Once we have settled on a perspective, we close off but one line of thought. Certain kinds of ideas occur to us, but only those kinds and no others. What if the crippled man who invented the motorized cart had defined his problem as: “How to occupy my time while lying in bed?” rather than “How to get out of bed and move around the house?”

Leonardo Da Vinci believed that to gain knowledge about the form of problems, you began by approaching the problem on its own terms. He felt the first way he looked at a problem was too biased toward his usual way of seeing things. He would restructure his problem by looking at it from one perspective and move to another perspective and still another. With each move, his understanding would deepen and he would begin to understand the essence of the problem. Da Vinci discovered that genius often comes from finding a new perspective that no one else has taken.


By now most everyone has been challenged with the nine dot puzzle. If this is the first time you have seen it, spend a few minutes solving it before you read further. The challenge is to draw no more than four straight lines which will cross through all nine dots without lifting your hand from the paper.

nine dot














The first time a person tries to solve this puzzle they are stymied. This is because of our perception of the arrangement of the dots as a box or square. Once perceived as a box, most people will not exceed the imaginary boundaries of the imaginary box and are unable to solve the puzzle.

There is nothing in the challenge statement that defines the arrangement as a box and nothing demands the line must be drawn within the box, but people who make that assumption find the puzzle impossible.  The answer, as I’m sure you all now know by now, involves drawing a line that go beyond the limitations of the imagined box.  This is where the cliché “Think out of the box” comes from. To solve it, you have to start the line outside of the imaginary box.


The nine-dot puzzle was popularized by William North Jayme, a direct-mail copywriter who was hired by Esquire magazine in 1958 which wanted to abandon its unwholesome image for a more sophisticated one. Mr. Jayme came up with the ”puzzle letter”: an envelope with nine dots on it and a challenge to the recipient to connect them using no more than four uninterrupted lines. The enclosed letter showed that to do so, one had to go outside the box. Or, in other words, you had to break normal thinking patterns, something that the new Esquire said it could help modern men do. The letter was a phenomenal success, Esquire’s image was changed overnight and the subscriptions poured in.

Over time the puzzle became synonymous with creative thinking and the phrase “thinking outside the box” has now become a cliché for creativity. A cliché because the puzzle has become commonplace and most people remember the solution from their past experience with it. When the brain recognizes the pattern and we solve the problem it seems like a new insight has been sparked.

However when asked to search for other ways to solve the puzzle, the rationalizations begin. We think “If I can’t see it right away, it either isn’t there or not worth finding.” Apparently, if we think “outside the box” once, we are done and our thinking is done. Surrendering to this rationalization limits our thinking, our creativity, and our ability to apply ideas and skills to novel situations.

THE DIFFERENCE BETWEEN THE AVERAGE PERSON AND THE CREATIVE GENIUS. Albert Einstein was once asked what the difference was between him and the average person. He said that if you asked the average person to find a needle in the haystack, the person would stop when he or she found a needle. He, on the other hand, would tear through the entire haystack looking for all the possible needles. With creative thinking, one generates as many alternative approaches as one can.

Most of us have been educated to think exclusively which means we think in deficit by focusing our attention on specific information and excluding all else.  In these instances, exclusive thinking leads us to neglect potentially important pieces of the puzzle. Exclusive thinking doesn’t merely inhibit irrelevant facts and perceptions it can also smother the imagination.

Creative thinking is inclusive thinking. You consider the least obvious as well as the most likely approaches, and you look for different ways to look at the problem. It is the willingness to explore all approaches that is important, even after one has found a promising one.

THERE IS NO ONE RIGHT ANSWER. To begin with, the original “Think Outside the Box” solution was just one way to solve the puzzle. Reality is ambiguous. Aristotle said it is either (A) or (not-A). It cannot be both. The sky is either blue or not blue. This is black and white thinking as the sky is a billion different shades of blue. A beam of light is either a wave or not a wave (A or not-A). Physicists discovered that light can be either a wave or particle depending on the viewpoint of the observer. The only certainty in life is uncertainty. When trying to get ideas, do not censor or evaluate them as they occur. Nothing kills creativity faster than self-censorship of ideas while generating them. Think of all your ideas as possibilities and generate as many as you can before you decide which ones to select. The world is not black or white. It is grey.

Experimental psychologists like to tell a story about a professor who investigated the ability of chimpanzees to solve problems. A banana was suspended from the center of the ceiling, at a height that the chimp could not reach by jumping. The room was bare of all objects except several packing crates placed around the room at random. The test was to see whether you could teach the chimp to stack the crates and make them into steps to reach the banana.

The chimp sat quietly in a corner, watching the psychologist arrange the crates into steps and then distributed them randomly again. The chimp understood and performed the task. The professor invited his associates to watch the chimp conceptualize and build the steps to the banana. The chimp waited patiently until the professor crossed the middle of the room. When he was directly below the fruit, the chimp suddenly jumped on his shoulder, then leaped into the air and grabbed the banana.

Though the chimp had learned how to build steps out of boxes, when another more direct easier alternative presented itself the chimp did not hesitate. The chimp learned how to solve the problem but instinctively kept an open mind to other more effective solutions. In other words, building steps was just one of many ways to reach the banana. Humans, on the other hand, once we learn something or are taught to do something a particular way by someone in authority (teacher, boss, etc.), seem to keep repeating the one method we know — excluding all else from our thought.


APPROACH THE PROBLEM ON ITS OWN TERMS. Approaching the puzzle and framing it with this wording “In what ways might I connect all nine dots with a continuous line without lifting my hand from the paper?” The phrase (“In what ways might I ….?”) is commonly used as an invitational stem by creative thinkers to shape their conscious and subconscious minds to actively search for alternatives.

Looking at the puzzle from this perspective gets you thinking about the number of lines, the lengths of the lines, the width of the lines, the box of dots, the size of the box and positions of the dots.

For instance, there is no requirement that you must use four consecutive straight lines. The puzzle states no more than four straight lines. Why not three, two or even one line? When linking things such as dots we are used to linking the centers and our first attempts are to draw lines through the centers of the dots. This is another false assumption based on past experiences. After a period of trials and errors we discover we can link the dots by having the line just touch the dots as illustrated.


GET RID OF THE BOX. Now, let’s look at from the perspective of the way the dots are arranged. There is nothing that prohibits us from rearranging the dots, so another solution is to cut out the dots and tape them into one straight row and draw one line straight through.


WHAT IS THE ESSENCE?  Over time we have cultivated an attitude which puts the major emphasis on separating human experience into different domains and universes. We’ve been tacitly taught that perception is the activity of dividing a complex scene into its separate parts followed by the activity of attaching standard labels to the parts. For example, in our nine-dot puzzle we tend to think of pre-established categories such as “dots must be in a box, the line must go through the center of the dots, there must be four lines, the line must be made with a pencil or pen, the size of the dots cannot be changed, the paper cannot be changed in any way, and so on.” This kind of thinking is exclusive. Its goal is to separate and exclude elements from thought based upon what exists now. The goal of exclusive thinking is to limit possibilities to the obvious. It discourages creative thought.

Creative thinkers are inclusive thinkers which means they think in terms of essences and principles. They then look in other domains for examples of these essences and then try to make metaphorical-analogical connections between their subject and something dissimilar. The essence of this problem is “connecting.” This motivates creative thinkers to look in other domains to see how things are connected. How does an artist connect different shapes? How does a painter connect unpainted boards? How wide can you make a connection? How long? What instruments can be used to connect things? What substances can be used lines?

Most people assume you must use a pencil or pen and draw a normal-sized line because of their past experiences. But there is nothing in the challenge statement that prohibits the person from using an alternative instrument and substance.  In the domain of house painting the painting connects unpainted boards with paint. One solution is to use a wide paint brush, dip it in paint and connect all nine dots with one straight continuous wide swipe of paint. You have now connected all nine dots with one line.

PAINT BRUSH SOLUTION                                                  

IMAGINATION.  Creative thinkers consider imagination to be more important than knowledge. One way a creative thinker would approach the problem is to ask “What is impossible to do with a line, but if it were possible would change the nature of the problem forever?”

There is no limit on how long you can draw a straight line. So, another solution is to imagine drawing the line around the world three times intersecting and linking up all nine dots.


This, of course, is impossible to do.  But it is not impossible to imagine. Your brain is a dynamic system that evolves its patterns of activity rather than computes them like a computer. It thrives on the creative energy of feedback from experiences real or fictional. You can synthesize experience; literally create it in your own imagination. The human brain cannot tell the difference between an “actual” experience and a fantasy imagined vividly and in detail. This discovery is what enabled Albert Einstein to create his thought experiments with imaginary scenarios that led to his revolutionary ideas about space and time. Imagination gives us the impertinence to imagine making the impossible possible. In the nine dot puzzle we take the impossible solution of going around the world three times and imaginer this idea into a solution that is realistic and practical as illustrated.

Imagineering  means you take an impossible or fantastical idea and engineer it into something realistic and feasible. How can I make this happen? What are the features and aspects of the idea? Can I build ideas from the features or aspects? What is the essence of the idea? Can I extract the principle of the idea? Can I make analogical-metaphorical connections with the principle and something dissimilar to create something tangible?

In this case, we take the principle of going around the world and create a mini-world by rolling the paper up into a cylinder and then rotating a pencil around it connecting all nine dots.


An alternative solution is to place the paper with the dots on the center of a turntable and replace the needle at the tip of the recording arm with a tiny pen. Turn on the turntable and the pen will draw a line through all nine dots.


TAKE IT APART. The average person has been inculcated with a functional fixedness mindset, which is a movement in psychology that emphasizes holistic processing where the whole is seen as being separate from the sum of its parts. Functional fixedness can be defined as mental block against using an object in a new way that is required to solve a problem. This block then limits that ability of an individual to use the components given to them to make a specific item, as they cannot move past the original intention of the object.

When creative thinkers embrace a subject, they see the whole but would move from one detail to another and examine each separately. By mentally taking the subject apart they are able to break out of his stereotypical notion of a subject as a continuous whole and to discover new relationships and ways to use the items that are available to them at the givens.

The dots and the paper that dots are drawn on are two of the major components of the puzzle. Paper can be rearranged into new forms by folding. Taking the puzzle apart by folding the paper as shown below enables you to discover new relationships between the dots and ways to fold the paper until the dots are arranged in a row. Now simply draw a straight line through the dots.


Once observed and accepted, thoughts become loose and move freely around in your mind. The more work you put into thinking about a problem, the more thoughts and bits of information you set in random motion combining and recombining into different combinations and associations. These thoughts breed intuitive guesses and hunches. Previous solutions of rearranging the dots into one straight line sparks the idea of cutting out the dots, arranging them in a stack and then punching a pencil through the center of the dots linking all nine dots.


The more ideas you generate, the more connections you make. These connections and their associated ideas often spark new ideas and new questions. The creative mind synthesizes all that is created and goes beyond them to create more creative products. For example, the above idea of stabbing a pencil through the cut our dots triggers another idea. That is to rumple up the puzzle into a small wad of paper and punch a pencil through the wad. You may have to do this several times, but probability being what it is sooner or later, you will punch the pencil through the dots linking them together.


In genius, there is a patience for the odd and the unusual avenues of thought. This intellectual tolerance for the unpredictable allows geniuses to bring side by side what others had never sought to connect. Think of how Albert Einstein changed our understanding of time and space by fantasizing about people going to the center of time in order to freeze their lovers or their children in century-long embraces. This space he imagined is clearly reminiscent of a black hole, where, theoretically, gravity would stop time. Einstein also fantasized about a woman’s heart leaping and falling in love two weeks before she has met the man she loves, which lead him to the understanding of acausality, a feature of quantum mechanics. A caricature of special relativity (the relativistic idea that people in motion appear to age more slowly) is based on his fantasy of a world in which all the houses and offices are on wheels, constantly zooming around the streets (with advance collision-avoidance systems).

Even the “Many worlds” interpretation which is espoused by some physicists, including Stephen Hawkins is based on Einstein’s fantasy of a world where time has three dimensions, instead of one, where every moment branches into three futures. Einstein summarized value of using your imagination to fantasize best when he said “The gift of fantasy has meant more to me than my talent for absorbing positive knowledge.”

In genius, there is a patience for the odd and the unusual avenues of thought. This intellectual tolerance for the unpredictable allows geniuses to bring side by side what others had never sought to connect. An unusual and imaginative solution is to widen the dots with a pencil so that each dot touches the adjacent dots?  Now the nine dots are linked together with no lines.


The playful openness of creative geniuses is what allows them to explore unthinkable ideas. Once Wolfgang Pauli, the discoverer of electron spin, was presenting a new theory of elementary particles before a professional audience. An extended discussion followed. Niels Bohr summarized it for Pauli’s benefit by saying that everyone had agreed his theory was crazy. The question that divided them, he claimed, was whether it was crazy enough to have a chance of being correct. Bohr said his own feeling was that it wasn’t crazy enough.

Logic hides in Bohr’s illogic. In genius, there is a tolerance for unpredictable avenues of thought. The result of unpredictable thinking may be just what is needed to shift the context and lead to a new perspective.

Another unusual solution is to light a match and burn the paper with the puzzle into a pile of ashes. Then carefully form the ashes into one straight line.

MATCH Within a short time, we came up with a quantity of solutions because we approached the problem on its own terms, looked at the problem from several different perspectives, did not settle for the first good idea, did not censor ideas because they looked silly or stupid and consequently created several ideas, thought unconventionally, changed the way we looked at the puzzle, worked with the essence of the problem, thought discontinuously and used our imagination.


Creative thinking expert and author, Michael Michalko





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