Let N=102024. S is a square in the Cartesian plane with side length N and the sides parallel to the coordinate axes. Inside there are N points P1, P2, …, PN all of which have different x coordinates, and the absolute value of the slope of any connected line between these points is at most 1. Prove that there exists a line l such that at least 2024 of these points is at most distance 1 away from l. combinatorics2024 CTSTexpected value