2)", "description": "", "templateType": "anything", "can_override": false}, "b12": {"name": "b12", "group": "Ungrouped variables", "definition": "repeat(random(-15..15),5)", "description": "", "templateType": "anything", "can_override": false}, "s110": {"name": "s110", "group": "Ungrouped variables", "definition": "if({kx1*a12[1] + ky1*b12[1] <\u2004a1,1,0)", "description": "", "templateType": "anything", "can_override": false}, "s000": {"name": "s000", "group": "Ungrouped variables", "definition": "if({kx1*a12[0] + ky1*b12[0] <\u2004a1,1,0)", "description": "", "templateType": "anything", "can_override": false}, "s220": {"name": "s220", "group": "Ungrouped variables", "definition": "if({kx1*a12[2] + ky1*b12[2] <\u2004a1,1,0)", "description": "", "templateType": "anything", "can_override": false}, "s330": {"name": "s330", "group": "Ungrouped variables", "definition": "if({kx1*a12[3] + ky1*b12[3] <\u2004a1,1,0)", "description": "", "templateType": "anything", "can_override": false}, "s440": {"name": "s440", "group": "Ungrouped variables", "definition": "if({kx1*a12[4] + ky1*b12[4] <\u2004a1,1,0)", "description": "", "templateType": "anything", "can_override": false}, "s001": {"name": "s001", "group": "Ungrouped variables", "definition": "if({kx2*a12[0] + ky2*b12[0] >\u2004a2,1,0)", "description": "", "templateType": "anything", "can_override": false}, "s111": {"name": "s111", "group": "Ungrouped variables", "definition": "if({kx2*a12[1] + ky2*b12[1] >\u2004a2,1,0)", "description": "", "templateType": "anything", "can_override": false}, "s221": {"name": "s221", "group": "Ungrouped variables", "definition": "if({kx2*a12[2] + ky2*b12[2] >\u2004a2,1,0)", "description": "", "templateType": "anything", "can_override": false}, "s331": {"name": "s331", "group": "Ungrouped variables", "definition": "if({kx2*a12[3] + ky2*b12[3] >\u2004a2,1,0)", "description": "", "templateType": "anything", "can_override": false}, "s441": {"name": "s441", "group": "Ungrouped variables", "definition": "if({kx2*a12[4] + ky2*b12[4] >\u2004a2,1,0)", "description": "", "templateType": "anything", "can_override": false}, "s0": {"name": "s0", "group": "Ungrouped variables", "definition": "if(s000+s001=2,1,0)", "description": "", "templateType": "anything", "can_override": false}, "s1": {"name": "s1", "group": "Ungrouped variables", "definition": "if(s110+s111=2,1,0)", "description": "", "templateType": "anything", "can_override": false}, "s2": {"name": "s2", "group": "Ungrouped variables", "definition": "if(s220+s221=2,1,0)", "description": "", "templateType": "anything", "can_override": false}, "s3": {"name": "s3", "group": "Ungrouped variables", "definition": "if(s330+s331=2,1,0)", "description": "", "templateType": "anything", "can_override": false}, "s4": {"name": "s4", "group": "Ungrouped variables", "definition": "if(s440+s441=2,1,0)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a1", "a2", "a12", "sol0", "sol1", "sol2", "sol3", "sol4", "kx1", "ky1", "kx2", "ky2", "b12", "s110", "s000", "s220", "s330", "s440", "s001", "s111", "s221", "s331", "s441", "s0", "s1", "s2", "s3", "s4"], "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>Which of the following values of $X,Y$ statisfy the constraint</p>\n<p>($\\simplify{{kx1}X + {ky1}Y &lt;\u2004{a1}}$) $\\land$ \u2005($\\simplify{{kx2}X + {ky2}Y\u2004&gt;\u2004{a2}}$) ?</p>\n<p></p>\n<p>(<em>Put</em> $ 1$ <em>for</em> \"Yes\" <em>and&nbsp;</em> $ 0$ <em>for</em> \"No\")</p>\n<p>a) $X\u2004=\u2004\\var{a12[0]}, Y\u2004=\u2004\\var{b12[0]} $ &nbsp; [[0]]</p>\n<p>b) $X\u2004=\u2004\\var{a12[1]}, Y\u2004=\u2004\\var{b12[1]} $&nbsp; [[1]]</p>\n<p>c) $X\u2004=\u2004\\var{a12[2]}, Y\u2004=\u2004\\var{b12[2]} $ &nbsp; [[2]]</p>\n<p>d) $X\u2004=\u2004\\var{a12[3]}, Y\u2004=\u2004\\var{b12[3]} $ &nbsp; [[3]]</p>\n<p>e) $X\u2004=\u2004\\var{a12[4]}, Y\u2004=\u2004\\var{b12[4]} $ &nbsp; [[4]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "0.2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{s0}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": "0.2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{s1}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": "0.2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{s2}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": "0.2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{s3}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": "0.2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{s4}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "SIT316-Constraint Programming - Q3", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Lauren Richards", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1589/"}, {"name": "Musa Mammadov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4417/"}], "tags": [], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a1": {"name": "a1", "group": "part a", "definition": "random(1..4)", "description": "", "templateType": "anything", "can_override": false}, "b1": {"name": "b1", "group": "part a", "definition": "random(3..6)", "description": "", "templateType": "anything", "can_override": false}, "a2": {"name": "a2", "group": "part a", "definition": "random(8..11)", "description": "", "templateType": "anything", "can_override": false}, "b2": {"name": "b2", "group": "part a", "definition": "random(12..16)", "description": "", "templateType": "anything", "can_override": false}, "a3": {"name": "a3", "group": "part a", "definition": "random(15..18)", "description": "", "templateType": "anything", "can_override": false}, "b3": {"name": "b3", "group": "part a", "definition": "random(5..8)", "description": "", "templateType": "anything", "can_override": false}, "c11": {"name": "c11", "group": "part a", "definition": "b2-b1", "description": "", "templateType": "anything", "can_override": false}, "c12": {"name": "c12", "group": "part a", "definition": "a1-a2", "description": "", "templateType": "anything", "can_override": false}, "c1": {"name": "c1", "group": "part a", "definition": "a1*b2-a2*b1", "description": "", "templateType": "anything", "can_override": false}, "c2": {"name": "c2", "group": "part a", "definition": "a2*b3-a3*b2", "description": "", "templateType": "anything", "can_override": false}, "c3": {"name": "c3", "group": "part a", "definition": "a1*b3-a3*b1", "description": "", "templateType": "anything", "can_override": false}, "c21": {"name": "c21", "group": "part a", "definition": "b3-b2", "description": "", "templateType": "anything", "can_override": false}, "c22": {"name": "c22", "group": "part a", "definition": "a2-a3", "description": "", "templateType": "anything", "can_override": false}, "c31": {"name": "c31", "group": "part a", "definition": "b3-b1", "description": "", "templateType": "anything", "can_override": false}, "c32": {"name": "c32", "group": "part a", "definition": "a1-a3", "description": "", "templateType": "anything", "can_override": false}, "xf1": {"name": "xf1", "group": "part a", "definition": "c31-c32*c11/c12 ", "description": "", "templateType": "anything", "can_override": false}, "f1": {"name": "f1", "group": "part a", "definition": "c3-c32*c1/c12", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "part a", "variables": ["a1", "b1", "a2", "b2", "a3", "b3", "c11", "c12", "c1", "c2", "c3", "c21", "c22", "c31", "c32", "xf1", "f1"]}], "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>P-{a1+1}{a2-1}{a3+2}{b1+2}{b2-2}{b3+1}: Is the following constraint satisfiable?</p>\n<p>$(\\simplify{{c11} X + {c12} Y = {c1}})$ $\\land$ $(\\simplify{{c21} X + {c22} Y = {c2}})$ $\\land$ $(\\simplify{{c31} X + {c32} Y} \\leq \\var{c3})$</p>\n<p><strong>Step 1: </strong>Isolate $Y$ in the first primitive:</p>\n<p>$Y$ = [[0]]</p>\n<p><strong>Step 2: </strong>Propagate:</p>\n<p>$(Y=$[[0]]$) \\land ($[[1]]$=&nbsp; \\var{c2}) \\land ($[[2]]$\\leq \\var{c3})$</p>\n<p></p>\n<p><strong>Step 3-</strong><strong>Conclusion:</strong> We find that given constraint is satisfied for any number</p>\n<p>$X$[[5]][[3]]</p>\n<p>and $Y$ = [[4]]</p>\n<p></p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{-c11/c12}*X+{c1/c12}", "showPreview": false, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}]}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "({c21 - c22*c11/c12})X+{c1*c22/c12}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}]}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "({c31 - c32*c11/c12})X+{c1*c32/c12}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, 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"showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{-c11/c12}*X+{c1/c12}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}]}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["&lt;=", "&gt;="], "matrix": ["if(xf1>0,1,0)", "if(xf1<0,1,0)"], "distractors": ["", ""]}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "SIT316-Constraint Programming - Q4", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Lauren Richards", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1589/"}, {"name": "Musa Mammadov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4417/"}], "tags": [], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a1": {"name": "a1", "group": "part a", "definition": "random(-3..3 except 0)", "description": "", "templateType": "anything", "can_override": false}, "k1": {"name": "k1", "group": "part a", "definition": "random(-1..4 except 0)", "description": "", "templateType": "anything", "can_override": false}, "b1": {"name": "b1", "group": "part a", "definition": "random(-3..3 except 0)", "description": "", "templateType": "anything", "can_override": false}, "k2": {"name": "k2", "group": "part a", "definition": "random(-1..4 except 0)", "description": "", "templateType": "anything", "can_override": false}, "c1": {"name": "c1", "group": "part a", "definition": "random(-3..3 except 0)", "description": "", "templateType": "anything", "can_override": false}, "c2": {"name": "c2", "group": "part a", "definition": "random(-3..3 except(c1/b1))", "description": "", "templateType": "anything", "can_override": false}, "k3": {"name": "k3", "group": "part a", "definition": "random(-1..4 except 0)", "description": "", "templateType": "anything", "can_override": false}, "kk": {"name": "kk", "group": "part a", "definition": "k2-b1*k1", "description": "", "templateType": "anything", "can_override": false}, "kk1": {"name": "kk1", "group": "part a", "definition": "k3-c1*k1-c2*kk", "description": "", "templateType": "anything", "can_override": false}, "x1": {"name": "x1", "group": "part a", "definition": "a1*(c2*b1-c1)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "part a", "variables": ["a1", "k1", "b1", "k2", "c1", "c2", "k3", "kk", "kk1", "x1"]}], "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>Is the following constraint satisfiable?</p>\n<p>$(\\simplify{{a1} X +&nbsp; Y = {k1}})$ $\\land$ $(\\simplify{{b1} Y + Z = {k2}})$ $\\land$ $(\\simplify{{c1} Y + {c2} Z} &gt; \\var{k3})$</p>\n<p><strong>Step 1: </strong>Isolate $Y$ in the first primitive:</p>\n<p>$Y=$ [[0]]</p>\n<p><strong>Step 2: </strong>Propagate:</p>\n<p>$(Y=$[[0]]$) \\land ($[[1]]$=&nbsp; \\var{k2}) \\land ($[[2]]$&gt; \\var{k3})$</p>\n<p><strong>Step 3: </strong>Isolate $Z$ in the second primitive:</p>\n<p>$Z=$[[3]]</p>\n<p><strong>Step 4: </strong>Propagate:</p>\n<p>$(Y=$[[0]]$) \\land (Z=$[[3]]$) \\land ($[[4]]$&gt; \\var{k3})$</p>\n<p><strong></strong></p>\n<p><strong>Step 5-</strong><strong>Conclusion:</strong> We find that given constraint is satisfied for any number&nbsp;</p>\n<p>$X$[[5]] [[6]]</p>\n<p>and $Y=$[[7]], $Z = $[[8]]</p>\n<p></p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{-a1}*X+{k1}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}]}, {"type": "jme", "useCustomName": false, "customName": "", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{-b1*a1}*X + Z +{b1*k1}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}, {"name": "z", "value": ""}]}, {"type": "jme", "useCustomName": false, "customName": "", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{-c1*a1}*X + {c2}*Z +{c1*k1}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}, {"name": "z", "value": ""}]}, {"type": "jme", "useCustomName": false, "customName": "", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{a1*b1}*X +{kk}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}]}, {"type": "jme", "useCustomName": false, "customName": "", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{x1}*X + {c1*k1}+{c2*kk}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}]}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["&lt;", "&gt;"], "matrix": ["if(x1<0,1,0)", "if(x1>0,1,0)"], "distractors": ["", ""]}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, 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