SMT 2023 Discrete #4
Source:
May 3, 2023
Problem Statement
Michelle is drawing segments in the plane. She begins from the origin facing up the -axis and draws a segment of length . Now, she rotates her direction by , with equal probability clockwise or counterclockwise, and draws another segment of length beginning from the end of the previous segment. She then continues this until she hits an already drawn segment. What is the expected number of segments she has drawn when this happens?