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How to Solve It
George Pólya's four-step framework for approaching any problem — mathematical or otherwise. Scroll through the steps below; the rail on the left tracks your progress.
- 01
Understand the Problem
Before searching for a method, get clear on what you're actually solving. Name the unknown, the data you've been given, and the condition that ties them together. Restate the problem in your own words — if you can't paraphrase it, you don't understand it yet — and sketch it out if a diagram would help.
- 02
Devise a Plan
Look for a bridge between what you have and what you want. Has a similar problem been solved before, and can its method be adapted here? Try a simpler or related version first, or work backward from the goal. A plan rarely arrives fully formed — it's built from small, testable connections between the known and the unknown.
- 03
Carry Out the Plan
Execute the plan step by step, but don't just push forward — check each step as you take it. A step should be provably correct, not merely plausible. Patience here matters more than speed; a fast wrong turn costs more than a slow, correct one.
- 04
Look Back
Once you have a result, don't move on immediately. Check it against the original problem — does it actually answer the question that was asked? Look for a different way to reach the same result, and consider whether the method generalizes. This is the step where a solved problem turns into reusable knowledge.