Creativity is often equated with "thinking outside the box," but we think that's topsy-turvy. By playing with our open-ended puzzle, you can discover why.
Readers have made favorable comments on our recent post concerning the role of constraints in defining the creative process (Oct. 6, 2009). But recognizing that constraints free rather than fetter the creative mind has implications. Most importantly, it challenges the efficacy of "out of the box" thinking. Embracing rules and strictures can and often does stimulate discoveries that might otherwise go, well, undiscovered. To illustrate this point, we've invented the puzzle illustrated below, which has correct answers and incorrect answers. You'll notice it's a box. All the solutions take place INSIDE. And yet there are many, many solutions. In fact the point of the puzzle is to find as many viable solutions as possible. For this you have to use your imagination. You have to "see" patterns that will only appear when you INVENT them!
The rules are simple. Using the tiling illustrated below, find all possible differently shaped sets of four rectangular tiles sharing the length of a short edge wherever they touch. In other words, the tiles must touch, and wherever they touch, they must overlap along all of a short edge, or half of a long edge. Tiles that touch at just one point (a corner) or that do not touch any other tile cannot be part of a set. Two valid examples of sets of four rectangles are illustrated in red.
If you find all the different sets of four too easy to figure out, try sets of five and six. They become exponentially more diverse and exponentially more surprising. Just imagine what happens when you get up to sets of eight or ten!
Here's what we think you'll experience. You'll probably find the easy and obvious solutions first, often symmetrical sets. You will discover the inobvious and counter-intuitive patterns - often ones that are asymmetrical and disjointed - later, sometimes much later! Just as a guide, so far we've found more than twenty different sets of four. Note: we define sets as being different if they cannot be mapped onto one another by simply rotating them.
We should also warn you that you won't be able to fit all your solutions into the box that we've provided you: there aren't enough tiles. So you may want to print out several copies of the figure to play with.
If you analyze your "obvious" first solutions, you'll probably find that you begin by searching for patterns you're used to observing. The "inobvious" solutions are more difficult precisely because you have to reject the patterns you expect to find. In the process, you will probably find yourself redefining what makes a different yet acceptable pattern. The box stays the same, but new rules or constraints change what you can do inside it!
The other thing you may realize is that these kinds of puzzles can be used to exercise your creative imagination. Novelist Vladimir Nabokov recalled great sensitivity to patterns as a child, which he later realized trained his mind to discover hidden patterns among diverse things. Particularly when he was supposed to be preparing for bed, young Nabokov would begin to move the bathroom door back and forth to the sound of the dripping faucet. Then, "fruitfully combining rhythmic pattern with rhythmic sound, I would unravel the labyrinthian frets on the linoleum, and find faces where a crack or a shadow afforded a point de repère for the eye" - all the while singsonging a "youthful verse" of his own invention. (1)
In fact, our puzzle, too, was invented by looking at our bathroom floor, which is tiled just as in the figure above. Our creative leap was to recognize in a bathroom floor an analogy to creative thinking in general. Shades of Nabokov!
After all the head-scratching and tile-shading, we suggest that creativity isn't necessarily about getting out of the box. Sometimes it's about staying inside the box long enough to rethink and restate constraints, to reconceive and explore its almost infinite possibilities. And the great advantage is that by staying inside the box, and working with its rules, you can have complete assurance that every solution you reach solves the problem at hand.
© Robert and Michele Root-Bernstein 2009
(1) Nabokov, Vladimir. 1947 (reprint 1966). Speak, Memory: An Autobiography Revisited. New York: G.P. Putnam's Sons, p. 85.
