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

# Problem

We have a rectangular grid of cells, where each cell can be in one of the following states:

- It can have a number from 1 to 8 representing the count of mines in the adjacent cells (including diagonals).

- It can be an empty cell that represents neither a mine nor a number.

- It can be a mine. 

The game starts as follows:

- All the squares are covered at the start. We can uncover a square by left-clicking it.

- When we uncover a square, it will either be empty, contain a number, or contain a mine. If a mine is uncovered, the game ends. The number represents how many mines are adjacent to that square (in the eight surrounding squares). If a square has no mines nearby, it will be completely empty.

- If we suspect a square contains a mine, we can mark it with a flag by right-clicking it to prevent accidental clicks.


In this game, the goal is to utilize the provided clues to accurately locate all the mines, mark them with flags, and uncover all the cells without triggering any explosions.



Get an overview of the problem in this chapter and try to understand it.

Polyas method

Bottom-Up Approach

Top-Down Approach

Wire Length Calculator

Stepwise refinement

Guessing Games

Minesweeper Game

Triangular Wall

Pattern Identification

Conclusion

Understanding the Problem

Problem