Thinking Cap

Problem of the Month

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), ..., (xn,yn) 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 (xi,yi) is greater than or equal to n.