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 sum of all the numbers from 1 to 50. Here are some questions to note:

- Can we simply sum all the numbers on paper?

- Do we need to use a calculator to add these numbers?

While it’s possible to add these 50 numbers using a calculator or pen and paper, the process is quite difficult and prone to errors. 

Forgetting to include a number or accidentally adding one more than once are common mistakes. Furthermore, when dealing with a larger set of numbers, verifying the accuracy of the result becomes difficult.  

These are tough challenges. Is there a way to tackle these issues? Has anyone previously solved a similar problem?

## The genius of Gauss

The brilliant mathematician Carl Friedrich Gauss was just a young student when he astounded his teacher by discovering a quick and elegant method to find the sum of consecutive numbers.

One day, Gauss’s teacher asked his class to add all the numbers from 1 to 100, assuming that this task would occupy them for quite a while. He was shocked when young Gauss, after only a few minutes, wrote down the answer. The teacher couldn’t understand how his pupil had calculated the correct solution so quickly in his head, but the eight-year-old Gauss pointed out that the problem was actually quite simple.

It was undoubtedly a challenging problem, especially for young children. Nevertheless, the eight-year-old Gauss devised a solution that ingeniously solved the problem.

He observed that there are a total of 100 numbers from 1 to 100, and if we add the first and last numbers in the sequence, the second and second-last numbers in the sequence, and so on, they will add to 101 for each pair.

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

The genius of Gauss