I’m not normally interested in education stuff, but we’ve had a flurry of emails from various people telling us about their projects, and I’ve got nothing else to do today, so I thought I’d round them up.

# You're reading: cp’s mathem-o-blog

### The magic number 25641

Reader of the site Bhaskar Hari Phadke has written in to tell us this fun fact about the number $25641$. It’s easier to show than to describe, so here goes:

\begin{align}

25641 \times \color{blue}{1} \times 4 &= \color{blue}{1}02564 \\

25641 \times \color{blue}{2} \times 4 &= \color{blue}{2}05128 \\

25641 \times \color{blue}{3} \times 4 &= \color{blue}{3}07692 \\

25641 \times \color{blue}{4} \times 4 &= \color{blue}{4}10256 \\

25641 \times \color{blue}{5} \times 4 &= \color{blue}{5}12820 \\

25641 \times \color{blue}{6} \times 4 &= \color{blue}{6}15384 \\

25641 \times \color{blue}{7} \times 4 &= \color{blue}{7}17948 \\

25641 \times \color{blue}{8} \times 4 &= \color{blue}{8}20512 \\

25641 \times \color{blue}{9} \times 4 &= \color{blue}{9}23076

\end{align}

A good one to challenge a young person with.

I did a little bit of Sloanewhacking and found a couple of sequences containing $25641$ which almost, but don’t quite, describe this property. So, semi-spoiler warning: you might enjoy A256005 and A218857. I’d like to come up with the ‘magic number’ which looks the least like it’ll have this property – any ideas?

Thanks, Bhaskar!

### “π – It’s Complicated” – a talk I gave on Pi Day 2016 at Ustinov College Café Scientifique

I was invited to give a talk for Ustinov College’s Café Scientifique on π Day this year. The turnout wasn’t great and I put quite a bit of effort into the slides, so I wanted to put it online. I’ve finally got hold of the recording, so here it is. Unfortunately they didn’t set the camera’s exposure properly, making the screen illegible, so you’ll probably want to follow along with the slides in another window.

*I tried to come up with a way of writing today’s date as a multiple of π Day, but couldn’t make it work. However, I did realise that Halloween (31/10) is the best approximation to π between now and the next π day (I think). Sπooky!*

### The world’s smallest Rubik’s cube is 5.6mm wide and absolutely adorable

I just found this video of a very focused man showing off a teeny tiny Rubik’s cube. It’s 5.6mm on each side, which apparently makes it the smallest in the world, beating some relatively gigantesque efforts of 6mm and larger.

Watch this video; I’ll warn you now that the squee factor gives way to some very dry detail quite quickly.

The cube was made by Tony Fisher, by filing down a 3D-printed 6mm cube. I hadn’t heard of Tony before, which surprises me – his site is full of all sorts of incredible twisty puzzles.

### Do you use mixed fractions?

I’m at the MATRIX conference in Leeds, where I’ve just been talking to Adam Atkinson. He told me that he’s trying to compile a definitive list of countries that don’t use mixed fractions.

Here’s a mixed fraction: \[ 2 \frac{2}{3} \]

And here’s a non-mixed fraction: \[ \frac{8}{3} \]

Actually, here’s an interesting fact about that number: \[ 2 \sqrt{ \frac{2}{3} } = \sqrt{ 2 \frac{2}{3} } \]

This only makes sense if you believe in mixed fractions (and unicode character U+2062, “invisible times”)

This is going to be one of those wipe-your-bum-standing-up situations: it’s entirely possible that you can be on either side of this divide and not know the other exists. Apparently, in some countries mixed fractions just don’t exist: an integer written next to a fraction is incorrect.

So, to help Adam on his way, I thought I’d start another in our long-running series of Aperiodical Surveys. Please tell us where you live, and if mixed fractions are OK in your book.

### Integer Sequence Reviews: A075771, A032799, A002717

It’s been almost two years since I last sat down with my friend David Cushing and did what God put us on this Earth to do: **review integer sequences**.

This week I lured David into my office with promises of tasty food and showed him some sequences I’d found. Thanks to (and also in spite of) my Windows 10 laptop, the whole thing was recorded for your enjoyment. Here it is:

I can only apologise for the terrible quality of the video – I was only planning on using it as a reminder when I did a write-up, but once we’d finished I decided to just upload it to YouTube and be done with it.

### CLP reads “Non-sexist solution to the ménage problem”

I rediscovered this nice paper by Kenneth P. Bogart in my Interesting Esoterica collection, and decided to read through it. It turned out that, while the solution presented is very neat, there’s quite a bit of hard work to do to along the way. I’m not particularly experienced with combinatorics, so the little facts that the paper skips over took me quite a while to verify.

Once I was happy with the proof, I decided to record a video explaining how it works. Here it is:

*I probably made mistakes. If you spot one, please write a polite correction in the comments.*