As many of you will undoubtedly know, mathematics underpins much of our everyday life, in aspects such as love and warfare, to ancient creatures and Mean Girls: areas which have been previously explored in past articles. But what makes mathematics so beautiful is that it allows us to solve problems, both simple and complex. Some of these problems may initially seem counter-intuitive, or not at all obvious. But by expressing them in mathematics, their true nature/solution can be revealed.

## Birthday problem

A famous one to play at parties! In a group of 23 people, there is approximately a 50% chance that two people will share the same birthday, and a 99.9% chance with 70 people. But, to get 100%, if we include pesky leap years, we need 367.

## Monty Hall problem

This (slightly paraphrased) problem is as follows: You’re on a game show, and you have a choice of three doors. Behind two doors are deadly scorpions, but behind the other door is a Chalkdust T-shirt! You pick a door, say No 1, and the host, who knows what’s behind the doors, opens another door, say No 2, containing an evil scorpion. He then proposes to you: “Do you want to pick door No 3?” How do you increase your chances of winning that awesome T-shirt?

## The curious tale of the accountant

This problem was actually initially presented to me only a week ago during a maths circle here at UCL. Throughout the year 2016, the accountant noticed that in any five consecutive months, his income was less than his expenses. But overall, his income was more than his expenses. How can this be? A small hint:

$12\mod5 \not \equiv 0$

## Rubik’s Cube

We all can remember spending countless hours trying to solve the pesky Rubik’s Cube, with most of us giving up in frustration and going on to solve simpler puzzles (or eat pizza). But in fact, all positions of the Rubik’s Cube can be solved in 20 positions (or less!).

And while I’m sure that that $\exists$ many more curious problems, half the fun of mathematics is discovering them yourself (and then sharing them)! If you have any curious problems to share tweet us @chalkdustmag and you might even be featured in future articles!

**Attributions:**

Question Marks: Flickr user Valerie Everett, CC BY-SA 2.0

Birthday cakes: Flickr user Felix, CC BY-SA 2.0

Money: Flickr user 401(K) 2012, CC BY-SA 2.0

Rubik’s Cube: Flickr user Sonny Abesamis, CC BY-SA 2.0

Rubik’s Cube is a registered trademark of Seven Towns, Ltd.