// Numbas version: finer_feedback_settings
{"name": "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": [{"variablesTest": {"condition": "", "maxRuns": 100}, "variables": {"ans": {"templateType": "anything", "group": "Ungrouped variables", "definition": "ceil(a/12)", "description": "", "name": "ans"}, "a": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(50..500)", "description": "", "name": "a"}}, "ungrouped_variables": ["a", "ans"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "name": "Pigeonhole principle - greatest number of people with birthdays in the same month, ", "functions": {}, "variable_groups": [], "showQuestionGroupNames": false, "parts": [{"scripts": {}, "gaps": [{"correctAnswerFraction": false, "showPrecisionHint": false, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "ans", "minValue": "ans", "showCorrectAnswer": true, "marks": 2}], "type": "gapfill", "prompt": "<p>Largest $N=\\;$?[[0]]</p>", "showCorrectAnswer": true, "marks": 0}], "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>", "tags": ["checked2015", "combinatorics", "counting", "MAS1701", "MAS2216", "pigeon-hole principle"], "rulesets": {}, "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "<p><strong>7/02/2013:</strong></p>\n    <p>First draft finished. Need to find out what description and tags are needed.</p>", "licence": "Creative Commons Attribution 4.0 International", "description": ""}, "advice": "<p>The generalized pigeon hole principle shows that there are at least $\\displaystyle \\frac{\\var{a}}{12}$ &nbsp;people who share a birthday in the same month. This gives an answer of $\\var{ans}$ .</p>", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}