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Creative thinking puzzle number 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 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.
Have a go now and then scroll down the page to find out the solution. Do not look at the answer below until you have either given up or found a solution of your own. Do not give up too easily!


No cheating now. Please do not 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 your thoughts you needed have 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 do not 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 the puzzle. Your pencil or mouse must go outside the box of the dots to be able to solve it.

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 it because:
  1. There is nothing outside the set of dots to associate to. There are no dots to join a line to outside the puzzle so they assume a boundary exists.
  2. 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.
  3. You are so close to doing it that you keep trying the same way but harder.

Lessons to be learned from this puzzle

Look beyond the current definition of the problem.

  • Analyse 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 - 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 which the solution must fit into?
  • 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 Puzzle number 2

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