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.

Since the problem states "no tricks allowed" I'm assuming that the points must all be of zero radius, and that it's impossible, but I can't figure out how to do a proof of that.

Another thought, which is probably trick and thus not allowed, is to consider the paper to be on the surface of a sphere, which means the straight lines could be like lines of longitude on the earth.  So if the lines go 1/4 the circumference of the sphere in each direction, then it could be done in 3 lines.

Posted by Larry on 2005-07-15 01:22:51