Dan Asimov: For those of you who found this too easy, here is a problem I don't know the answer to that is inspired by the last one: Let N be a positive integer. Suppose we are given 3N points in 3-space such that no 4 of them are coplanar. Say the points are divided into 3 mutually exclusive groups of N points each: the reds, the greens, and the blues. True or false: There exists a partition of the 3N points into sets of size 3 that each contains one red, one green, and one blue point, such that there are no intersections among the resulting N triangles. (The triangle of a triple is the convex hull of its 3 points.) --WDS: The answer is true. More generally, given N*D points in D-dimensional space, N of each color (D colors), no D+1 lying on a hyperplane, there is a way to draw N disjoint all-color (D-1)-simplices using them as vertices. Regard each point as a normal distribution unit-mass "blob" with very small variance (limit as variance-->0). Use the "ham sandwich theorem" from topology to see each of the D color-measures can be simultaneously cut exactly in half by a hyperplane. https://en.wikipedia.org/wiki/Ham_sandwich_theorem Do so. If N is odd then hyperplane will necessarily pass thru exactly 1 point of each color and use that simplex and "discard" those D points. Subdivide into the points on each side of the cutplane and recursively solve the two subproblems. QED