One of my least favorite misconceptions about creativity is that creativity and its associated goals, methods, and outcomes are inherently distinct from “logical thinking.” To think creatively, the misconception goes, we have to simply release our inhibitions, think wildly and weirdly, and broaden the range of possibilities we’re willing to aim for in our work. This outlook views structure as the mortal enemy of creativity, and assumes that a sort of unpredictability is a necessary consequence of allowing ourselves to think creatively to solve problems.

Of course, this sort of “freeness” can be an important part of thinking creatively, but creativity also often means using approaching a problem in an unusual but totally reliable way that allows us to work our way to solutions that are perfectly logical.

It’s kind of like a good metaphor. Lots of metaphors associate two things that are unexpected or weird – grief with an orange, a raccoon with our mother, a slinky with anxiety – but the best metaphors are the ones that despite being unexpected only make more and more sense as we consider the defining concepts of each subject, thereby revealing the underlying logic that proves the metaphorical connection to be warranted.

Check out this example that illustrates how creative and logical thinking can work together to help us solve problems.

Imagine I asked you to add up every number from 1 to 10 (inclusive). It would probably only take you a minute to figure out in your head that doing this leads you to the number 55.

But let’s say that I now asked you to do the same thing with ever number from 1 to 100.

Mental math doesn’t seem quite as practical anymore.

If we want to solve this problem without making our brains sweat more than they need to, we now need to search for other creative ways of looking at the problem that might get us to the solution faster.

Here’s just one of those ways:

First, let’s line up every number in the sequence in ascending order.

1 2 3 … 98 99 100

Ok. We know that if we add up those numbers, we’ll get our answer.

That means that if we do the same thing with a second row of the same numbers below the first…

1 2 3 … 98 99 100

1 2 3 … 98 99 100

…Adding up all of those numbers will lead us to 2x the answer to the problem.

But now, that doesn’t really make it any easier to calculate the answer. So what if we lined up the second row of numbers below the first in descending order?

1 2 3 … 98 99 100

100 99 98 … 3 2 1

It only takes a few seconds of looking at these two rows of numbers to realize that each pair of numbers stacked on top of each other add up to 101.

1 2 3 … 98 99 100

100 99 98 … 3 2 1

101 101 101 … 101 101 101

Now we’re getting somewhere! We can now say with confidence that all of the 101s in the third row of numbers add up to 2x the answer we want, since 101 is just the sum of each pair of numbers. There are 100 101s in the sequence, 100*101=10,100. That means 10,100=2x (where x=our desired answer), so x = 5050!

This method involved us taking a non-conventional approach to a problem whose most straightforward path to completion would’ve been to just add up 1 + 2 + 3 + 4 + 5… all the way up to 100 which would’ve taken a long time, even on a calculator.

But by remaining clear about what we know to be true when applying our unconventional method, we can have the utmost confidence that our creative approach is logical, and it will work without fail.

So next time you assume that creativity involves a mere wildness, keep in mind that while this sometimes is true (and can be, if we want it to be), creativity produces its most reliable results when guided by assumptions we know to be true.