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Real knowledge is created by the learner, not given by a teacher.

Here is another exercise to help you increase your ability to solve problems creatively.

Creative Exercise 4 -   Breaking out of the box

Most of us impose too many imaginary boundaries, restrictions, and constraints upon our problems, and hence fail to solve them.

Below are nine dots arranged in a set of three rows. Your challenge is to draw four or fewer straight lines which go through all of the dots without lifting the pencil.

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

The key to the solution is, of course, that the imaginary boundaries formed by the dots need not be observed. Once freed from this restriction, you will find the solution easy, as shown here.

Creativity coaching can help you solve your problems in the way that you need.

Researchers at Stanford University have come up with an even more interesting solution to this puzzle. One subject realized that it wasn't necessary to draw four lines through the centres of the dots; the problem can be solved with only three lines.

Another solution requires only one line, but needs a piece of paper that is very long and looped around - perhaps right around the world.

The beauty of this nine-dot puzzle is that you literally have to ‘think out of the box’ to solve the puzzle. Your pencil 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.

What can 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 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 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 arrange an introductory session to find out more.