It is well-known the solution to the problem of connecting nine dots, arranged in three rows of 3 dots, with four straight lines, without lifting up the pencil from the paper where they are drawn, and without any tricks at all, like folding the paper, etc...

           o        o        o


           o        o        o


           o        o        o

The question is: given the nine dots above, is it possible to connect them with only 3 straight lines ? The restrictions are the same, that is, without lifting up the pencil from the paper where they are drawn, no tricks allowed, and if you retrace a line, you must count one more line.

Prove your answer!

Note: this is a revisit to the problem Nine Dots already posted in this site and you can use that drawing for reference.

(In reply to Solution by Brian Smith)

The term "straight line" would seem to imply Euclidean geometry.  "Great circle" would be the spherical equivalent, or "geodesic" in a more general setting. Non-Euclidean geometry, at least beyond  spherical geometry, is probably outside the scope of perplexus. And for this problem, I would consider ringing in spherical geometry to be a trick.

Posted by Richard on 2005-07-15 02:51:47