# 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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169
##### Problem #023 - guess the polynomial

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

44
##### 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.

46
##### 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 $$a = b = \frac{k}{2}$$.

130
##### 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.

294
##### 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.

390
##### 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.

374
##### 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.

464
##### 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!

520
##### Problem #018 - circle of hats

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

560
##### 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..?

485
##### 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?

153
##### 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.

269
##### 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!

272
##### 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!

210
##### 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!

326

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.

342
##### 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..?

314
##### Problem #002 - a bag full of numbers

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

483
##### 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.

166
##### 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!