How to Solve Difficult Problems

Life throws problems our way constantly. From fixing a leaky faucet to figuring out the best career path, navigating these challenges can feel overwhelming. But what if there was a secret weapon you could use to solve difficult problems with confidence?

In 1945, mathematician George Pólya wrote a powerful, little book titled “How to Solve It“. This timeless classic goes beyond just math problems and offers a powerful framework for tackling any challenge life throws your way. This book isn’t just a collection of dusty equations; it offers some practical steps to sharpen your thinking and conquer any problem.

The Four Pillars of Problem-Solving Success

Pólya doesn’t just throw problem-solving techniques at you. Instead, he offers a structured approach with four key steps that guide you from confusion to solution. He basically breaks solving difficult problems into four steps:

1. Understanding the Problem: This might seem obvious, but it’s the foundation for any successful solution. Pólya emphasizes the importance of truly grasping the problem’s core.
   
   What are you trying to find (the unknown)?
   What information do you have (the data)?
   Is the problem even solvable with the given information?
   
   Most of the time we rush to solve the problem thinking we know what the problem is. But I found out that this isnt always the case for me. Sometimes I think I know what the problem is but when I go and search for the solution, I end up raw away from the solution. And this is because I dont really understand the problem. By wrestling with the above questions, you gain a clear understanding of the battlefield before diving into strategies.
   
2. Devising a Plan: Now that you understand the enemy (the problem), it’s time to formulate a battle plan. Pólya suggests looking for similar problems you’ve encountered before.
   
   Have you ever tackled something like this?
   Is there a related problem whose solution can be adapted to your current situation?
   
   Sometimes, the key lies in recognizing familiar patterns and applying past knowledge in new ways. There is always a solution out there but the solution isnt always complete. It has to be pieced together, bits and pieces.
   
3. Carrying Out the Plan: This is where you put your carefully crafted plan into action. Following your chosen strategy, you actively solve the problem. Pólya emphasizes the importance of working through the solution step-by-step. Don’t be afraid to break down complex problems into smaller, more manageable chunks.
   
   There is only one way to eat an elephant: one bite at a time.
   
4. Examining the Solution Obtained: Did you conquer the problem? Here’s where you double-check your answer. Is your solution logical and consistent with the given information? Sometimes, a fresh look can reveal errors or even lead to more elegant solutions. Don’t be afraid to revisit your steps and refine your answer! In chess, the famous world champion, Gary Kasparov used to say, “When you find a solution, find another!”

Beyond Math: A Universal Approach to Life’s Challenges

The beauty of Pólya’s approach – it’s not limited to the realm of mathematics. These four steps can be applied to any problem life throws your way. Stuck on a project at work? Use Pólya’s framework to understand the project’s goals, devise a plan to achieve them, execute your plan step-by-step, and finally, evaluate your progress and results.

A Timeless Classic: Why “How to Solve It” Still Matters

Published in the mid-20th century, “How to Solve It” might seem like a relic from a bygone era. However, its core message – a structured approach to problem-solving – is as relevant today as ever. In a world filled with information overload and complex challenges, Pólya’s book equips you with a practical framework to navigate uncertainty and find solutions.

Sharpen Your Thinking and Embrace the Challenge

Whether you’re a student tackling a challenging math problem or a working professional navigating complex projects, by embracing Pólya’s four-step approach, you can transform problem-solving from a daunting task into an empowering journey of discovery.

So, the next time you encounter a challenge, remember the wisdom of “How to Solve It” and approach it with a structured plan and a confident mind.