// Numbas version: exam_results_page_options
{"name": "Euclidean Algorithm", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Euclidean Algorithm", "tags": [], "metadata": {"description": "<p>This question aims at getting the students to demonstrate their ability to apply the Euclidean algorithm to find the GCD between two numbers.</p>\n<p>We provide two randomly generated numbers and ask the students to enter the steps of the Euclidean algorithm, as well as the GCD between the numbers.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<h2>Euclidean Algorithm</h2>\n<p>Apply the Euclidean algorithm to find the greatest common denominator between {pq[0]} and {pq[1]}. Show the steps.</p>", "advice": "<p>In order to apply the Euclidean algorithm to find the gcd, you need to apply integer division repeatedly, until the remainder is 0.</p>\n<p>Once you know the gcd between two numbers $p$ and $q$ you can find their lcm using the following formula: \\[\\mathrm{lcm}(p,q) = \\frac{p\\times q}{\\mathrm{gcd}(p,q)} \\]</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"g": {"name": "g", "group": "Solutions", "definition": "Matrix(euclid)", "description": "<p>The steps from Euclid, stored in a matrix (for the purpose of checking the solution).</p>", "templateType": "anything", "can_override": false}, "m1": {"name": "m1", "group": "Random parameters", "definition": "repeat(random(2..9),random(2..4))", "description": "", "templateType": "anything", "can_override": false}, "pq": {"name": "pq", "group": "Random parameters", "definition": "common_multiples(r0,m1)", "description": "", "templateType": "anything", "can_override": false}, "r0": {"name": "r0", "group": "Random parameters", "definition": "random(2 .. 30#1)", "description": "<p>Number of elements in the array.</p>", "templateType": "randrange", "can_override": false}, "l": {"name": "l", "group": "Solutions", "definition": "pq[0]*pq[1]/r0", "description": "<p>Lowest common multiple of the numbers in pq.</p>", "templateType": "anything", "can_override": false}, "euclid": {"name": "euclid", "group": "Solutions", "definition": "euclidean(pq[0],pq[1])", "description": "<p>This variable contains the steps of Euclid's algorithm. Each row contains four numbers that correspond to the integer division performed at that step.</p>", "templateType": "anything", "can_override": false}, "ee": {"name": "ee", "group": "Ungrouped variables", "definition": "euclid[1]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "pq[0]<5000 && pq[0]>200 && pq[1]<5000 && pq[1]>100 && numrows(g)>2", "maxRuns": "100"}, "ungrouped_variables": ["ee"], "variable_groups": [{"name": "Random parameters", "variables": ["r0", "m1", "pq"]}, {"name": "Solutions", "variables": ["euclid", "g", "l"]}], "functions": {"common_multiples": {"parameters": [["r0", "number"], ["factors", "list"]], "type": "list", "language": "javascript", "definition": "// Generate a pair of numbers with n as a common divisor.\n//var n = factors.length;\nvar r1 = r0;\nvar r2 = 0;\nvar l = [r1];\n//for(var i=0;i<n;i++){\nfor(let m of factors) {\n  r3 = m*r1+r2;\n  r2 = r1;\n  r1 = r3;\n  l.push(r1);\n}\nreturn [r1,r2];"}, "euclidean": {"parameters": [["p", "number"], ["q", "number"]], "type": "list", "language": "javascript", "definition": "var r0 = Math.max(p,q);\nvar r1 = Math.min(q,p);\nvar l = [];\nvar m;\nwhile(r1>0) {\n  m = Math.floor(r0/r1);\n  r2 = r0%r1;\n  l.push([r0,m,r1,r2]);\n  r0 = r1;\n  r1 = r2;\n}\nreturn l;"}}, "preamble": {"js": "", "css": ".matrix-input .matrix .cell:nth-child(2)::after {\n  content: ' = ';\n}\n.matrix-input .matrix .cell:nth-child(4)::before {\n  content: '\u00d7 ';\n}\n.matrix-input .matrix .cell:last-child::before {\n  content: ' + ';\n}\n\n.matrix-input .matrix .cell:nth-child(12) {\n  margin-right: 0;\n  padding-right: 0;\n}\n\n.matrix-input .matrix .cell:nth-child(4) {\n  margin-left: 0;\n  padding-left: 0;\n}\n\n.matrix-input .left-bracket, .matrix-input .right-bracket {\n    display: none !important;\n}\n\nlabel.num-columns { display: none;}\n/*label.num-rows:before {content: 'Number of Steps:';visibility: visible}\nlabel.num-rows {visibility: hidden;}\nlabel.num-rows input {visibility:visible;}*/\n\n.penaltyMessage {font-weight: bold; color: red}"}, "parts": [{"type": "matrix", "useCustomName": true, "customName": "Part a) Algorithm", "marks": 1, "scripts": {"mark": {"script": "var variables = this.question.scope.variables;\nvar unwrap = Numbas.jme.unwrapValue;\n\nvar g = unwrap(variables.g);\nvar A = this.studentAnswer;\n\nvar nrows = A.length;\nvar ncols = A[0].length;\n\nconsole.log(\"Hello\")\n\nif(ncols != 4) {this.setCredit(0,\"You need to have 4 entries on each line.\");return;}\nif(nrows != g.length) {this.setCredit(0,\"Wrong number of steps.\");return;}\n\nfor(i=0;i<nrows;i++) {\n  v = (A[i][0] == g[i][0]) && (A[i][3] == g[i][3]) &&\n  ((A[i][1] == g[i][1]) && (A[i][2] == g[i][2])) || \n  ((A[i][1] == g[i][2]) && (A[i][2] == g[i][1]));\n  if (!v) {this.setCredit(0,\"You made a mistake on line No\" + (i+1) +\".\"); return;}\n}\nthis.setCredit(1);", "order": "instead"}}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Please enter all the steps of the Euclidean algorithm below (please enter the number of steps you need in the \"Rows:\" box.)</p>", "correctAnswer": "g", "correctAnswerFractions": false, "numRows": 1, "numColumns": "4", "allowResize": true, "tolerance": 0, "markPerCell": false, "allowFractions": false, "minColumns": "4", "maxColumns": "4", "minRows": 1, "maxRows": 0}, {"type": "numberentry", "useCustomName": true, "customName": "Part b) gcd", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>gcd({pq[0]},{pq[1]})=</p>", "minValue": "r0", "maxValue": "r0", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Part c) LCM", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<h3>Lowest Common Multiple</h3>\n<p>Use the information above to calculate the lowest common multiple between {pq[0]} and {pq[1]}.</p>\n<p>lcm({pq[0]},{pq[1]})=</p>", "minValue": "l", "maxValue": "l", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Julien Ugon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3575/"}]}]}], "contributors": [{"name": "Julien Ugon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3575/"}]}