{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"math","formal_name":"MATH","introduction":"MATH organises 12,500 high-school competition problems into seven subjects and five difficulty levels, each with a full worked solution. It underlies much of the later mathematics evaluation work; this catalogue imports the full test split: 5,000 problems across all seven subjects.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://github.com/hendrycks/math","indexing_mode":"index","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[],"history":"","construction":"","limitations":"","saturation":"","scores":[]}},"task_id":"64d96cca-7247-5a08-a50f-75e26722c228","task_key":"counting~5fand~5fprobability--test--64d96cca-7247-5a08-a50f-75e26722c228","task_revision_id":"1","upstream_id":"","short_description":"There is a total of 70 squares of three sizes whose vertices are points on this…","config":"counting_and_probability","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"There is a total of 70 squares of three sizes whose vertices are points on this rectangular $3\\\\times n$ grid of points. What is the value of $n$?\\n\\n[asy]\\n\\nunitsize(0.4 inch);\\n\\ndot((0,0),linewidth(9bp));\\ndot((1,0),linewidth(9bp));\\ndot((2,0),linewidth(9bp));\\ndot((0,1),linewidth(9bp));\\ndot((0,2),linewidth(9bp));\\ndot((1,1),linewidth(9bp));\\ndot((2,1),linewidth(9bp));\\ndot((1,2),linewidth(9bp));\\ndot((2,2),linewidth(9bp));\\n\\nfilldraw((2.95,-0.05)--(3.05,-0.05)--(3.05,0.05)--(2.95,0.05)--cycle,black);\\nfilldraw((2.45,-0.05)--(2.55,-0.05)--(2.55,0.05)--(2.45,0.05)--cycle,black);\\nfilldraw((3.45,-0.05)--(3.55,-0.05)--(3.55,0.05)--(3.45,0.05)--cycle,black);\\n\\nfilldraw((2.95,0.95)--(3.05,0.95)--(3.05,1.05)--(2.95,1.05)--cycle,black);\\nfilldraw((2.45,0.95)--(2.55,0.95)--(2.55,1.05)--(2.45,1.05)--cycle,black);\\nfilldraw((3.45,0.95)--(3.55,0.95)--(3.55,1.05)--(3.45,1.05)--cycle,black);\\n\\nfilldraw((2.95,1.95)--(3.05,1.95)--(3.05,2.05)--(2.95,2.05)--cycle,black);\\nfilldraw((2.45,1.95)--(2.55,1.95)--(2.55,2.05)--(2.45,2.05)--cycle,black);\\nfilldraw((3.45,1.95)--(3.55,1.95)--(3.55,2.05)--(3.45,2.05)--cycle,black);\\n\\ndot((4,0),linewidth(9bp));\\ndot((5,0),linewidth(9bp));\\ndot((4,1),linewidth(9bp));\\ndot((5,1),linewidth(9bp));\\ndot((4,2),linewidth(9bp));\\ndot((5,2),linewidth(9bp));\\n\\n[/asy]\",\"type\":\"Counting & Probability\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}