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

# Applying the solution

Let’s execute the plan we made in the previous step. The first step is to have the 9-quart pail full and put one quart of water in a 4-quart pail by performing the following:

To measure six quarts of water in the 9-quart pail, we should have one quart of water in the 4-quart pail.

We know how to measure one quart of water from the previous lesson. Let’s follow the same steps.

To measure one quart of water, we need five quarts of water in the 9-quart pail. To measure five quarts, we need the 9-quart pail full and the 4-quart pail empty.

1. Fill the 9-quart pail.
2. Fill the 4-quart pail from the 9-quart pail, leaving 5 quarts in the 9-quart pail.
3. Empty the 4-quart pail.
4. Fill the 4-quart pail from the 9-quart pail, leaving 1 quart in the 9-quart pail.

The entire process is illustrated in the slides below.

Polyas method

Bottom-Up Approach

Top-Down Approach

Wire Length Calculator

Stepwise refinement

Guessing Games

Minesweeper Game

Triangular Wall

Pattern Identification

Conclusion

Carrying Out the Plan

Applying the solution