# Problem of the Month

- Everyone is welcome to participate, but only undergraduate OU students are eligible for the prizes.
- At the end of the academic year, a prize will be awarded to the undergraduate OU students with the most correct solutions.
- A complete solution to the problem must include a proof.
- Solutions to the Problem of the Month can be submitted in the Math Department's office (PHSC 423), or via email to nickmbmiller [at] ou [dot] edu
- Make sure that your submission includes your name and OU email.
- The deadline for submission is the last day of the month.
- The problem of the month during the summer months of May, June, July, and August will not be graded and are just for fun.

Winners of the academic year 2022/23 are Matthew Hudson and Jacob Norris.

### June 2023

## Points in the disc

Suppose that D is the closed unit disc in the plane, that is, the set of points (x,y) in ℝ^{2} such that x^{2}+y^{2}≤1. Let (x_{1},y_{1}), ..., (x_{n},y_{n}) be n points in D. Prove that there is some point (x_{0},y_{0}) in D such that the sum of the Euclidean distances from (x_{0},y_{0}) to each of the n points (x_{i},y_{i}) is greater than or equal to n.