As of now, my blog is being migrated here. You can find all the old content over here.

The 2020 APL programming competition was tough! In this post I share a couple of thoughts and my solutions.

Let's prove that, if a set has size \(n\), then that same set has exactly \(2^n\) subsets.

If there's one thing I like about Python is how I can use it to automate boring tasks for me. Today I used it to help me manage my own blog!

The 24 Game is a well-known maths game that is played with kids in school to help them master the four basic arithmetic operations. In this blog post we will study the game in depth.

Today we are visiting a specific instance of a well-known *basic* mathematics game, the 24 Game. The "24 Game" is usually played with younger students because it helps them develop skills related to the basic arithmetic operations.

Today is the day! Today is the day we take our APL programs and interpret them, so that something like `÷ 1 2 3 -⍨ 1.1 2.2 3.3`

can output `10 5 3.33333333`

.

Take out a piece of paper and a pencil, I am going to ask you to write some letters in your sheet of paper and then I am going to challenge you to fold the sheet of paper... with a twist!

\(n\) mathematicians with numbered party hats gather around in a circle... It is a matter of life or death!

Let's build a simple APL interpreter! APL is an array-oriented programming language I picked up recently. The ease with which I can write code related to mathematics, its strange built-ins (which look like `⍴`

, `⍨`

, `⍒`

or `⍣`

) and the fact that it is executed from right to left make it a fresh learning experience!

*Py-don'ts*
are anti-tips for writing good Python code. Sometimes learning what is good isn't enough. You have to compare it with what is bad as well!

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In high school I had a colleague that had his birthday on the same day as I did. What a coincidence, right? Right..?

Is it true that every integer you can think of has a multiple written out only with \(0\)s and \(1\)s?

In this post we will talk about three different, all very common, ways of writing proofs: proofs by construction, by contrapositive and by contradiction.

This post's problem is a really interesting problem I solved two times. The first time I solved it I failed to prove exactly how it works... then some years later I remembered the problem statement and was able to solve it properly. Let's see how you do!

I have always loved solving mazes... so naturally I had to write a program to solve mazes for me!

**HueHue** is a very colourful game I wrote with my colleague @inesfmarques.

In this post I talked about the riddle of the water buckets. Now I challenge you to prove that in some situations it is *impossible* to solve it!

Can you measure exactly \(2\)L of water with two plain buckets with volumes of \(14\)L and \(5\)L? Of course you can!

A regular expression, without much rigor, is a very compact way of representing several different strings. Given a regular expression (regex), can I find out all the strings the regex can find?

Let's prove that there are two irrational numbers, call them \(a\) and \(b\), such that \(a^b\) is a rational number! And let's do it in a tweet.

Gandalf has some Hobbits to appease but his task seems to go on forever. Can you give him a hand..?

Two friends were bored and decided to play a game... a mathematical game with a paper bag!

This post's format will be a bit different from the usual and the first of a series of posts of this type. In this post, I will state a problem and then present my solution.

Here's how I like to solve my equations: just walk around randomly until I trip over a solution!

Think of a drunk man that continuously tumbles left and right, back and forth, with no final destination.

Progress is great and new things are always exciting... but that doesn't mean old things don't have any value!

The filled Julia set is a really cool fractal that kind of resembles the Mandelbrot set!

In this post I just ramble a bit through some mathematician's definition of what a recursive function is...

I have always liked the concept of fractal. They are very beautiful, they have a notion of infinity embedded in them, and they make no sense (seriously though, *self-similarity*?). How could they not be loved?

This blog post has a single purpose, which is to show you the weird game I made, inspired by Flappy Bird and my crazy English teacher.

Minesweeper has to be one of the most well-known minigames of all time, no? I spent my fair share of Sunday mornings playing minesweeper in my Windows XP computer...