2017 Theme #9
Source:
May 8, 2018
combinatorics
Problem Statement
New this year at HMNT: the exciting game of RNG baseball! In RNG baseball, a team of infinitely many people play on a square field, with a base at each vertex; in particular, one of the bases is called the home base. Every turn, a new player stands at home base and chooses a number n uniformly at random from . Then, the following occurs:
• If , then the player and everyone else currently on the field moves (counterclockwise) around
the square by n bases. However, if in doing so a player returns to or moves past the home base,
he/she leaves the field immediately and the team scores one point.
• If (a strikeout), then the game ends immediately; the team does not score any more points.
What is the expected number of points that a given team will score in this game?