Question 48
Wendy is playing darts with a circular dartboard of radius $20$. Whenever she throws a dart, it lands uniformly at random on the dartboard. At the start of her game, there are $2020$ darts placed randomly on the board. Every turn, she takes the dart farthest from the center, and throws it at the board again. What is the expected number of darts she has to throw before all the darts are within $10$ units of the center?
Proposed by: Vincent Bian
Proposed by: Vincent Bian