I notice that our post queue is filling up with interesting mathematical apps, so I thought I’d deal with them all in one big roundup post. Read on for a mix of mathematical games, apps to help with calculations, and some frankly awful art.

# You're reading: Features

### Tiling a finite plane

One of the many jobs we’re gradually getting round to in our new flat is that of tiling a small section of the kitchen surface, which for some reason was left blank by the original builders and all intervening owners. And what better thing to tile it with than binary numbers?

### Take the 30 second arithmetic challenge

My wife’s grandmother is a fearsome character. She’s in her nineties but still has all her wits about her. In fact, she’s got more than her fair share of wits. Whenever we visit her, she hits me with a barrage of questions and puzzles collected from the last several decades of TV quiz shows and newspaper games pages. My worth as a grandson-in-law is directly proportional to how many answers I get right.

One of her favourite modes of attack is the “30 Second Challenge” from the Daily Mail. It looks like this:

You start with the number on the left, then follow the instructions reading right until you get to the answer at the end. It’s one of Grandma’s favourites because it’s very hard to do in your head when she’s just reading it out!

I decided it would be a fun Sunday morning mental excursion to make a random 30 second challenge generator.

### How many ways to shuffle a pack of cards?

*This is an excerpt from friend of The Aperiodical, Matt Parker’s book, “Things to Make and Do in the Fourth Dimension”, which is out now in paperback.*

There’s a lovely function in mathematics called the factorial function, which involves multiplying the input number by every number smaller than it. For example: $\operatorname{factorial}(5) = 5 \times 4 \times 3 \times 2 \times 1 = 120$. The values of factorials get alarmingly big so, conveniently, the function is written in shorthand as an exclamation mark. So when a mathematician writes things like $5! = 120$ and $13! = 6,\!227,\!020,\!800$ the exclamation mark represents both factorial and pure excitement. Factorials are mathematically interesting for several reasons, possibly the most common being that they represent the ways objects can be shuffled. If you have thirteen cards to shuffle, then there are thirteen possible cards you could put down first. You then have the remaining twelve cards as options for the second one, eleven for the next, and so on – giving just over 6 billion possibilities for arranging a mere thirteen cards.

### I’ve made my own numbers-in-a-grid game

For the past couple of weeks, I’ve been obsessively playing the game *Twenty* on my phone. The fact that my wife has consistently been ahead of my high scores has nothing to do with it.

*Twenty* is another in the current spate of “numbers-in-a-grid” games that also includes *Threes*, *1024*, *2048* (and its $2^{48}$ clones), *Just Get 10*, and *Quento*.

The basic idea is that you have a grid of numbered tiles, and you combine them to build up your score. While there are lots of unimaginative derivatives of the bigger games, there’s a surprisingly large range of different games following this template.

With so many different games being created, I thought that a chap like me should be able to come up with a numbers-in-a-grid game of my own. Yet, for a long time, I just couldn’t come up with anything that was any good.

Yesterday I had a really nice shower, and the accompanying feeling that I’d come up with a really good idea – make a game to do with arithmetic progressions.

### #thatlogicproblem round-up

C:$K_A m; \\ K_B d.$

A:$\neg K_A d; \\ m \vDash \neg K_B m.$

B:$d \not\vDash K_B m; \\ (K_A(\neg K_B m)) \vDash K_B (m,d).$

A:$m \wedge K_B(m,d) \vDash K_A (m,d).$

Albert, Bernard and Cheryl have had a busy week. They’re the stars of #thatlogicproblem, a question from a Singapore maths test that was posted to Facebook by a TV presenter and quickly sent the internet deduction-crazy.

First of all: no, it’s not meant to be answered by an average Singaporean student. It’s a hard question from a schools Olympiad test.

### Pi Day 2015: The Aperiodical goes π mad

Happy π day everyone! I hope you’re having a great day, and having lots of fun mathematical parties.

You may have noticed that here at The Aperiodical, we’ve been posting exciting π-related items all week – and here’s a list of them all, collected into one handy place. Enjoy!