Fixing A Broken Tap With George Pólya

In this post, I use the principles in “How To Solve It” by George Pólya to diagnose and fix my broken kitchen tap. Yes – really.

Table of Contents


Bit of a change this time. Let me set the scene.

It’s time to top up Wolfie’s water bowl, so to the kitchen sink we go. Two unexpected events happen when the tap is turned on:

  1. The water flow goes mental and starts spraying everywhere.
  2. Something gets launched out of the tap into the water bowl:
Aerator Initial

My first thought is that the tap is broken and that I’ll need to buy a new one. And then get a plumber to fit it. Great.

But wait. Last year I fixed some broken panes in our greenhouse. This year I’ve built a potting bench, fixed a leaky water butt and mounted a shower rail. Is this a problem I can solve?

This Doesn’t Sound Like Technology

True. It is, though, a chance to write a post I’ve fancied doing for a while. And this set of circumstances was too compelling to pass up.

Last year I became aware of a book called “How To Solve It” by George Pólya. The recommendation included a chart based on the book, similar to this one:

Source: KPMathematics

What struck me was how close these steps were to the Systems Development Life Cycle I was taught at college. My interest was piqued.

Around the same time, I was getting to grips with my new Data Engineer role. Since then, I’ve used the “How To Solve It” principles to help me complete work both for my role and for this blog.

Now, faced with a new unfamiliar situation, I can demonstrate how the “How To Solve It” principles can be applied beyond mathematics. In this case I’m fixing a broken tap, but this could just as easily be a Python bug, a poorly performing SQL query or an AWS authentication issue.

Here is my plan:

  • Firstly, I’ll examine the “How To Solve It” book.
  • Secondly, I’ll look at the author of the book – George Pólya.
  • Then I’ll look at each of the George Pólya principles, relating them to the broken tap problem I want to solve.

Let’s start with the book.

How To Solve It

Source: Penguin

‘A superb book on how to think fresh thoughts … A walk inside Pólya’s mind as he builds up maxims on how to comprehend a problem, how to build up a strategy, and then how to test it.’

David Bodanis, Guardian

‘Everyone should know the work of George Polya on how to solve problems’

Marvin Minsky

How To Solve It can be bought on Penguin’s website.


How To Solve It was written in 1945 by George Pólya. Since then, the book has stayed in print and has been translated into over a dozen languages. It has sold more than 1 million copies, making it one of the most widely circulated mathematics books in history.

Four Principles

How To Solve It explains in non-technical terms how to think about invention, discovery, creativity and analysis. Central to this are four principles:

  1. First. You have to understand the problem.
  2. Second. Find the connection between the data and the unknown. You may be obliged to consider auxiliary problems if an immediate connection cannot be found. You should obtain eventually a plan of the solution.
  3. Third. Carry out your plan
  4. Fourth. Examine the solution obtained.

The book also poses several questions for each principle. They aim to stimulate thought and produce the answers needed to satisfy each principle.

These can be seen in the below image from the book’s first edition:

2022 10 25 HowToSolveItInsideCover

They are also available as text from the University of Utah’s summary of 1957’s second edition.

Although How To Solve It was written with mathematics in mind, the book’s principles have been applied to additional disciplines over the decades. Pólya seems to take great care not to limit the scope of How To Solve It, speaking of problems in general terms throughout the book.

One such example is this extract:

A great discovery solves a great problem but there is a grain of discovery in the solution of any problem. Your problem may be modest; but if it challenges your curiosity and brings into play your inventive faculties, and if you solve it by your own means, you may experience the tension and enjoy the triumph of discovery.

“How To Solve It” – George Pólya

How To Solve It remains in high regard to this day. The Math Sorcerer produced this video in July 2022, and his affection for the book is clear.


Next, let’s look at the book’s author – George Pólya.

George Pólya

George Pólya
Source: MacTutor

George Pólya (December 13 1887 – September 7 1985 aged 97) was a Hungarian mathematician. He was a professor of mathematics from 1914 to 1940 at ETH Zürich in Hungary, and from 1940 to 1953 at Stanford University in North America having moved there during World War 2.

After retiring from Stanford, Pólya remained active in his field. He continued his association with Stanford as Professor Emeritus well into his 90s and taught a course in their Computer Science Department in 1978.


In pure mathematics, Pólya made important discoveries in fields including probability, real and complex analysis, combinatorics, geometry, number theory and mathematical physics.

Several of his discoveries bear his name, including:

Pólya also authored and contributed to numerous books and articles throughout his life, a selection of which can be seen on Wikipedia.


Pólya was well-regarded by his peers and awards given to him included:

“He has given a new dimension to problem-solving by emphasizing the organic building up of elementary steps into a complex proof, and conversely, the decomposition of mathematical invention into smaller steps.”


“Problem solving a la Polya serves not only to develop mathematical skill but also teaches constructive reasoning in general.”


There is much more to know about Pólya. The following links detail his life, works and legacy in far greater detail:

Now I’m going to apply the George Pólya principles to my broken tap!

Applying The Principles

In the following sections, I will apply each George Pólya principle from How To Solve It to my tap problem. In each section I will:

  • Quote each principle in full.
  • State the supporting questions that I’ll answer.
  • Relate these to my tap problem.

Principle 1: Understanding The Problem

First. You have to understand the problem.

“How To Solve It” – George Pólya
  • What is the unknown? What are the data? What is the condition?

The Unknown

The unknown is what I want. Here, I want to restore the tap’s original flow rate.

The Data

The data is the information available. This is what was expelled from the tap:

Aerator Initial

Other data:

  • Water was still flowing from the tap.
  • The flow of water was under more pressure than before.

The Condition

The condition is the link between the unknown and the data. Here, whatever has come out of the tap has changed the water’s flow but hasn’t obstructed it.

Principle 2: Devising A Plan

Second. Find the connection between the data and the unknown. You may be obliged to consider auxiliary problems if an immediate connection cannot be found. You should obtain eventually a plan of the solution.

“How To Solve It” – George Pólya
  • Do you know a related problem? Do you know a theorem that could be useful?
  • Here is a problem related to yours and solved before. Could you use it? Could you use its result? Could you use its method?

I searched Google for the phrase “kitchen tap water flow changed”. There was an immediate common thread in the results:

2022 10 26 GoogleResults

The Estes Services link gave a useful definition of an aerator:

“The aerator on your faucet is a mesh screen and covers the water outlet. The aerator catches minerals and other debris in your pipes. It also helps save water by introducing air into the water stream.”

“How to Fix Low Water Pressure in Kitchen” on Estes

Getting somewhere! This led me to “Everything you Need to Know About Tap Aerators” on TapWarehouse, which includes this:

“They save you water by adding oxygen to the flow (and that means saving pennies) and reduce splashing around the bowl of the basin.”

“Everything you Need to Know About Tap Aerators” on TapWarehouse

Mesh screen? Reduced splashing? This definitely sounded like the right area!

Solved Problems

At this point, what came out of the tap sounded very much like an aerator. However, there’s no cleaning something that’s disintegrated, so it was time for a replacement.

TapWarehouse to the rescue again:

“If your existing tap already has an aerator, simply turn it anticlockwise until it’s unscrewed from the tap. Then, simply screw in the new aerator until it’s secure, being careful not to screw it too tightly.”

How can I Install a Tap Aerator?” on TapWarehouse

TapWarehouse also gave advice on aerator types. There are male and female aerators depending on the tap. There are also various aerator sizes ranging from 16mm to 28mm.

Planned Solution

Based on this research, the solution needed the following steps:

  • Remove the broken aerator.
  • Confirm the aerator type.
  • Confirm the aerator size.
  • Buy a replacement aerator.
  • Fit the replacement aerator.
  • Test the replacement aerator.

Principle 3: Carrying Out The Plan

Third. Carry out your plan.

“How To Solve It” – George Pólya
  • Carrying out your plan of the solution, check each step. Can you see clearly that the step is correct?

Time to remove the broken aerator! Straight into a problem. It wouldn’t budge.

Fortunately, there’s a DIY StackExchange! Advice ranged from WD-40 to vinegar to a hammer and chisel (!), but in the end I used my heat gun on the aerator and removed it with pliers.

I then determines that I needed a 24mm male aerator as a replacement. One trip to B&Q later and:

Aerator Replacement

Fitting the new aerator was a simple matter of screwing it on.

Principle 4: Looking Back

Fourth. Examine the solution obtained.

“How To Solve It” – George Pólya
  • Can you check the result?


Tap with running water


In this post, I used the principles in “How To Solve It” by George Pólya to diagnose and fix my broken kitchen tap. I applied each of the Pólya principles to my problem, and was able to solve it by answering the relevant questions and doing some investigation with the knowledge gained.

If this post has been useful, please feel free to follow me on the following platforms for future updates:

Thanks for reading ~~^~~


My First Technical Job

In this post I respond to the May 2022 T-SQL Tuesday #150 Invitation “Your First Technical Job” and talk about my time as an Application Support Developer.

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This month, Kenneth Fisher’s T-SQL Tuesday invitation was as follows:

This month for TSQL Tuesday I’d like to hear about your first technical job(s). I know most DBAs don’t start out working with databases so tell us how you did start.

So let’s go back in time!

Application Support

My first technical job was as an Application Support Developer at Think Money Group. I’d been with TMG for almost six years at the time, starting in a customer service role before moving into an administrative role in 2012.

By 2016 I had a deep understanding of the organisation’s front and back ends, and had built several Excel and Sharepoint-based solutions to make various internal and regulatory processes easier to manage.

When a vacancy in Application Support became available that Summer, I went to meet the team and put an application in. My roles to date, knowledge of the organisation and technical skills were a good fit, and so I was welcomed aboard!

Application Support was responsible for supporting TMG’s bespoke applications. We had several tasks that I will give a brief overview of.

Ticketing System Triaging

This was my introduction to a ticketing system. As a team, we completed tickets from the backlog based on priority and age.

Incoming tickets needed to be triaged before they entered the backlog. This involved a couple of checks like:

  • Prioritisation: How urgent is the ticket?
  • Relevance: Is the ticket a reasonable request? Is it a duplicate of an existing ticket?
  • Serviceability: Is anything missing from the ticket? Can it be completed in its current form?

A correctly triaged and well-maintained backlog was essential. As a team, it helped us meet our SLAs and prevent bottlenecks and duplication. As individuals, it increased productivity and simplified the working day.


Common tickets would involve giving users access to services or features within the application. For example, granting access to certain reports, or changing a user’s setup to alter their view on certain screens.

This didn’t need any code changes as it was handled within the application. Even so, care was needed to make sure requests were handled correctly, and that principles of least privilege were followed.


Other common tickets would involve changing data at scale. For example, adding notes onto accounts when letters were sent. The application could handle this with small amounts of letters. However, it made more sense to insert notes directly into the database when there were thousands of them.

These tickets served as my introduction to SQL Server. I inserted new data into tables. I updated tables using temp tables and cursors. Every test customer once ended up with the same surname when I didn’t use a WHERE clause properly.

Mistakes are part of learning though. At least it wasn’t production…

Learning about the testing and production servers then introduced me to other SQL Server concepts like Agent Jobs, Linked Servers and Replication. So the floodgates were well and truly opened!


Users would sometimes get errors that they would send in for investigation. Common ones might be caused by:

  • Insufficient permissions for a certain screen.
  • Deadlocked processes in the backend database.
  • Unsupported application version.
  • Bugs in a new release.

Firstly, I would contact the user to explain what was happening. I would then either fix the problem or record it as a bug.

For the unclear errors, I would make contact with one of the Software Engineers for guidance. We’d then either go through the error together, or I’d escalate the error if it was very complex.


In conclusion, I have talked about my time as an Application Support Developer and have given an overview of what the role involved. In addition, I have explained how the role introduced me to SQL Server.

Thanks to Kenneth for this month’s topic! My previous T-SQL Tuesday posts are here.

If this post has been useful, please feel free to follow me on the following platforms for future updates:

Thanks for reading ~~^~~



It gives me great pleasure to introduce! A project that I started in October 2021 is now seeing the light of day and I thought I’d take the time to go through some of the decisions behind it and what my ambitions for the site are.

What Is amazonwebshark For?

At time of writing I’ve been a Data Engineer for a few months and there are several elements of the role that I’d like to get more familiar with – for example my Python skills need sharpening and I’ve not used Git properly yet. By writing about my experiences I can check and confirm my understanding of new topics, give myself points of reference for future projects and exam revision, evidence my development where necessary and help myself out in the moments when my imposter syndrome sees an opportunity to strike.

How Did You Set amazonwebshark Up?

The domain was purchased using Amazon Route 53. This keeps my setup and overall billing somewhat simplified and also means I can try out Route 53’s integrations with other AWS services.

My hosting is via Bluehost. For around £2.66 a month they’re sorting out my server, database, CDN and SSL – that price was a Black Friday special and goes up after a year but so far I’ve been very impressed with their communication and customer service so I’ll see how it goes.

Why Didn’t You Use AWS For Hosting?

Besides the bargain price, Bluehost brings with it a level of convenience. I could have used my own EC2/RDS setup. Or Lightsail. Or even a static S3 site. But my main focus was to get the ball rolling and get something online. I’ve wanted to start a blog for some time, but have run into problems like knowledge gaps, time pressures and running out of enthusiasm. Bluehost offered a quick and simple process that sorted out everything I needed, letting me get the actual blog started.

This is not to say I’m unwilling to roll my own in the future, of course. Stay tuned.

Why Start A Blog At All When LinkedIn And Medium Are Around?

I’m not keen on the Medium model. Many times I’ve seen an article that I fancy reading, only to be met with forced login requests or paywalls. Both of which are deeply frustrating. And LinkedIn is great for articles, but this way I have all my content ringfenced together and under my control. Social media platforms change constantly and there is no guarantee that features, formats and content availability will stay the same or continue to exist from month to month. This site will hopefully let me sidestep any unpleasant surprises of that nature.

What’s The Plan For The Next Few Months?

I’m currently studying towards the AWS Certified Developer – Associate certification, and want to try using my work with the Strava API as the basis for a Lambda function and a CI/CD pipeline to get experience with some AWS services I’ve yet to use. Plus I have a Trello board full of ideas and an unused Rasberry Pi, so plenty to get on with!

Why amazonwebshark?

The name for the site comes from the original Amazon Web Shark – Terabyte:

amazonwebshark Terabyte

He hails from Lanzarote and his favourite topics are FinTech, Dy-Nom-oDB and S3 (Shark Storage Service).

Thanks for reading ~~^~~