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 Another way by Richard)

In order for your statements to be true, my line also has to be of zero width.  If my lines are of some width, then I can still draw the line with some angle and connect the three zero radius dots.

The problem did state however that we are using a pencil, and even the most fastidious pencil sharpener, no matter how well trained in grade school, cannot make it sharp enough to draw a zero width line.

Cheers!

Posted by Bob Smith on 2005-07-15 14:10:04