The Math Forum

Ask Dr. Math - Questions and Answers from our Archives
Associated Topics || Dr. Math Home || Search Dr. Math

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 

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:   

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   
Associated Topics:
Middle School Geometry
Middle School Puzzles
Middle School Two-Dimensional Geometry

Search the Dr. Math Library:

Find items containing (put spaces between keywords):
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

Math Forum Home || Math Library || Quick Reference || Math Forum Search

Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.