// Numbas version: exam_results_page_options
{"name": "Simon's copy of Pigeonhole principle - greatest number of people with birthdays in the same month,", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"ungrouped_variables": ["a", "ans"], "preamble": {"js": "", "css": ""}, "variablesTest": {"condition": "", "maxRuns": 100}, "statement": "<p>Suppose there are $\\var{a}$ &nbsp;people at a party. &nbsp;What is the largest $N$ such that there are at least $N$ people who share a birthday in the same month?</p>", "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "variable_groups": [], "parts": [{"variableReplacements": [], "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "customMarkingAlgorithm": "", "sortAnswers": false, "scripts": {}, "unitTests": [], "useCustomName": false, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "customName": "", "showFeedbackIcon": true, "marks": 0, "gaps": [{"maxValue": "ans", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "correctAnswerFraction": false, "correctAnswerStyle": "plain", "customMarkingAlgorithm": "", "showFractionHint": true, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "minValue": "ans", "unitTests": [], "useCustomName": false, "variableReplacementStrategy": "originalfirst", "type": "numberentry", "customName": "", "mustBeReduced": false, "showFeedbackIcon": true, "allowFractions": false, "marks": 2, "mustBeReducedPC": 0}], "prompt": "<p>Largest $N=\\;$?[[0]]</p>"}], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "2*random(20..250)+1"}, "ans": {"name": "ans", "group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "ceil(a/12)"}}, "name": "Simon's copy of Pigeonhole principle - greatest number of people with birthdays in the same month,", "functions": {}, "extensions": [], "tags": [], "rulesets": {}, "advice": "<p>If we were able to share the $\\var{a}$ birthdays equally amongst the 12 months, this would mean that there would be&nbsp;$\\frac{\\var{a}}{12}=\\var{precround(a/12,3)}$ birthdays per month.</p>\n<p>Of course, this is impossible since we cannot have a decimal number of birthdays in a month. However, rounding up does mean that at least one month must have&nbsp;$\\var{ans}$ birthdays.</p>\n<p></p>\n<p>(This method is an application of the Pigeonhole Principle).</p>", "type": "question", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}