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 ℝ² such that x²+y²≤1. Let (x₁,y₁), ..., (x_n,y_n) be n points in D. Prove that there is some point (x₀,y₀) in D such that the sum of the Euclidean distances from (x₀,y₀) to each of the n points (x_i,y_i) is greater than or equal to n.