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

# Strategy

We need to figure out a strategy to find the correct number in the given range of numbers. However, first, we need to think of a way to find a number out of the 50 numbers with minimal guesses.

Can we use random guesses?

Guessing 20 will give one of the three possible outputs. Either we would guess the number correctly, or the number would lie in the range of either 1–19 or 21–50. We need to keep the following questions in mind while making guesses:

- Do we have to be specific while guessing the number?

- Is there any pattern in our guesses?

Guessing 25 divides the range into two almost equal ranges, 1-24 and 26-50.

We've gathered all the information from the problem statement, and now we need to develop a pattern of guesses to achieve our goal. However, we do not know how to do that.

It's important to ask ourselves if we've encountered such problems before.

We see problems similar to this daily, like finding a specific item (e.g., keys, phone, or glasses) in our houses.

Is there any specific strategy to solve this number-guessing game? We can divide the problem into smaller parts, solve each part independently, and then merge the solution to solve the bigger problem.

We can break our problem up like this:

- We can start with the middle number (25) in the given range as our initial guess.
- Based on the computer’s hint, we can divide the search range in half:
    - If the hint is higher, we have a new updated range.
    - If the hint is lower, we have another specific range of numbers.

Polyas method

Bottom-Up Approach

Top-Down Approach

Wire Length Calculator

Stepwise refinement

Guessing Games

Minesweeper Game

Triangular Wall

Pattern Identification

Conclusion

Devising a Plan: Strategy

Strategy