Learning

Art of Problem Solving

Frameworks and mental models for effective problem solving.

Art of Problem Solving

Problem solving is a skill that improves with deliberate practice and the right mental frameworks.

Core Frameworks

Define Before Solving

Most failed solutions solve the wrong problem. Spend more time understanding the problem than jumping to answers.

Break It Down

Decompose complex problems into smaller, solvable pieces. Solve each piece. Combine.

Work Backwards

Start from the desired outcome and trace back to the current state.

Analogies

Find similar problems in different domains. Solutions often transfer.

First Principles

Strip away assumptions. What do you know to be true? Build up from there.

Practice

  • Math competitions (AMC, AIME) build rigorous thinking
  • Programming challenges (LeetCode, Project Euler) build implementation skill
  • Real-world problems build judgment about which framework to apply

The best problem solvers aren't the smartest — they're the most systematic.

Original reference on problem-solving frameworks