The Jigsaw Puzzle

Watching kids grow is fascinating. Sometimes you feel you are re-living your own life and re-learning things you thought you knew very well. Sometimes in their struggle you find a perfect analogy to some of your own problems. Sometimes they teach you a business lesson. 

One such incident happened a couple of months after my son, Rohan’s,  second birthday. We were at a public library and I saw him solve a 12-piece jigsaw puzzle for the first time. A little surprised I thought to myself, “Mamma’s boy must have learned it from his Mamma. Lets give him a bigger challenge.” I got a 20-piece puzzle and stepped back to see how he did!

I did not grow up with jigsaw puzzles, and until that day I had never really thought how to go about solving one. As I was watching Rohan assemble the various pieces I started thinking about a fast way to solve the puzzle. The first idea was obvious; identify the corners, and try and guess their correct position. Then find the side pieces and try to guess their position. For the remaining pieces you can simply use a greedy [1] strategy.

My train of thought was broken when I noticed that my son had assembled two separate groups of about five pieces each. “Divide and conquer!” [2] I thought to myself. The rules I described above were not obvious to him yet, but he had indeed discovered Divide and Conquer on his own! The library was about to close in five minutes. Rohan was struggling with the remaining 5-6 pieces. I thought he had plenty of time on his hands, but to my surprise he was unable to complete the puzzle. That did not feel right.  Unlike most games designed for kids, the Jigsaw puzzle gets easier as the game proceeds. The last 10 pieces should have been far more easier to assemble than the first 10. Yet, the board in front of me told a different story.

I told Rohan that we needed to go as the library was closing. “Paa help Rohan do,” he pleaded. So I started putting the remaining pieces together, and when no pieces were left I realized why Rohan had failed. “One missing, two missing,” I heard Rohan say as he counted the two empty spots. There were two pieces missing, and that completely threw off Rohan’s strategy. He must have tried to fill one of those spots, and could not find a piece that fit. I guess he then tried a different spot; only to find that nothing fit in that other spot either. He probably went in circles trying to fill those spots and did not make progress. Suddenly everything made sense. A few days later when we were back in the library, I proved my theory by giving Rohan a 20-piece puzzle with no missing pieces. Sure enough, he solved it in a reasonable amount of time.

Someday Rohan will understand that problems is real life have missing pieces. Solutions have holes; things don’t quite fit perfectly. Even when we are very close to a solution, it never feels like we are because we are fooled by missing pieces. The goal then is to fill in those pieces with your imagination and charge forward with the rest of the solution. Sometimes you will be dead wrong, but often times as you gain more clarity into your problem, the missing pieces will fall in place.

[1]. A greedy strategy is a strategy that follows the problem solving heuristic of making the locally optimal choice at each stage with the hope of finding a global optimum.

[2]. A divide and conquer algorithm works by breaking down a problem into two or more sub-problems, until these become simple enough to be solved directly.