How to Solve It

Life is full of problems.

The more you solve them, the more new ones come up.

And you can sweep problems under the carpet or run away from them.

Wherever you go, sooner or later there will be problems for you to solve.

Since this is a fact of life, you may as well develop some skills on how to handle problems in life.

Here are some insights on how to deal with problems in life so that you may achieve success and happiness.

One of the best ways to handle problems is to have the right attitude towards them.

Sometimes problems may be blessings in disguise.

Problems may be a way that existence is trying to assist us to create opportunities for us to grow and become better human beings.

Problems can hide opportunities not only for personal growth but also to create wealth and success.

For every problem, there should be a solution.

Whenever you encounter any problem that has no solution, you may well understand that it is not a problem to begin with.

Problems are also the first step in a new invention.

We wouldn't have automobiles today if people had not had problems getting from place to place quickly.

Every single invention was created because people had problems with something, so problems can really be motivational!

Problems also help you to meet new friends. If you are recently divorced,
you may join a group and meet some wonderful friends that will bring you
into a better life than the life you were living previously.

If you have a problem getting back and forth to work, you may decide to join a carpool and save money while meeting others.

Problems also are always a learning experience. You don't actually realize
that fire burns until you get burned with it!

Unless a problem occurs, you do not learn why something happens the way it does. You cannot change your viewpoints and opinions unless you experience problems first hand.

Problems also cause you to become active in helping others. The organization
M.A.D.D. (Mothers Against Drunk Drivers) would have never been born if the
founder didn't lose her daughter in a car accident caused by a drunk driver.

Without problems, we couldn't solve a lot of future turmoils and save people
a lot of money in business.

Any company that introduces a new product will hire people to try it out before it is introduced to the market.

These people report the problems they find and the company refines it until it's right.

Without problems developing early in these tests, the company could never
improve and fine tune their product to perfection.

Attack the core of the problem! Dig until you uncover it! Face facts! Admit you have problems!

Stop trying to make people think you are problem-free. It's unnatural!

When you solve a problem that most people try to avoid or can't solve, you get recognition and their admiration.

You may become a hero or heroine.

So, next time you have a problem, look at it logically and with enthusiasm.

That may sound a little strange but most problems can be dealt with this way.

Love the fact that you have problems because they will give you something to work on and solve.

They also will give you a way to invent new ways of doing something, new ways that will save you time and make you happier with your life.

And when you solve problems, you not only gain experience in solving other problems as they occur, but you build respect for yourself.

Then you can have the admiration of all those people who encountered the same problems but didn't do anything to solve them.

You also will find that when you look at problems with a POSITIVE mind, you
will accomplish more, relieve stress and succeed.

May these insights about problem solving help you to succeed in life and be all you can be.

Four principles

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

  1. First, you have to understand the problem.
  2. After understanding, then make a plan.
  3. Carry out the plan.
  4. Look back on your work. How could it be better?

If this technique fails, Pólya advises: "If you can't solve a problem, then there is an easier problem you can solve: find it." Or: "If you cannot solve the proposed problem, try to solve first some related problem. Could you imagine a more accessible related problem?"

Heuristic Informal Description Formal analogue
Analogy Can you find a problem analogous to your problem and solve that? Map
Generalization Can you find a problem more general than your problem? Generalization
Induction Can you solve your problem by deriving a generalization from some examples? Induction
Variation of the Problem Can you vary or change your problem to create a new problem (or set of problems) whose solution(s) will help you solve your original problem? Search
Auxiliary Problem Can you find a subproblem or side problem whose solution will help you solve your problem? Subgoal
Here is a problem related to yours and solved before Can you find a problem related to yours that has already been solved and use that to solve your problem? Pattern recognition
Pattern matching
Specialization Can you find a problem more specialized? Specialization
Decomposing and Recombining Can you decompose the problem and "recombine its elements in some new manner"? Divide and conquer
Working backward Can you start with the goal and work backwards to something you already know? Backward chaining
Draw a Figure Can you draw a picture of the problem? Diagrammatic Reasoning
Auxiliary Elements Can you add some new element to your problem to get closer to a solution? Extension

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