problem solving

Triangle apollonius
Strategy for problem-solving by scaling and inversion

Problem-solving is another word for engineering. All engineering can be thought of as problem-solving. Problems or potential problems in a product or process can be identified and solved at any time – before, during or after something happens. There is a lot of emphasis on the critical thinking to solve the problems, but more importantly, finding the problems and determining what to solve are necessary and fundamental to the engineering design process. It is called the engineering design process to highlight the creativity and analytical aspects of problem solving.

  • Asking Questions and Defining Problems – identifying the problem to solve requires creative and skill
  • when products or processes fail, so corrective action can be taken to prevent further failures.
  • prior to an actual fail event, i.e., when a potential problem can be predicted and analyzed, and mitigation applied so the problem never actually occurs. Techniques such as Failure Mode Effects Analysis can be used to proactively reduce the likelihood of problems occurring.

Forensic engineering is an important technique of failure analysis that involves tracing product defects and flaws. Corrective action can then be taken to prevent further failures.

Reverse engineering attempts to discover the original problem-solving logic used in developing a product by taking it apart.

George Polya, a famous mathematics educator, believed that the skill of problem solving could and should be taught – it is not something that you are born with. He identifies four principles that form the basis for any serious attempt at problem solving:

  1. Understand the problem
  2. Devise a plan
  3. Carry out the plan
  4. Look back (reflect)

This is so important for engineers that it is part of the [/Engineering%20Design%20Process Engineering Design Process]

Abstraction – the ability to simultaneously consider multiple states of a system in order to analyze it for patterns, behavior and predictability.

  • A lot of people simply don’t see the world abstractly. Not even slightly abstractly. There are things that are nearly impossible to express to someone rooted in the concrete (like, say, recursion, fractals, complexity, etc) that are really the basis of 21st century thinking.


  • 5 Whys –
  • Theory of Inventive Problem Solving – TRIZ (“trees”)
  • heuristic – a mental rule-of-thumb strategy, allows people to simplify complex problems and reduce the total number of possible solutions to a more manageable set.
  • trial-and-error – trying a number of different solutions and ruling out those that do not work. This approach can be a good option if you have a very limited number of options available.
  • scaling, inversion

Devise a plan – partial list of Problem Solving Strategies include:

  • Guess and check
  • Solve a simpler problem
  • Make an organized list
  • Experiment
  • Draw a picture or diagram
  • Act it out
  • Look for a pattern
  • Work backwards
  • Make a table
  • Use deduction
  • Use a variable
  • Change your point of view

Sink or Swim School of Engineering
[/Instagram Instagram] Co-Founders Kevin Systrom and Mike Krieger talk about courses taught them to define questions and provided the freedom to seek the answers, and importance of connecting with other members of the entrepreneurial community.
Video: Sink or Swim School of Engineering (3:44)

Building solutions for most problems is the easy part; the hard part is finding the right problem to solve. Systrom and Krieger identified the problems they wanted to solve around sharing photos through mobile devices. Simple solutions often delight users and customers.
Video: Finding the Problem is the Hard Part (3:28)

In the videos, Systrom and Krieger talk about their steps through the [/Engineering%20Design%20Process Engineering Design Process] on their way to building a successful business, while solving a simple problem for millions of users.

  • Ask – Kevin Systrom outlines the specific steps that he and Mike Krieger took to identify the problem. People with cell phones wanted to share photos they took. The pictures weren’t going to be great. Uploads were slow. People want to share via Facebook, Twitter, etc. This is the “what” problem.
  • Imagine – The next step was “how” – Their job was to figure out how to fix these problems. By looking at the requirements, they came up with ways to provide improvements – fixing the photos, limiting size of display, transferring the photo while the user was adding the caption, and sharing with multiple other services. What technologies were available? How could they provide the service that people wanted?
  • Design, Build – The planning and design went well. They planned to launch Instagram in a small way and grow as they learned more about user needs and preferences. When they had built what they thought was a pretty good product, they released it, expecting a few people to try it out. These early users would give them feedback so they could see where they were providing the right services and add or fix their product. Boy, were they surprised! 20,000 users wanted to use it!
  • Improve – Usually, after a product release, users use the product and provide feedback, and the creators get to see how the product is used. Then they can decide what changes to make and schedule a good time upgrade the product. Sometimes changes must be made immediately because of some unforeseen problem – like unexpectedly high number of users that overwhelmed the Instagram server. To their credit, Systrom and Krieger were able to recover and “improve” the scalability of their product quickly and go on to great success.

That’s engineering

  • deductive reasoning – attempts to show that a conclusion must follow from a set of premises or hypotheses. A deductive argument is valid if the conclusion follows necessarily from the premises.
  • Consistency – no premise contradicts another.
  • Validity – rules of proof never allow a false inference from true premises.
  • Completeness – if a formula is true, it can be proven

Engineering ideas

  • recursion, fractals, complexity, states of a system, logic, patterns, behavior, predictability, scalability, consistency, validity, soundness, completeness, premise, hypotheses, deduction

Do it
Here are some challenges for you to work on…

  • Tinkerbox (game-based learning, app, free) Stretch your brain through the devious Puzzle mode. Get immersed in physics-based puzzles and mechanical concepts, where your only hope for success is your creative problem solving.
  • PBS Kids – interactive games – problem solving for younger kids.
  • Sector 33 (game-based learning, app, free) – As the lead air traffic controller for Sector 33, merge the arriving planes into a single traffic stream as they pass over Modesto, CA on the western edge of the sector. The planes must be properly spaced and arrive over Modesto as soon as possible.
Learn more...