MathDB

Let

k

be a fixed positive integer. For each

n = 1, 2,...,

we will call configuration of order

n

any set of

kn

points of the plane, which does not contain

3

collinear, colored with

k

given colors, so that there are

n

points of each color. Determine all positive integers

n

with the following property: in each configuration of order

n

, it is possible to select three points of each color, such that the

k

triangles with vertices of the same color that are determined are disjoint in pairs.

Problem Statement