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

A $19^{th}$ century naval commander devised an ingenious means of communicating with other ships in their fleet. They employed light signals by devising a set of special bulbs, each capable of toggling between red and green states. Intrigued by their potential, they explored how different arrangements could convey different messages. Initially, with only two bulbs, they found that they could transmit four distinct messages by altering the bulbs’ states.

As they delved deeper, experimenting with larger arrays of bulbs, they pondered the potential messages that were achievable with a 10-bulb array. Counting arrangements with up to four bulbs was manageable, but they sought assistance as the complexity grew with each added bulb. Their future endeavors hinged on the number of messages they could convey with these bulbs. Can we assist them in deciphering this puzzle?

> **Note:** "R G" and "G R" are two different combinations.

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