How to Solve Any Problem

I find most people fail at solving a problem because they first do not understand how to fundamentally solve any problem.

This is a copy/paste from the original source where I found it. I did not want to lose the content as it looks like that site has been abandoned.

How To Solve It is a short volume by mathematician George Polya describing various methods of problem solving. The book has achieved classic status in its field because of its considerable influence.

In reading Polya’s book, I found distinct parallels to popular self development resources throughout history. Although the book outlines techniques used in mathematical problem solving, the same formulas can be applied to the practice of goal setting.

How To Solve It suggests the following steps when solving a problem:

  1. Understand the goal.
  2. Devise a plan.
  3. Carry out the plan.
  4. Look back on your work.

A more definitive description of each of the above techniques follows:


This principle is often neglected as being cliché and obvious. Yet individuals remain stifled with their efforts to achieve goals, simply because they don’t understand them. To remedy this oversight, Polya taught teachers how to prompt each student with appropriate questions dependent on their desired outcome:

  • What are you seeking to complete?
  • Can you state the goal in your own words?
  • Can you think of a picture or a diagram that might help you understand the goal?
  • Is there enough information to enable you to find an outcome?

The teacher is to select appropriate questions to ascertain if the student understands the goal at their core, and continues until the individual can respond with something focused and constructive.


Polya mentions that there are many reasonable ways to achieve goals. You will find it to be increasingly easy as you progress and learn how to overcome different limitations. A partial list of strategies include:

  • Guess and then check.
  • Make an orderly list.
  • Use symmetry. [Mimic success.]
  • Consider special cases.
  • Use direct reasoning.
  • Look for a pattern.
  • Draw a picture.
  • Solve a simpler problem. [Work on menial but relevant tasks.]
  • Use a model. [Implement available resources.]
  • Work backward.
  • Be creative.
  • Use your head.


This step is usually easier than devising the plan itself. In general, all you need are the following strategies in achieving your goals:

  • Care and patience.
  • Faith that you have the necessary skills.
  • Persist with the plan that you have chosen.
  • If it continues not to work: discard it and choose another.
  • Don’t be misled. [This is simply how shit is done.]


Polya mentions that much can be gained by taking the time to reflect and look back at what you have done. What worked? What didn’t?

Doing this will enable you to predict which strategy to use to solve future problems. If all else fails and you cannot achieve the proposed goal, try to solve first some related goals. Can you imagine a more accessible related achievement? Make it happen.

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