Explore different problem-solving strategies that are essential for personal growth, academic success, and sustained professional achievement.

Computer Science Bootcamp

Problem-solving skills empower individuals to adapt and face challenges resiliently, resulting in efficiency, innovation, and effective decision-making. This versatile skill set is more than an immediate problem-solving tool; it is a lifelong asset essential for personal growth, academic success, and sustained professional achievement.

In this module, you’ll learn and apply Polya’s problem-solving process, using it as your guide to tackle various games and puzzles. Additionally, you’ll explore different problem-solving strategies, including the top-down approach, bottom-up approach, divide and conquer, stepwise refinement, analogy, and induction/pattern identification.

After completing this module, you’ll acquire the expertise to apply Polya’s systematic approach to resolving intricate problems and establish the groundwork for a lifelong skill set. This comprehensive understanding will empower you to master effective strategies for problem-solving.

Learn Problem-Solving with Pólya

# 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.

Introduction

Measuring Quantities with a Bottom-Up Approach

Solving the Farmer’s Dilemma by Embracing a Top-Down Approach

Using an Analogy for Calculating the Length of Wire

Unveiling the Bear’s Color with a Stepwise Refinement Strategy

Using Divide and Conquer to Win the Number Guessing Game

Applying Divide and Conquer for Mastering Minesweeper

Cherishing Gauss’s Genius of Spotting Patterns

Utilizing Pattern Identification for Counting

Conclusion

Understanding the Problem

Problem