Problem Solving

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There once was a fantastic television show called MacGuyver, which followed the adventures of the most exceptional problem solver you can think of. The show was not about characters or drama or action, although each episode had little bits of each. The show was about heaving MacGuyver ever-more-difficult problems to solve with ever-fewer resources.

The very first MacGuyver I ever saw, when I was probably in Jr High school, had MacGuyver stopping a deadly acid leak with a chocolate bar and preventing a missile launch with the wrapper. Now that’s a good problem solver!

Looking back I think that MacGuyver (and my father, and my grade 9 science teacher, among many others) helped shape the way I approach problems. I thought it might be interesting if I wrote down some of the skills I use day to day in solving problems and how I think they can be acquired.

Here’s the list:

First Section: Pre-problem

1. Build a big toolkit of knowledge: This is common problem solving advice. Large toolkits allow a person to “synthesize” more, which simply means bringing in more ideas to solve problems.

   Example: If you only know how to drive then it is quite easy to get almost anywhere, but you have a problem if your car doesn’t work. Mechanical knowledge could help get the car working and knowledge of the transit system might help you get there without the car.

2. Pre-packaged blocks: This might be the most important. You can reduce the complexity of any problem by breaking it up into pieces that you know how to solve. Small pieces can be combined to form bigger pieces and bigger pieces can be broken up as needed.

   Example: Suppose I’m talking to a house builder. I can give him a picture of the house I want and tell him to build it because he has enough pre-packaged blocks to solve that problem. He knows that a roof is made of interior supports, an outer skin of wood, shingles on top of that and insulation inside. Furthermore, he knows how to select wood, cut it, fasten it, protect it, and every other skill. But ask that same person to change the oil in his car, which is a much simpler task, and he may not know how to do it. Perhaps he’s missing the skills of how to select his grade of oil and his filter, how to figure out if it’s full, which tool to use to unscrew the oil filter, how to pre-treat the filter, nor how to dispose of the old oil.

Second Section: The Problem

1. Understand the solution: Imagine what the solution must look like. The house builder starts from the picture of the final house before he goes to the lumber.
2. Break it down: From the solution start splitting the problem into chunks, whether you know how to solve them or not. Obviously you are not done until you know how to solve all the chunks. Keep breaking it down until you either can’t break it down any more or you know what to do. THIS IS WHERE ALMOST ALL SCHOOL “PROBLEMS” END. They simply make you combine skills that were taught earlier.
3. Develop new knowledge: If the problem is easy (for you!) there won’t be much of this. However, if the problem is harder and more interesting then you may be left with chunks that you don’t know how to solve. Now you have to learn something new, specifically for this problem. Maybe you have to do an experiment, find someone who knows, construct a proof, or something else. This is a great opportunity to have an original thought!
4. Do the work: You’ve broken it into chunks, each of which is easy for you to solve. Now you solve all the chunks, combine them and build the solution. If the problem is complicated and involves a lot of work and resources then maybe you have to develop a plan to manage it.

Third Section: After the Solution

1. Check your work: You may know how to solve the problem but the work of solving may have been done wrong. Devise some tests that will help you decide if the solution is good. By the way, in the real world this is often a very difficult thing to do – a major problem in itself! How did NASA engineers know their probes would work on Mars? How does the movie theatre managers know that everyone in the R-rated slasher flick is old enough to be there.
2. Learn: Be proud if you succeeded at a tough problem. Hold on to any new knowledge you acquired. Most of all, be glad that you got to practice the important skill of problem solving.

Remembering back to my school days I definitely remember that many of my classmates basically start and end on “Do the work”, when in reality this stage is very far down the line and far from the end of the problem solving process. Looking at a math problem they develop an instinct to look at their formula sheet for a formula that accepts the data they have.

If you have never seen a MacGuyver it would definitely be worth it to rent a few episodes. It’s not instructional and it isn’t realistic but it is inspiring to see that, just maybe, one person with a stick of gum and a lot of ingenuity can escape from prisons, stop weapons of mass destruction or rescue damsels in distress. And if a person can do so much with so little, then maybe a math student can figure out how many marbles can fit in a jar.