Challenge Assumptions

Two people are stacking cans for a display in a grocery store. They stack 250 cans in 1 hour. How many cans could four people stack in an hour?

The obvious answer is 500. Twice the manpower in the same amount of time will yield twice the stacked cans. However, this answer is very rigid and does not take into account many real life components of such a question. It rests on many assumptions. If we look just beyond our assumption horizon we might ask:

Will the four people get in each other’s way and thus reduce their rate of stacking?
Will the four people adapt a system of cooperation and speed up their rate?
Does the store even have 500 cans of this product?
Do four people doing the work of two increase the chance of knocking down the display?
Will there be twice as many stacks or will the stack have twice as many cans?
Does the store even have room in the aisles for four people to effectively work?
What if one of the employees is really clumsy?

This list could easily be grown into dozens if not hundreds of similar questions. The reason these questions arise is because each one challenges one or more assumptions we took with us when answering the original question. We may have assumed all four employees have equal strength and hand-eye coordination. We may have assumed that the store has twice the workspace to allow twice as many employees to work. And yet, most of these questions do not occur to us immediately because we focus first on finding the one true solution.

We have trained our whole lives to find the “right” solution, the sole truth, the mathematically sound proof. Since an early age we have practiced using linear problem solving to find solutions: The ones where everyone in the class reaches the same solution! Challenge yourself to look beyond your assumptions, to sidestep your initial pull to the obvious answer.

Think Again

Since many of us have become so accustomed to stay on the comfortable side of our assumption horizon, we don’t take the time to find alternative solutions. It can be a little scary to go outside of our comfort zones, and challenging the way we think is no different. I firmly believe that challenging the way you think will lead you to amazing discoveries. You may come up with a great way to improve your life or decide that the second or third solution to a problem is more beneficial or rewarding. You may even find that “thinking again” is a fun and playful way to think!

Consider the Nine Dots Puzzle that has been used in countless book and websites as an example of “thinking outside the box.”

Instructions: Connect the dots by drawing four straight, continuous lines, and never lifting the pencil from the paper. The solution is linked below, but try to figure this one out first. Challenge your assumptions. Draw the dots on a piece of paper so you have another perspective on it. Nine Dots Solution.

Do not read on until you find a solution or give up. Give yourself a real chance to figure this out - it’s worth it!

As you can see, the dots create the illusory assumption that the outside dots are somehow a boundary, which we cannot go beyond. Only when we break out of this “box” can we see how this can be done.

Let’s take the challenge even further. How about solving the puzzle with three lines? What about one continuous line? What assumptions are you making that prevent you from doing it? What if the dots are not the “mathematical” entities we call “points,” which have no area? What if each of the dots was a foot in diameter and the paper was the size of a small apartment? Then we could draw a huge zig-zag with three lines and easily hit all the “dots.” What if the paper is on a sphere? This would allow one continuous line wrapped around the sphere to go through all nine dots. Hey, we could draw that on an egg and use it as a logo!

This exercise is not meant to make anyone feel bad. If you did not come up with any of the solutions above, don’t despair! I certainly didn’t get it the first time I saw it, but once I did it has a huge Aha! moment for me. Use the examples to open up your perception of problems and challenge yourself to think again when faced with a problem. With a little practice you’ll never return to one-stop problem solving.

Lateral Math

Even the most linear of academic disciplines, mathematics, can be bent beyond the assumption horizon. I’d like to share an example from my own life. This memory came to me while writing this article and I had never realized the significance of it until now.

I remember challenging my math teachers when I was in the ninth grade. I don’t remember the details of the problem, but I do remember it was a word problem. There was not much room for debate within the formulas he was testing us on, but boy did I find some ambiguity in his wording! I carefully read his seemingly simple questions, I realized that there were at least two ways to interpret the problem, and thus at least two answers. What I did was submit multiple answers to two of the questions in the homework and waited with excitement for his reaction. His response was largely positive although there was still a hint of treating it like a novelty (the rest of the class had clearly understood the linear path he intended us to travel). I was ecstatic and proud of myself. I didn’t know it at the time, but I was practicing lateral thinking in a math class. I wish I could remember his name. I’d like to thank him now.