## You're reading: Posts Tagged: MathsJam

### The Double Back puzzle is a nice mix of Towers of Hanoi and Solitaire

This post is both a video and text. The content is largely the same in both versions, so you can pick one to look at.

I’d like to show you a puzzle, or game for one person, that Ed Kirkby came up with. Ed showed this to me at the Big MathsJam gathering last year.

I was walking around MathsJam and people were doing all sorts of stuff and Ed was quietly sat at a table with some cards in front of them, and a couple of people were gathered around with thoughtful faces, so I thought “oh that looks interesting” and I walked over and Ed explained the rules of this game to me.

And like most things at MathsJam, I didn’t immediately know the solution but it really got to me, so I went away and tried to find a solution myself. It was really fun and it was one of those pure experiences of mathematical discovery that you really remember.

I kept grabbing other people and saying, “have you seen Ed’s puzzle? Come over here. Ed, explain this puzzle to this person!” I did that for the duration of the weekend, and for a little while after I got back home.

I’ll show you what the puzzle is.

Take two sets of cards numbered 1 to 4, and lay them out in two rows. The game is to get them the other way round, so each row goes 4, 3, 2, 1.

The things you are allowed to do are to swap two cards that are adjacent numbers and in adjacent columns.

So you can swap the four and three here:

You can also swap to the other row.

You can’t swap the four and the two here because they’re not adjacent numbers.

It’s a permutations puzzle. And with a bit of thinking, a lot of just making random moves, eventually I worked out how to do it for four cards (or two lots of four cards, to be precise).

It took me a few more goes to be sure that I’d found the shortest solution — the fewest moves — but then five really stumped me.

When I tried six cards, I wasn’t sure it was possible at all: there was a point where I kept getting stuck.

So I was really unsure, and Ed was unsure as well – they didn’t know if there was a solution for every number of cards. They’d written some code that very slowly churned out solutions for small $n$, but didn’t have a general solution.

So I did my usual problem solving technique which was, if I couldn’t do it with four cards, do it with three cards, and very briefly with two cards. Then after a while I sort of started seeing a pattern.

I came away from Big MathsJam not knowing how to solve this puzzle.

I kept playing with it when I should have been working, and eventually I think I’ve sort of got the vibe of how it works and I’m pretty sure now I can solve it for any number of cards. I haven’t written down a really rigorous algorithm for doing it but I’ve got a general idea.

### Interactive version

Something that often happened when I was playing with cards was that I’d forget which way I was going, because when you don’t have a strategy you’re sort of making lots of moves to see where they’ll go, and then maybe you want to backtrack a bit, and you go like wait wait — which end did the aces start at? You’re continually picking up cards and moving them, and if you’re as clumsy as I am they scatter all over the place and you end up unsure if you’re in a valid state.

So it won’t surprise you to learn that I made an online version of this.

Big MathsJam happens in November, and by the time I’d got this online version working it was getting close to Christmas and I thought, “we need something that’s not playing cards to be the pieces – why shouldn’t it be baubles? They’re circles, they’re easy to draw.”

So I spent some time drawing a bauble image and making it look Christmassy. I didn’t quite get it ready for last Christmas, so I spent some more time improving the interface and I made it fully keyboard accessible.

And then I made a note to write a post about it in December 2023. And here we are!

I think this is a nice Christmas puzzle: I think the set-up and the rules are easy to remember, and it only needs a pack of cards, which you’ll probably have lying around.

So over Christmas, if there’s a quiet moment, if you get some playing cards in your Christmas cracker or just some pieces that you can put in an easy to identify order, try showing this to someone.

So there you go, that’s the Double Back puzzle, invented by Ed Kirkby, online version made by me.

### Mathematical Drawing Hacks

At this year’s MathsJam UK Gathering, I had the pleasure of running one of the Saturday Night Tables – a chance to invite attendees at the Gathering to drop by and play with something. Together with fellow Manchester MathsJam regular Andrew Taylor, I ran a table of Mathematical Drawing Hacks – ways to make drawing complex mathematical objects and shapes easier.

### MathsJam Leuven recap, February 2022

It’s been a while since we’ve seen a MathsJam recap, but having restarted the MathsJam in Leuven after a hiatus, Dieter was too excited not to share what they’d been up to.

The first (re)edition of the Maths Jam in Leuven (Historic university city in Belgium) was a tiny success. I brought a couple of physical copies of the single page worksheet called the MathsJam Meta Shout with $\sim$10 problems from different sub areas of maths which I received earlier from Katie who coordinates MathsJams internationally.

The problems on the sheet were ranging from simple (?) Fold-and-cut fun, Tangrams (geometry), to some number theory, a touch of Linear Algebra and an easy arithmetic problem, solvable with 12-yo-level calculations (i.e. arrange all numbers from 1-15 so that each adjacent numbers sum to a square of a whole number under 16). Nice to see how broad the difficulty space is on the worksheet. Creative problem solving for (nearly) all ages!

On the second to last Tuesday of February 2022 (and hopefully each month from now), we were 3 in total. Which is a good number, I guess, for the Leuven revival anno 2022. Plenty of room to go from there – and a prime number, naturally! :-) Unfortunately we got kicked out of the venue at 21h30 (we started at 20h GMT+1) because we were the only ones left and the venue closes at 22h on Tuesdays (something I didn’t check, nor expected really). But puzzle minded we were, we just overflowed to someone’s home -after a rainy bike intermezzo which refreshened our minds. This didn’t stop us continuing our puzzling until 23h.

One of the attendees (a mathematician by degree) aced all the problems in <3h all the while (attempting) to explain his rationale. It was quite impressive to see! And fun too, because I definitely learned quite some things that night. I was still attempting to fold-and-cut the necessary T-shape with the proper dimensions (3 unit squares on top & 4 from top to bottom) when others had already finished their second tangrams (with some clever area proportion estimates). I forgot to bring my edition of the Set game so we didn’t participate in the online inter-MathsJam set-hunt – being only three we were too eager to just dive into the puzzles first.

After that second to last Tuesday, I tried some of the puzzles I hadn’t completed that night myself and I still haven’t finished them all just yet. (Some of them really make the gears in my brain grind!) I really liked the mix of complexity and variation in type of problems (kudos/thx/merci to all those involved in the making of the Shout).

I’m already eagerly looking forward to the next edition Shout and the next physical meetup by extension (Tuesday 22th of March), and have arranged a new venue for this month in the bar Café Entrepot of the local art center Opek. This seems very fitting for the subtle art of maths and I’ve got the guarantee that they will host us at length, yay! I sure hope to see you there on a second to last Tuesday soon. :-)

### MathsJam’s “Back of an Envelope” Fermi Challenge

Aperiodipal and MathsJam regular Rob Eastaway organised an inter-MathsJam competition for last month’s events, challenging Jams to make Fermi estimates on the back of an envelope. The prize was a copy of his new book, Maths on the Back of an Envelope. Here Rob gives a summary of the entries he received, and shares his favourites.

Regular attendees of MathsJam will know that in September, Katie Steckles kindly allowed me to hijack the evening (in the nicest possible sense) by posing some envelope-related challenges, in celebration of the publication of my new book Maths On The Back Of An Envelope. In addition to some envelope-related puzzles, there was also an open challenge to Maths Jam groups to come up with their own back-of-an-envelope problems, with the chance to win the book as a prize.

### Many-to-many Shape Sorter

Did you like playing with shape sorters as a toddler, but find them too simple as an adult? Well, I’ve got good news for you.

### The Maths Podcast to end all Maths Podcasts

At the MathsJam weekend gathering earlier this month, we found ourselves invited to join maths podcasting supremo Samuel Hansen for a recording session. Nothing unusual there: podcasts have been recorded at MathsJam before. But this time Samuel wanted to record more than one podcast at the same time – since many of the maths podcasting community were present, it seemed like a good plan to grab anyone who wasn’t already doing something else and record something quite unlike any podcast you’ve ever heard.

### Big MathsJam Highlights, 2018

The dust is settling on the ninth Big MathsJam, and before I get too sad that it’s nearly a year until the next one, I put down some thoughts about what was so good about this one.