# How To Solve It

**2023-04-27**

## Steps in solving a problem

Step 1: Understand the problem. Step 2: Devise a plan to solve the problem Step 3: Carry out the plan Step 4: Look back and review

## Understanding the problem

Ask the following questions: What are the data? What are the conditions? What are the unknown? Have we utilised all the information? For problems to prove, hypothesis and conclusion are principle parts. For problems to find, data and conditions are principle parts. Can the problem be represented as a figure? If so, draw a figure.

## Steps for arriving at solution

- Is there a related problem which can be solved? A problem can be varied by generalization, specialization, analogy, decomposing and recombining. A problem can be decomposed by seperating the various parts of the condition.
- Can a part of the condition be removed and solved?
- Can a related problem, a smaller problem be solved if you cannot solve the current problem?
- Have you seen it before?
- Can a solution of a different problem be used?
- Heuristic reasoning
- Make guesses but also examine and validate the guesses - our guesses can be wrong.
- Use notations to describe the problem - a good notation must be unambiguous, easy to remember, it should have no second meanings.

To arrive at a solution, we have to recall various facts, theorems, definitions and formerly solved problems from our memory. Information must be mobilized, organized and adapted to the problem at hand.

Carrying out the plan - start from the idea that leads to the solution. Look back and review - during review, we may find a new way to arrive at the solution or discover a new technique to solve the problem.