MathDB

Let

N=10^{2024}

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

P_1

P_2

\dots

P_N

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

Problem Statement