# Mathspp Blog

### A blog dedicated to mathematics and programming!

This blog has a really interesting assortment of articles on mathematics and programming. You can use the tags to your right to find topics that interest you, or you may want to have a look at

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##### Twitter proof: consecutive integers are coprime

Let's prove that if $$k$$ is an integer, then $$\gcd(k, k+1) = 1$$. That is, any two consecutive integers are coprime.

##### Twitter proof: maximising the product with a fixed sum

Let's prove that if you want to maximise $$ab$$ with $$a + b$$ equal to a constant value $$k$$, then you want $$a = b = \frac{k}{2}$$.

##### Problem #022 - coprimes in the crowd

This simple problem is an example of a very interesting phenomenon: if you have a large enough "universe" to consider, even randomly picked parts exhibit structured properties.

##### Problem #021 - predicting coin tosses

Alice and Bob are going to be locked away separately and their faith depends on their guessing random coin tosses!

##### Let's build a simple interpreter for APL - part 3 - the array model

In this blog post we will go over some significant changes, from implementing APL's array model to introducing dyadic operators!

##### 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.

##### 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.

##### 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!

##### 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.

##### 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.

##### 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.

##### 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!

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

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

##### 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!

##### 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..?

##### 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?

##### Problem #006 - stacks of beans

I find the problem in this post rather fun to think about because it is a problem about a game that can actually be played between two players.

##### 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.

##### 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!

##### Solving mazes with programming

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