Here is an excerpt from an article written by Vijay Govindarajan and Srikanth Srinivas for Harvard Business Review and the HBR Blog Network. To read the complete article, check out the wealth of free resources, and sign up for a subscription to HBR email alerts, please click here.

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In our last post, we asked the question, “What’s the connection between counting squares and innovation?” In order to come up with the answer, we presented you with the following figure and asked you how many squares you could find. It turns out, the answer isn’t so simple.

It was clear that this was a fun, engaging exercise, as we had 400 comments in the HBR blog post, an additional 312 comments in Facebook, and about 40 individual email responses. We enjoyed reading the comments and seeing the enthusiasm with which you wrote them. Given the number of good responses, we could not choose the top five; instead, we will be giving a copy of Reverse Innovation to 20 winners.

How you arrive at the answer can make a big difference in what you find. In the first “systematic” analysis, we can find 30 squares.

16 (1×1 squares) + 9 (2×2 squares) + 4 (3×3 squares) + 1 (4×4 square) = 30 squares.

The squares were always there, but you didn’t find them until you look for them. At first glance, you can easily see 16 squares. But the reality as it appears to be is often different from the reality as it is — 30 squares. You need to spend time and dig deeper to understand the reality as it is. Innovative solutions are always there for the problems we face, but you won’t find them unless you look for them.

There is a method to the madness (systematically going through 1×1, 2×2, 3×3, and 4×4 squares in this case). It takes time to find the method, but when you do, it opens up many more solutions and opportunities for any innovation problem. To quote one of the commenters, “We need to look beyond what meets the eye and what we are told, for more innovative perspectives both on the problem as well as the solutions born out of detachment to either.”

But can we do even better than a systematic analysis? On a more creative note, there are 30 squares with black edges and 30 squares with white edges. We’ve now discovered 60 squares. Out-of-the-box thinking can open up even more solutions. The foundation of systematic method, combined with out-of-the-box thinking, can result in order-of-magnitude change in performance. There were several creative replies with many more squares, all the way to infinity. Thank you for stretching our thinking. There are no limits to out-of-the box thinking. Only our own imagination is the limiting factor. To quote on of the commenters, “Don’t think it’s impossible, stretch the limits, bend the rules without breaking them — be curious — seek something new — have fun!”

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To read the complete article, please click here.

Vijay Govindarajan is the Earl C. Daum 1924 Professor of International Business at the Tuck School of Business at Dartmouth. He is coauthor of Reverse Innovation (HBR Press, 2012). Srikanth Srinivas is a retired management consultant. He is the author of Shocking Velocity.