Connect Nine Dots

Date: 11/4/96 at 14:8:42
From: gil sela
Subject: Re: Drawing problem
 
I saw a very beautiful problem but I couldn't solve it. It looked 
simple but after a second, I gave up:

Draw 4 lines connecting the 9 dots without lifting the pen

                      x   x   x

                      x   x   x
                      
                      x   x   x 
            

Date: 12/04/96 at 15:18:07
From: Doctor Keith
Subject: Re: Drawing problem


It is a nice problem.  Allow me to first give you a piece of advice 
and a picture instead of the answer. You can then try it again and 
see if you can get it on your own. If you get stuck then, the 
solution is below my suggestion.
 
My advice is to remember that you are not stuck with the nine dots as 
corners.  This means you can continue the line outside the dots and 
then turn.  So consider this diagram with two extra dots, which I 
claim can be done with the same 4 lines without lifting the pen.  Try 
drawing lines that include these points as corners and see what you 
get.
 
                               X
 
                       x   x   x
 
                       x   x   x
                       
                   X   x   x   x 
  

To see the solution on the Web, take a look at this page:

  http://mathforum.org/k12/k12puzzles/join.dots.html   

If you enjoy problems like this you might want to consider a 
book on graph theory or classic math problems, or look at more of our 
line puzzles (at the above URL).

Good luck!

-Doctor Keith,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/