Date: Wed, 17 Jul 1996 00:29:06

From: Gerhard Paseman

In checking the argument I gave previously, I found a better one that suggests another extension to the problem. This argument is based on observing the trajectories of the other travelers from the position of traveler #1, and noting that the other travelers stay on a line (of constant nonzero slope, if #1 is assumed traveling on the y axis) that contains traveler #1's position. This argument suggests that the lines be in general position in k-dimensional Euclidean space, and that the first two travelers meet each other and all the other travelers. Then lack of parallelism gives the remaining meetings. It additionally gives that the paths lie in a 2-dimensional plane. Perhaps you can extend this non-Euclidean geometries for us?

Gerhard Paseman 96.07.17 paseman@math.berkeley.edu