Expected area on a clock
Source: ICMC 2023 Round 2 P5
March 1, 2023
geometrycombinatoricsICMCcollege contestsexpected valuearea of a triangle
Problem Statement
A clock has an hour, minute, and second hand, all of length . Let be the triangle formed by the ends of these hands. A time of day is chosen uniformly at random. What is the expected value of the area of ?Proposed by Dylan Toh