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Creative thinking puzzle 1 - The nine dot problem to help you "think out of the box"

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 marker off the pad. Using the mouse on the drawing below you can start from any position on the pad and draw the lines one after the other without moving your mouse-marker somewhere else on the page. Each line must start where the last line finishes. Try this on the drawing below but first change the marker width from "35" to "10" using the arrow buttons in the bottom right of the box. (Reset the drawing by selecting another "Page" from the drop-down list in the top right of the box.) If you find it easier, feel free to use a real pencil and paper instead of our electronic version.

If you see nothing on the left then your browser cannot use Java applets, so click here for a non-Java page instead.

Have a go now, and then scroll down the page to find out the solution. Don't look at the answer below until you have either given up or found a solution of your own. Don't give up too easily!

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No cheating now. Please don't look at the solution until you have one yourself.


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.

How did you solve the puzzle?

Think back to how you were solving the puzzle. Did you solve it by trial and error or did you think through a strategy? Spend 30 seconds thinking about how you solved it and what changes in thought you needed to get you there.

"Knowledge is created by the learner, not given by the teacher." If you are trying to learn something then you will need to think about it. We are not trying to teach you anything you don't already know, you are merely using us to remind you of things you want to remember.

The beauty of this nine-dot puzzle is that you literally have to "think out of the box" to solve it. For the solution, your pencil or mouse must go outside the square of dots.

The usual difficulties we experience in solving this puzzle lie in that we try to draw all the lines within the set of dots and we are reluctant, initially, to draw lines outside it. Why?
  1. There is nothing outside the square of dots to associate to. There are no dots to join a line to outside the puzzle so we assume a boundary exists.
  2. We assume that drawing outside the dots is outside the scope of the problem, even though the problem definition doesn't say it is.
  3. We feel so close to solving it that we keep trying the same way, but harder.

Lessons to be learned from this puzzle

Look beyond the current definition of the problem.

  • Analyze the definition to find out what is allowed and what is not.
  • Are there any real rules to the problem anyway? (especially valid in human-related problems where there are only perceptions, not physical rules)
  • Look for other definitions of problems.
  • Do not accept other people's definitions of problems. They may be either wrong or biased.
  • If a problem definition is wrong, no number of solutions will solve the real problem.

Investigate the boundaries

  • What are the boundaries into which the solution must fit?
  • Are the boundaries your own perceptions, or reality?
  • What are the possibilities if you push the boundaries?
  • What are the benefits of small boundary changes?

Hard work is not the solution

  • Repeating the same wrong process again and again with more vigour does not work.
  • You can be very close to a solution while not getting any closer to it.
  • Thought is the solution, physical hard work will not work.

Click here to move to creative thinking Puzzle 2

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