osman@sprite.DEC (Eric Osman, dtn 283-7484) (01/29/85)
I'm responding to whomever believes the number of points can grow infinitely. It cannot !, which is what makes the problem pretty. However, the problem I'm referring to in which the number of points may not grow infinitely is as stated in Scientific American, like this: Place two points in separate halves of a line segment. Now MOVE them if necessary so that a third can be added such that all three are in separate thirds AND the original two are still in separate halves. Now MOVE the three if necessary in order that a fourth point may be added such that all four are in separate fourths AND the original three are in separate thirds and the original two are in separate halves etc. How many points can be added in this manner ? It's THIS problem to which the points may not grow infinitely ! Write a program, or ask me for mine. I'd very much like to hear an INTUITIVE feel for why n is not infinity. The reason I thought perhaps this is a different problem, is that the version I saw in net.puzzles yesterday didn't talk about MOVING the old points to make room for the new, plus the fact that someone claimed the number of points is infinite, which it is not.