Little known outside the community, Jane Street is one of the world’s largest market-maker who trades more than $17 trillion worth of securities in 2020. Yet, the company is also well known for its difficult interview questions. Here I list a few questions I find online, and I feel quite interesting.
Question 1
A random line segment of length D is chosen on a plane marked with an infinite checkerboard grid (i.e., a unit side length square grid). What length D maximizes the probability that the segment crosses exactly one line on the checkerboard grid, and what is this maximal probability?