MathDB

Let

n

be a positive integer and

N=n^{2021}

. There are

2021

concentric circles centered at

O

, and

N

equally-spaced rays are emitted from point

O

. Among the

2021N

intersections of the circles and the rays, some are painted red while the others remain unpainted.
It is known that, no matter how one intersection point from each circle is chosen, there is an angle

\theta

such that after a rotation of

\theta

with respect to

O

, all chosen points are moved to red points. Prove that the minimum number of red points is

2021n^{2020}

.
[I]Proposed by usjl.

Problem Statement