Problem Solving

Introduction

• Problem-solving is an inherent skill everyone possesses.
• Problems range from simple decisions (e.g., what to eat) to complex theories (e.g., theory of relativity).

Types of Problems

• Well-Defined Problems:
  • Clear starting and ending points.
  • Example: Making a dark room bright.
• Ill-Defined Problems:
  • Ambiguous starting and/or ending points.
  • Example: Living a happy life.

Methods of Problem Solving

1. Trial and Error

• Random guesses until a solution works.
• Example: Trying random passwords for an account.
• Not efficient and can be time-consuming.

2. Algorithm

• Logical, step-by-step procedure.
• Guarantees a solution but can be time-consuming.
• Example: Systematic password combinations.

3. Heuristic

• Mental shortcuts for quicker solutions.
• Doesn’t guarantee a correct solution but simplifies the process.
• Example: Using familiar number combinations for passwords.

Types of Heuristics

Means-End Analysis

• Break down the problem, solve the largest subproblem first.
• Example: Planning a trip by first booking a plane ticket.

Working Backwards

• Start with the goal state and trace back to the current state.
• Used in mathematical proofs and solving mazes.

Insight and Fixation

• Fixation: Getting stuck on a specific perspective.
• Insight: Sudden realization or "aha moment".
  • Example: Solving the matchstick problem by thinking in three dimensions.
• Incubation: Letting a problem "sit" in the mind might lead to a sudden insight later.

Conclusion

• Problem-solving involves various strategies and it’s important to find the most appropriate method depending on the problem.
• Insight and incubation are valuable but unpredictable in problem-solving.