Ten Steps to Logical Problem Solving

1. Be clear about what you are trying to find out.
• What are the givens?
• What are the boundary cases?
• What will the solution look like?
• What do I need to know to solve the problem?
2. Draw a picture or build a model if possible.
• Can I draw a table, graph, or picture?
3. Know the possibilities.
• Games: What moves are allowed?
• Programming: What commands do I know?
• In general: What steps are there to choose from?
4. Do some examples.
• Are there some small examples I can already do?
• Is there a way to simplify the problem specification to start with?
5. Find patterns.
• Can I do enough examples that I see a pattern in the answers?
• Can I categorize the problem into cases?
• Once the pattern emerges, can I use variables to give a generic answer?
6. Work backwards.
• Can I start with the end result and examine the process to get there?
7. Approximate the answer.
• Can I use estimation to get an idea of the answer?
8. Guess and check.
• Can I use process of elimination to zero in on the answer?
• Can I apply brute force?
9. Know the constraints.
• What is the limited resource?
• Am I making the most of it?
10. Verify your answers according to the first step
• Does the answer make sense?
• Does it match my initial estimation?