Perhaps another solution to consider may be more naturally phrased and reveal more information about the motions involved. Draw a line connecting travellers 1 and 2, and see how it varies through time. Because of general position of the travelers paths and the constancy of their speed, we see that travellers 3 and 4 must also be on the line as it travels given that 1 and 2 meet them. Now general position gives that 3 and 4 must also meet, since the line intersects their paths.

Perhaps this argument needs to be made more precise, but on first investigation, I see no flaw. What do you think?

Gerhard Paseman 96.07.11
paseman@math.berkeley.edu

Copyright © 1996-2010 Alexander Bogomolny

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