{"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":"a02ec1e5-abef-51f9-98a2-84cd334b8810","task_key":"counting~5fand~5fprobability--test--a02ec1e5-abef-51f9-98a2-84cd334b8810","task_revision_id":"1","upstream_id":"","short_description":"On the game board below Kendra will start at the center of the board. For each…","config":"counting_and_probability","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"On the game board below Kendra will start at the center of the board. For each turn she will spin this spinner with four congruent sectors once, and then she will move one space in the direction indicated on the spinner. The \\\"Start'' square does not have a numerical value, but Kendra may land on it during her turns. What is the probability that the sum of the numbers in the spaces on which she will land will be exactly 30 after her third complete turn? Express your answer as a common fraction.\\n\\n[asy]size(80);\\nimport graph;\\ndraw(Circle((0,0),1),linewidth(1));\\ndraw((-1,0)--(1,0),linewidth(1)); draw((0,-1)--(0,1),linewidth(1));\\nlabel(\\\"Move\\\",(sqrt(2)/4,sqrt(2)/4+.15),fontsize(10pt));\\nlabel(\\\"Left\\\",(sqrt(2)/4,sqrt(2)/4-.15),fontsize(10pt));\\nlabel(\\\"Move\\\",(-sqrt(2)/4,sqrt(2)/4+.15),fontsize(10pt));\\nlabel(\\\"Right\\\",(-sqrt(2)/4,sqrt(2)/4-.15),fontsize(10pt));\\nlabel(\\\"Move\\\",(-sqrt(2)/4,-(sqrt(2)/4-.15)),fontsize(10pt));\\nlabel(\\\"Down\\\",(-sqrt(2)/4,-(sqrt(2)/4+.15)),fontsize(10pt));\\nlabel(\\\"Move\\\",(sqrt(2)/4,-(sqrt(2)/4-.15)),fontsize(10pt));\\nlabel(\\\"Up\\\",(sqrt(2)/4,-(sqrt(2)/4+.15)),fontsize(10pt));\\ndot((0,0),linewidth(5)); draw((0,0)--1/2 dir(-70),linewidth(1.5),EndArrow(5));[/asy]\\n\\n[asy]size(200);\\npicture box10,box15,box5,box20;\\nfilldraw(box5,(-1,-.5)--(-1,.5)--(1,.5)--(1,-.5)--cycle,white,linewidth(1)); label(box5,\\\"5\\\",(0,0));\\nfilldraw(box10,(-1,-.5)--(-1,.5)--(1,.5)--(1,-.5)--cycle,gray(.6),linewidth(1)); label(box10,\\\"10\\\",(0,0));\\nfilldraw(box15,(-1,-.5)--(-1,.5)--(1,.5)--(1,-.5)--cycle,white,linewidth(1)); label(box15,\\\"15\\\",(0,0));\\nfilldraw(box20,(-1,-.5)--(-1,.5)--(1,.5)--(1,-.5)--cycle,gray(.6),linewidth(1)); label(box20,\\\"20\\\",(0,0));\\nvoid b10(real x, real y)\\n{\\nadd(shift(x*right)*shift(y*up)*box10);\\n}\\nvoid b15(real x, real y)\\n{\\nadd(shift(x*right)*shift(y*up)*box15);\\n}\\nvoid b5(real x, real y)\\n{\\nadd(shift(x*right)*shift(y*up)*box5);\\n}\\nvoid b20(real x, real y)\\n{\\nadd(shift(x*right)*shift(y*up)*box20);\\n}\\nfor(int i = 0; i<3; ++i)\\n{\\ndraw((8.5-2.5i,1.5i+2)--(-8.5+2.5i,1.5i+2),linewidth(1));\\ndraw((8.5-2.5i,-1.5i-2)--(-8.5+2.5i,-1.5i-2),linewidth(1));\\n}\\nfor(int i = 0; i<3; ++i)\\n{\\ndraw((8.5-2.5i,2+1.5i)--(8.5-2.5i,-2-1.5i),linewidth(1));\\ndraw((-8.5+2.5i,2+1.5i)--(-8.5+2.5i,-2-1.5i),linewidth(1));\\n}\\ndraw((8.5,0)--(-8.5,0),linewidth(1));\\ndraw((0,5)--(0,-5),linewidth(1));\\nfilldraw((-1,1)--(1,1)--(1,-1)--(-1,-1)--cycle,white,linewidth(1)); label(\\\"Start\\\",(0,0),fontsize(8pt));\\nb10(0,2); b10(-3.5,2); b10(3.5,2); b10(-3.5,0); b10(3.5,0); b10(0,-2); b10(-3.5,-2); b10(3.5,-2); b10(3.5,5); b10(-3.5,5); b10(3.5,-5); b10(-3.5,-5);\\nb5(6,0); b5(8.5,0); b5(0,3.5); b5(0,5); b5(0,-3.5); b5(0,-5); b5(3.5,-3.5); b5(3.5,3.5);b5(-3.5,-3.5);b5(-3.5,3.5); b5(-6,0); b5(-8.5,0);\\n\\nb20(6,3.5); b20(6,-3.5); b20(-6,3.5); b20(-6,-3.5); b20(8.5,2); b20(-8.5,2); b20(8.5,-2); b20(-8.5,-2);\\n\\nb15(6,2); b15(6,-2); b15(-6,2); b15(-6,-2);[/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":[]}