# Mathspp Blog

### A blog dedicated to mathematics and programming!

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

231
##### My two cents on the 2020 APL competition

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

33
##### Twitter proof: size of the set of subsets of a set

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

42
##### YAMLUtils: automating boring stuff with Python

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!

150
##### Studying the "24 Game"

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.

123
##### Problem #020 - make 24 with 3 3 8 8

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.

97
##### Let's build a simple interpreter for APL - part 2

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.

157
##### Problem #019 - fold the alphabet

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!

228
##### Problem #018 - circle of hats

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

222
##### Let's build a simple interpreter for APL - part 1

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!

219
##### Py-don't disrespect the Zen of Python

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!

227
##### The birthday bet

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

198
##### Problem #007 - binary multiples

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

3
##### The CCC of proof methods

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

36
##### Problem #005: number me right

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!

15
##### Solving mazes with programming

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

22
##### HueHue: a colourful game

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

40
##### Problem #004 - solvability of the water buckets

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!

30
##### Water buckets riddle

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

64
##### Finding all strings a regular expression can find

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?

66

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.

55
##### Problem #003 - a quarrel in the Shire

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

67
##### Problem #002 - a bag full of numbers

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

235
##### Problem #001 - a dancing triangle

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.

34
##### Solving diophantine equations with random walks

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

40
##### Random walk simulations in 2D

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

39

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

143
##### Fractals and the filled Julia set

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

179
##### On recursive functions and Kleene's approach

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

200
##### Creating a programming language from scratch

This blog post tells the short story of how I wrote a simple interpreter for a toy programming language!

243
##### Fractals and the Mandelbrot set

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?

115
##### Pigeon Pooping Simulator

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.

159
##### Minesweeper remake

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...

188