Nowadays, the reasons why people got trouble is that misunderstanding the problem and don't have the proper way of solving it. In solving problem requires practical knowledge about the specific situation. If you misinterpret either the problem or underlying situation you may fail to solve it. So today our main goal is to become a better problem solver.

Before anything else here are the four-step approach to solve the problem.

Polya's Four-Step Approach To Problem Solving

1.Preparation: Understand the Problem

• Find the necessary underlying mathematical concepts.
  

• Consider the terminology and notation used in the problem.

  1. What sort of a problem is it?
     This process you need to know what kind of problem it is.
  2. What is being ask?
     
  3. What do the terms mean?
     The term is to each other it means 28 persons should say hellos to each other. It means that you will multiply 28 persons to 27. Why 27 ? You will not include yourself in multiplying because you will not say hello to yourself.
  4. Is there enough information or is more information needed?
     In problem #1 it gives enough information. You have the given which is the 28 persons and the problem being asked.
  5. What is known or unknown?

• Rephrase the problem in your own.
  If you don't understand well the problem you will translate it in your own language for you to understand the situation well.

• Write down specific examples of the conditions given in the problem.
  

2. Thinking Time: * Devise a plan

• You must start somewhere so try something. How are you going to attack the problem? So here are the possible strategies.

Possible Strategies

1. Draw pictures.
   • Draw pictures if necessary.
2. Use a variable and choose helpful names for variables or unknowns.
   • Use names or variables in solving the problem so that you may not confuse.
3. Be systematic.
   • Be careful in using systematic ways. Be sure that method is related or suit to the problem.
4. Solve a simpler version of the problem.
   • Solve the problem in easier ways so that you may not be stress or confuse in solving it.
5. Guess and check. Trial and error. Guess and test.
   • Trying out to solve the problem is fine. You may not answer it correctly at first time but you can in second time. Trial and error as we can call it.
6. Look for pattern or patterns.
7. Make a list.
   

3. Insights: Carry out the plan

• In solving the problem you need to have a plan first. You need to think what approach you should use to start answering the problem.
• If your plan seems not working,then start over again and try another approach. Often the first approach does not work, it doesn't mean that you get it wrong. You actually accomplished something, Knowing a way does not work is part of tge process of elimination.
• Once you have thought about a problem or returned to it enough times, you will often have a flash of insight: a new idea to try or a new perspective on how to approach solving the problem.
• This key is to keep trying until something works.

4. Verification: Look back

• Once you have a potential solution, check to see if it works.
  1. Did you answer the questions?
  2. Is your result reasonable?
  3. Double check to make sure that all of the conditions related to the problem are satisfied.
  4. Double check any computation involved in finding yiur problem.
• If you need that your solution does not work, there may only be a simple mistake. Try tonfix or modify your current attempt before scrapping it. Remember what you tried--it is likely that at keast part of it will end up being useful.
• Is there another way of doing the problem which may be simpler?( You need to become flexible in your thinking. There usually is not one right way.)
• Can the problem or method be generalized so as to be useful for future problems?

To evaluate if you get some knowledge of the approaches here are some problems that you may try to answer.

Thank you and God bless!