Join the Dots

Date: 09/02/2001 at 21:34:39
From: Christi
Subject: Geometry

If you have 9 dots, like this:

.  .  .

.  .  .

.  .  .

how can you connect them with only 4 lines without picking up your 
pencil or going through a dot more than once?  Please help.

Date: 09/06/2001 at 08:36:33
From: Doctor Ann
Subject: Re: Geometry

Hi Christi,

This question brings back happy memories for me because it is the 
first "brain teaser" that I remember working.  It is also a good 
example of thinking "outside the box."

For clarity, I am going to number the dots:

  1   2   3 
  4   5   6
  7   8   9

Start at point 4. Draw the first line from point 4 and through point 
7.

However, (here's the trick), DRAW THE LINE BEYOND POINT 7 AND INTO THE
SPACE JUST BELOW THE 7. The second line is drawn from the space below 
the 7, and through points 8 and 6.  

Again, don't end the line segment at 8. Continue the line outward 
(northeast) until it is just to the right of point 3, then stop.  

Line Three starts at that point, then goes (left) through points 2 and 
1, then stops AT 1. The last line connects 1 with 9 (through 5).

For an illustration, see:

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

I hope that is a clear explanation of the problem.  If not, or if you 
have another question, feel free to write again.

- Doctor Ann, The Math Forum
  http://mathforum.org/dr.math/