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.

I don't know if this counts as a trick or not, I'll let someone else judge...

Assuming the dots are on a "large" sheet of paper, start the line at top edge of the upper left dot, continue through the middle of the upper middle dot, and on to the lower edge of the upper right dot.  Continue drawing the line out to where you can double back and pass at a similar angle through the middle three dots.  Repeat for the lower 3 dots.

If you say that the dots are infinitesimally small, then my fat #2 pencil would allow me to accomplish the same effect.

Edited on July 14, 2005, 5:33 pm

Posted by Bob Smith on 2005-07-14 17:25:46