How to Solve It

Pólya's Four Principles of Problem Solving

1. Understand the problem.
2. Make a plan.
3. Carry out the plan.
4. Check your work & try to improve it.

Note: if you can't solve a problem, try first to solve a related easier problem.

Principle 1:

Understand the Problem

• What are you being asked to find?
• Can you restate the problem in your words?
• Can you think of a picture or diagram to understand the problem?
• Is there enough information to find a solution?
• Do you understand the words used in stating the problem?
• Do you need to ask a question to solve the problem?

Principle 2:

Make a Plan

Develop a strategy to attack the problem. Example strategies which can be applied separately or together:

• Guess and check.
• Look for a pattern.
• Eliminate possibilities.
• Consider special cases.
• Use a formula or equation.
• Exploit a symmetry.
• Solve a simpler problem.

Principle 3:

Carry out your Plan

• Try to solve the problem using the plan or strategy you decided is best.
• Be patient and persistent... but remember that you are not married to your first plan.
• If you hit a wall, you can cut your losses and try a different plan.

Principle 4:

Review & Extend

• Look back at your result.
• What worked?
• What didn't work?
• Can you use what you learned in future problems?