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.) —Dan
On Jan 6, 2016, at 10:18 AM, Dan Asimov <asimov@msri.org> wrote:
I just read this puzzle and thought math-fun might enjoy it:
Let N be a positive integer.
Suppose that we are given 2N points in the plane such that no 3 of them are collinear.
Assume N points are chartreuse and the other N are heliotrope.
Prove there exists a one-to-one correspondence between the chartreuse points and the heliotrope points such that if each point is connected to its buddy by a line segment, then the N line segments are disjoint.