You're reading: cp’s mathem-o-blog

Zeckendorf cup arithmetic

My 5-minute talk at the big MathsJam conference this weekend was about some stacking cups that my daughter is too young to appreciate. Here’s the really quick version, in just over a minute:

I gave the answer at MathsJam, but the title of this post contains a big hint that should get you there with a bit of googling.

This matrix joke is only barely worth your time

If you see me doing a maths thing, I’m probably wearing one of my maths t-shirts. I’ve got quite a few, but the one that reliably produces the much-sought-after look of total indifference even once I’ve explained the joke is this one:

Photo of a t-shirt with a drawing: 4 by 4 matrix with N E R D along the diagonal

It’s a NERD identity matrix, get it?

That t-shirt was made by Festival of the Spoken Nerd, and by the way they’ve recently put together some new designs.

It’s long bothered me that the nerd identity matrix contains so many zeros. It’s also only an identity matrix if $N = E = R = D = 1$. Surely there’s a joke matrix somewhere with a bit more meat to it?

A puzzle for another day

A few months ago, my faculty’s PR person sent an email round asking if anyone would like to write a puzzle for the Today programme’s “Puzzle for Today” slot, to be broadcast during the programme’s trip to Newcastle in Freshers’ Week. A colleague said this might be the kind of thing I’d like to do, which it was, so I started thinking, and eventually came up with a brand new puzzle which I thought would work well.

If you listened to the Today programme this Thursday morning, you’ll have heard not my name, but that of Dr Steve Humble, who’s got a lot more experience doing this kind of thing. Turns out, they wanted something more ‘visual and interactive’, so asked him instead. I think that was a polite way of saying they just didn’t like my puzzle. Oh well!

Steve chose a classic puzzle that coincidentally appeared on Twitter about a month ago, prompting much discussion. It’s a good puzzle, much better than the one I came up with, but I don’t think Steve was completely right to say “It is possible that you can always create a winning game” – that’s only the case if there are an even number of coins, but his statement said “around ten coins”. I suppose he might’ve meant that, starting from having a handful of coins, you can decide to only use an even number of them.

The upside is that I can now talk about the puzzle here, where someone might actually enjoy it.

The incredible palindromic hat-trick

Would you like to see something AMAZING?

I’ve made another one of my interactive online maths doodads. You should have a go at it right now. It doesn’t require any effort on your part, other than coming up with a positive integer.

Exactly how bad is the 13 times table?

Let’s recite the $13$ times table. Pay attention to the first digit of each number:

\begin{array}{l} \color{blue}13, \\ \color{blue}26, \\ \color{blue}39, \\ \color{blue}52 \end{array}

What happened to $\color{blue}4$‽

A while ago I was working through the $13$ times table for some boring reason, and I was in the kind of mood to find it really quite vexing that the first digits don’t go $1,2,3,4$. Furthermore, $400 \div 13 \approx 31$, so it takes a long time before you see a 4 at all, and that seemed really unfair.

The OEIS now contains 300,000 integer sequences

The Online Encyclopedia of Integer Sequences just keeps on growing: at the end of last month it added its 300,000th entry.

Especially round entry numbers are set aside for particularly nice sequences to mark the passing of major milestones in the encyclopedia’s size; this time, we have four nice sequences starting at A300000. These were sequences that were originally submitted with indexes in the high 200,000s but were bumped up to get the attention associated with passing this milestone.

Google+