Problem Solving

In the course “Effective Thinking Through Mathematics“, Prof. Michael Starbird uses puzzles to teach his students, the methodology of solving problems. I think, we can use the same approach in our daily lives to solve problems or to develop new ideas. Lets take a simple maze puzzle and see what we can learn by solving them.

Try to solve this puzzle before going forward.


How did I solve this puzzle?

a. I started with a path from the man and proceeded all the way until I reached the flag pole or a dead end.

b. If I have reached a dead end, I mark that path as wrong.

c. I then selected a different path and proceeded all the way until I reached the flag pole or again another dead end.

d. If I have reached a dead end again, I mark that path as wrong.

e. I repeated the steps ‘c’ and ‘d’ until I reach the flag pole.

What did I learn from this approach? 

Do not prejudge the solution until the evidence is seen:

It is important to establish evidence before deciding that the current strategy won’t work. Why? Well, what if the current strategy is actually the correct strategy?

In the book “The 5 Elements of Effective Thinking“, Prof. Michael Starbird discuss on what happen when you make a mistake.

When you see or make a mistake, you have at least two actions to take: (1) let the mistake lead you to a better attempt, and or (2) ask whether the mistake is a correct answer to a different question

So, when we make a mistake, instead of immediately diving to find an alternative solution, we can analyze what did we do wrong, we can also ask ourselves whether our mistake is an answer to a different question. Here is an extract from the book to illustrate this point.

In 1970, 3M scientist Spencer Silver was working hard to create a stronger adhesive. His creation was resounding failure, In fact, the bond was actually weaker than other 3M products of the day, it was so weak it could be stuck to objects and then easily lifted off them without a trace. Four years later it gave birth to 3M’s most lucrative products, the Post-it note.

When solving puzzles, we also tend to over think and jump to conclusions before attempting to go through every step and reach an end.

Over thinking while solving a problem might lead us to abandon a path in the middle of solving it. In the event, that our abandoned approach is the correct approach and if we had abandoned it before finding an evidence, we would then be draining our valuable time and resource in chasing a strategy that never exists. Therefore it is important to establish evidence that the strategy you are working is wrong before switching to a new strategy.

With every mistake, we move one step closer to our solution

By identifying a strategy that did not work, we successfully eliminate one thing that did not work. What’s left after all the successful elimination of things that didn’t work is the one thing that would work.

Howard Schultz’s and his colleagues had to try hundreds of ideas, on everything from non stop opera music to barista’s wearing bow ties, to hundreds of different types of beverages before being able to define the Starbucks experience.

As Thomas Edition puts it,

Many of life’s failures are people who did not realize how close they were to success when they gave up.

Working Backwards:

The approach we saw so far is to work forward, in other words, iterating each possible way until we reach a successful solution. Another efficient approach is to work backwards. Here is the video of Maurice Ashley explaining the benefits of working backwards.

In our puzzle, check how efficient is to solve the maze puzzle by drawing the path from flag pole to the man.

In real world situations, during a software development, we may first want to figure out answers to few questions such as… how we want our application to work? who are our users? what values do we intend to create? who are the competitors? and how are we going to be different? Answering these will help us to work backwards in constructing our application which would save time and money.

Fail Forward:

Establishing positive attitude towards failure is another important characteristics that is seen repeatedly from people who developed break through innovations. Here is a story about Thomas Edison when his factory was burning down.

At around 5:30 in the evening on Dec. 10, 1914, a massive explosion erupted in West Orange, New Jersey. Ten buildings in legendary inventor Thomas Edison’s plant, which made up more than half of the site, were engulfed in flames. Between six and eight fire departments rushed to the scene, but the chemical-fueled inferno was too powerful to put out quickly.
According to a 1961 Reader’s Digest article by Edison’s son Charles, Edison calmly walked over to him as he watched the fire destroy his dad’s work. In a childlike voice, Edison told his 24-year-old son, “Go get your mother and all her friends. They’ll never see a fire like this again.” When Charles objected, Edison said, “It’s all right. We’ve just got rid of a lot of rubbish.”

Later, at the scene of the blaze, Edison was quoted in The New York Times as saying, “Although I am over 67 years old, I’ll start all over again tomorrow.”

I think Silicon Valley thrives on Fail Forward mentality. Check this podcast to have an inside look at Silicon Valley.

Here is an extract about Pixar from the book “Little Bets: How breakthrough Ideas emerge from small discoveries” with respect to failing forward.

As Pixar director Andrew Stanton, director of Finding Nemo and WALL-E, describes this way of operating, “My strategy has always been: be wrong as fast as we can. Which basically means, we’re gonna screw up, let’s just admit that. Let’s not be afraid of that. But let’s do it as fast as we can so that we can get to the answer.”

Lateral Thinking:

A lot of innovation happens by refining old ideas (what is called as tinkering) and also by expanding the old ideas from when it was left to one step further. In some instances if we go backwards and look the problem at a different vantage point, we might discover a new better solution. Here is Edward de Bono explaining the lateral thinking.

The idea of this article is to change the way we think of failures. While developing new ideas, though our goal is to succeed at the first trial, when we fail, we can think of using the failures as a means of learning to drive towards our success.

2 thoughts on “Problem Solving

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s