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. geometrypointscombinatorial geometry