Introduction to Pólya’s Problem-Solving Process

We’ve tried out a few games, and at first glance, it might seem like winning or losing in these games is purely random. However, behind each game lies logical steps that lead to victory. Our goal is to discover the winning strategies for such games. To achieve this, let’s take guidance from an expert named George Pólya.

G. Pólya was a mathematician who introduced the art of problem-solving by breaking the problem into multiple steps. His method has since become a cornerstone in teaching problem-solving skills across various disciplines. In this course, we will learn about problem-solving skills and how to solve different problems using G. Polya’s renowned 4-step method.

The steps of problem-solving

G. Pólya’s 4-step method, which solves a problem by breaking the problem up, will be our guide throughout this course. He outlined this method in his book “How to Solve It” These steps provide a structured and systematic approach to problem-solving.

Step 1: Understand the problem

Before moving forward with finding the possible solution to a problem, we have to understand the problem. This includes contemplating the points outlined in the image below:

Step 2: Devise a plan

Next, we should think of the best possible plan to solve the problem. There are a number of strategies we can consider:

While discussing the problem-solving process, it is important to discuss problem-solving techniques.

There are a variety of problem-solving techniques at our disposal but the approach we choose greatly relies on the nature of the problem itself. Here are some of these techniques:

• Bottom-up approach
• Top-down approach
• Divide and conquer
• Stepwise refinement
• Analogy
• Induction/pattern matching

Step 3: Carry out the plan

After the second step, we execute the plan we made and solve the problem. The following image shows some key points to consider during the problem-solving process:

Step 4: Look back

After the execution, we need to look back at the problem and review the solution we found. We need to assess if it is the right approach and confirm our solution by following the steps outlined in the image below.

In the following lessons, we’ll focus on mastering the intricacies of the first three of these four steps, exploring them in detail through practical applications in various games and puzzles. During this process, we’ll try to discover the winning strategies for the challenges. Now let’s move forward and open the door to a world of exciting possibilities by solving problems!