Below are nine dots arranged in a set of three rows. Your challenge is to draw four straight lines which go through the middle of all of the dots without taking the pencil off the paper. If you were using a pencil, you must start from any position and draw the lines one after the other without taking your pencil off the page. Each line starts where the last line finishes.

Try this now by quickly drawing nine dots on a piece of paper and have a go with a pencil. Place your pencil somewhere, draw four straight lines without taking your pencil off the page. Each line must start where the last line finished.

image of the Puzzle

Scroll down for the solution.

 

 

Solution to the nine dot puzzle:

The picture below will show you a solution to this problem. It rotates through the solution so please wait until it starts with an empty grid of dots.

animated image of The Puzzle solved

How did you solve the puzzle?

The most frequent difficulty people have with this puzzle is that they try to draw all the lines within the dots and they do not initially want to draw lines outside of the dots because:

  1. There is nothing outside the set of dots with which to associate.
  2. There are no dots with which to join a line outside the puzzle so they assume a boundary exists.
  3. It is assumed that doing this is outside the scope of the problem, even though the problem definition does not say you are not allowed to. You are so close to doing it that you keep trying the same way but harder.

Lessons to be learned from this puzzle:

  1. Don’t fall prey to general interpretations.
  2. Perception and reality can often contrast.
  3. Do not accept other people’s definitions of problems. They may be either wrong or biased.
  4. What are the boundaries into which the solution must fit.
  5. Are the boundaries your own perceptions or reality?
  6. What are the possibilities if you push the boundaries.