In my last article, we went through the process of how to modify and rebuild the kernel while adding a simple system call.

This time, after we got a bit more comfortable, I would like to go a bit deeper and add a more complex functionality.

If you missed the previous article, make sure you read it first unless you are already familiar with the process.

The functionality we are about to add today is called process weights.
As the name suggests, we will assign every process a weight that will represent how “heavy” it is.

Two behaviors that we…

You're in a forest on a distant island.
After walking for a whole day in search of food, you come across a small village and you think it is a good idea to introduce yourself and ask for shelter and some food.
One villager agrees, under one condition,

Tell me what is 4616134 x 411351

You look at him, quite bewildered by the unusual and very specific request, and wonder why you didn’t listen in your math classes which wouldn’t even help in that case either way.

Before we solve the villager request, let’s start with a much simpler exercise.

…

Let’s wear our “city-planner’s” hats for this article. Assume that we are building a new city with n neighborhoods and m one-way roads between them.

Being city planners, we have a passion for pizza, and we want to place a minimal amount of pizzerias such that from each pizzeria the delivery guy could drive to a certain neighborhood and go back as well.

Math is beautiful for a lot of reasons. Some would appreciate the little details in a rigorous proof and others might be fascinated with complex patterns that emerge from seemingly simple equations.

In this article, we are going to concentrate on a different aspect that makes math beautiful, at least in my opinion, and it’s the ability to prove mathematical statements without saying a word — just with a drawing.

The mathematician’s patterns, like the painter’s or the poet’s must be beautiful; the ideas, like the colours or the words must fit together in a harmonious way. Beauty is the…

I was never too impressed with paradoxes, to be honest. It seemed like the most popular ones were pretty unimportant, non-interesting and just misusing the language in order to create some ambiguity or lack of meaning.

You probably heard about the most famous paradox- ”The liar paradox”, which is a good example of a non-impressive paradox, at least in my eyes.

In case you have no idea what I am talking about, this paradox is a sentence stating “This statement is false”.
If the statement itself is true then it is actually false and vice versa.

In this article, we…

Around 100 AD, Nicomachus of Gerasa in the book “Introduction to Arithmetic” presented a classification of numbers based on the concept of perfect numbers. Nicomachus goes on and describes a few results concerning perfect numbers without attempting to prove them.
Two of these result are

• All perfect numbers are even
• There are infinitely many perfect numbers

Both of the statements above haven’t been proved or disproved yet, making them the oldest open problems in mathematics.

“Whether … there are any odd perfect numbers is a most difficult question” — Leonhard Euler

What are perfect numbers?

A perfect number is a positive integer that is…

Pick any number. Did you pick 10003? what a coincidence, so did I.
Now let’s perform a simple operation on this number — take the sum of the squares of all digits.
1²+0²+0²+0²+3² = 10
Now let’s perform the same operation on the result 10
1²+0²=1
One more time with the number 1 this time
1²=1
I believe you can see that we will yield the number 1 every time we will repeat this operation now.

In this article, we are going to investigate together the nature of the operation I have described above. We will answer questions like ‘Do…