"On each planet in a planetary system of an odd number of planets, there is an astronomer observing the nearest planet. Assume the distances between each pair of planets are all different. Prove that there is at least one planet that is not being observed by any astronomer." This seems like it should be really easy, but I'm just not quite sure how to do it. I think it has something to do with the well-ordering principle. Anyway, in a system of n planets, there will be a total of n(n-1)/2 pairs of planets, and all of the distances between each of the pairs will be different. Where do I go from here?