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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In this problem you have to devise a strategy to beat the computer in a "guess the polynomial" game.

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

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

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.

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


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.


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!


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!

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!

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!