Learn Polya’s problem-solving process and strategies, such as divide and conquer and pattern identification, to enhance your analytical skills, tackle puzzles, and solve real-world problems.

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Problem-solving skills are vital for personal growth, academic success, and professional achievement. They enable resilience, innovation, and effective decision-making. This course equips you with a lifelong skill set by teaching Polya’s problem-solving process and its applications in tackling real-world problems, games, and puzzles.

You will explore strategies, including top-down and bottom-up approaches, divide and conquer, stepwise refinement, pattern identification, and logical reasoning through puzzle-solving and computing logic.

By the end of the course, you’ll master analytical skills and critical thinking to apply Polya’s method and other strategies to complex challenges. This comprehensive approach establishes a strong foundation for systematically solving intricate problems.

Problem Solving

We have our strategy. Now, we can try to solve the problem.

# Solution

We have to repeat the steps discussed in the strategy in the previous lesson.

Let’s say the correct room number is 15, and we do not know it yet. Here is a viable plan to solve this problem:

- We can start with the middle number in the given range as our initial guess (e.g., 25).
- This guess is too high. Our new range will be 1–24.
- We can guess the middle number in the range. Let’s guess 12.
- This guess is too low. Our new range is 13–24.
- We can guess the middle number in the new given range. Let’s guess 18.
- The guess is too high. Our new range is 13–17.
- The middle number in the new given range is 15. Let’s guess it. It is the correct number.

This solution looks like this:


Polyas method

Bottom-Up Approach

Top-Down Approach

Wire Length Calculator

Stepwise refinement

Guessing Games

Minesweeper Game

Triangular Wall

Pattern Identification

Conclusion

Devise a Plan: Solution