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### 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/
```
Associated Topics:
Elementary Puzzles
Middle School Puzzles

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