Much has been made of the importance of thinking “outside the box.” To solve difficult problems, it is said, you need the ability to do this. I agree. Completely. Because I’ve seen supposedly insurmountable problems solved by this kind of thinking many times.

The origin of the phrase originated with an intelligence test called the Nine-Dot Box. You’ve probably seen it. Imagine three rows of three dots, each equally spaced, on a piece of paper. The challenge is to connect all the dots by drawing a minimum number of lines. The rules: You must draw a line through every dot once and only once. The lines must be straight (no curves). And your pen/pencil cannot leave the paper.

If you’ve seen this done as a “bar trick,” you know that most people cannot do it with fewer than five lines.

The trick to thinking outside the box is to ask yourself if you are making any unfounded assumptions. Specifically, ask yourself if you are limiting the possible solutions of the problem by some imagined restrictions that don’t exist. If you are, all you have to do is think “beyond” them.

In the case of the Nine-Dot Box, the assumption is that there is an imaginary boundary surrounding the perimeter dots. But there is no rule that says your lines cannot extend beyond that perimeter. By thinking “outside the box,” you can easily connect all the dots with four lines. There are several ways of doing it. (Search “9 Dots Puzzle” on YouTube.)

In fact, you can connect them all with three lines – even a single line if you roll the paper into a cylinder. Torque it so that the dots are at an angle to one other, and then they can be connected with one continuous straight line around the cylinder.