Take any four points in space. Draw all lines connecting pairs of them. Then draw all lines connecting pairs of points on those lines.

Can the resulting set of points cover all of space?

(In reply to re: Detailed Solution by Charlie)

Whoops. An infinite coordinate would be required in each case!  I missed an important consideration in my analysis.

I have edited my post --  too bad I cannot edit its title to Detailed Nonsolution. 

Posted by Richard on 2005-02-06 21:52:45