MathDB

Define a colouring in tha plane the following way: - we pick a positive integer

m

; - let

K_{1}

K_{2}

, ...,

K_{m}

be different circles with nonzero radii such that

K_{i}\subset K_{j}

K_{j}\subset K_{i}

i \neq j

; - the points in the plane that lie outside an arbitrary circle (one that is amongst the circles we pick) are coloured differently than the points that lie inside the circle. There are

2019

points in the plane such that any

3

of them are not collinear. Determine the maximum number of colours which we can use to colour the given points.

Problem Statement