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. :-)

Some, like the organisers, insist on calling it the Annual Gathering. There aren’t *many* things Colin Wright gets wrong, but…

Colin Wright has announced the dates for 2019 as 30 November-1 December — Ed.

Every year – generally mid-November – around 200 mathematicians of every stripe gather in Staffordshire for a weekend of puzzles, talks, games, songs, cakes, competitions… all things mathematical are fair game.

The weekend is structured around eight sessions of short talks, the idea being that you can’t *teach* anything in five minutes, but you can show people something cool. Also, if there’s a talk that doesn’t interest you… so what? There’s another one along shortly.

Beyond the talks, there are competitions of varying complexity (a crossword puzzle that developed into a chess endgame! a mathematical horror story contest! a guess the number competition!) and a mathematical-themed bake-off. On the Saturday night, the musicians gather in a side space and play popular songs rewritten with mathematical lyrics, while others play games, fold origami, build polyhedra, juggle…

It’s hard to imagine a better way to spend a weekend. So what were the best bits?

Good grief, the standard was high this year. I’m looking over Andrew Taylor’s notes and thinking “oo! I’d forgotten that one, that was really interesting!” But I’m going to try to whittle them down to five, in the order that they spring to mind.

**Tarim, on Snake Bridges**: If you walk along a canal, you might notice a bridge like this: straight up on one side, a loop on the other. It turns out that this is so your tow rope doesn’t loop over or around the bridge as you barge along the canal. How neat is that?

**Pat Ashforth, on Extending Tables**: How do you decorate an extending table with an aperiodic tiling? Cleverly and beautifully, using an Ammann tiling (which was sent their way by Penrose – and Pat has asked me to mention that it was Steve who did all the drawings to make it work!).

**Tim Chadwick, on Everything Nothing About Shells**: My children are nearly-five and three-and-a-half. I come to MathsJam to

**Barney Maunder-Taylor, on Collapsible Polyhedra**: It’s always important to carry Platonic solids with you – but they’re a bit bulky. So, how can you build ones that fold flat and pop out as needed?

**Sam Hartburn, on The Battle of the Slinkies**: One of several parents to make use of their children’s toys in a talk, Sam demonstrated the obvious superiority of the paper slinky over the plastic one. (I liked it best for the sound effect.)

Zebra zebra zebra zebra yeah!

(Several songs were recorded, and can be found here.)

MathsJam has grown year on year and is now at or about capacity for the venue. That makes for a very crowded room and a very crowded schedule – I felt like the breaks were getting a bit squashed, and I think I’d prefer somewhat fewer talks with somewhat longer recovery times between sessions.

Relatedly, while I love the Competition Competition, I’m not sure having a dozen people explaining their contests and awarding prizes is quite the best way to end the final session. (I don’t have an immediate solution to that – it’s just a lot less interesting than maths.)

I would have entered, and almost certainly won, had I not left mine on the train like a numpty

That said, if you can run an even where my biggest grumbles are “there was TOO MUCH INTERESTING MATHS!” and “there was a 20-minute spell near the end where THERE COULD HAVE BEEN MORE INTERESTING MATHS!”, I think you’re doing a pretty good job.

There’s a buzz in the room at a MathsJam. It’s people saying “I loved your talk, can you tell me more about…?”, or “Oh! I know you from Twitter!” or “Have you seen this cool book?” or “ring chain chain ring”. It’s fistbumps and high-fives, it’s the click-clack of mechanical gizmos, it’s the quiet cursing over failed puzzle attempts and collapsing polyhedra, it’s the giggles as another unsuspecting victim suddenly twigs what Adam Atkinson’s mediaeval French poetry books really are.

It’s an amazing weekend. I wouldn’t miss it for the world.

]]>The talk summaries and slides from last November’s MathsJam conference are now online!

MathsJam is a monthly maths night that takes place in over 30 pubs all over the world, and it’s also an annual weekend conference in November. The conference comprises 5-minute talks on all kinds of topics in and related to mathematics, particularly recreational maths, games and puzzles.

The talks archive has now been updated with the 2015 talks – there’s a short summary of what each talk was about, along with any slides, in PPT and PDF format, and relevant links.

]]>

I know I usually write up the goings-on at Manchester MathsJam, but since I spent much of the last month ‘In Residence’ at the University of Greenwich, I spent the second-to-last Tuesday evening of May at the London MathsJam. Here’s a summary of what transpired.

We spent a good while building Sierpinski tetrahedra for me to take back to the exhibit at Greenwich. Pub manufacturing standards are slightly lower, due to it being a bit dark and all the beer and so on, but we managed to construct a 64-tetrahedron pyramid, which I took back. The smallest pyramids are made using a simple tetrahedron net printed up with the Sierpinski triangle design, then taped together at the corners.

Some discussion of pyramid-related puzzles ensued:

- If you have a regular pentagon-based pyramid, is it possible to slice it in a single plane so that the cross-section is a regular hexagon?
- If you build a square-based pyramid with a square and four equilateral triangles, then disassemble it and use the same triangles to make a tetrahedron, what is the ratio between the areas of the two solids?
- If four ants stand at the corners of a tetrahedron, and each set off walking with the same speed along a randomly chosen edge, what’s the probability that no ants meet at a corner, or pass each other going in opposite directions?

A nice puzzle with overlapping circles was passed around: If three circles are placed in a line with overlaps between each pair, can you arrange the numbers 1-5 in each of the five sections so that the numbers in each individual circle total to the same answer?

Now, level up: four overlapping circles in a line, and the numbers 1-7?

Serious business: five overlapping circles, and the numbers 1-9?

Colm Mulcahy, aka Card Colm, was visiting London and came by to see us. He showed us some amazing card tricks, but I can’t remember any, so you’ll have to buy his book.

Some people were looking at the Advanced version of Cheryl’s Birthday Puzzle.

A pile of humans from UCL’s Chalkdust Magazine were in attendance, and are dead nice. They helped out with building tetrahedra, and also brought along a few puzzles, including their £100 prize number crossword.

]]>We started off with a nice logic puzzle to warm up, which we gave to everyone to see who could get an answer the quickest:

MAN: We think Eric did it. pic.twitter.com/ki8Gf2p03U

— Maths Jam (@MathsJam) January 20, 2015

Lots of toys and games were present this month – we built a truncated icosahedral structure using the tiny magnetic balls (so dangerous they’re banned in three-ish countries), and played with some Japanese box opening puzzles, which someone had found in a second-hand shop.

Then we instigated a large game of Tetris Jenga, while discussing the shortcomings of the Tetris/Jenga crossover format (not all the pieces have four squares to them, not all Tetris pieces are represented, it’s really difficult to play) and despite all this we managed to keep the game going for a good while.

At this point, for complicated logistical reasons, we moved tables, after which the group split across two tables and various games were played. On one table, a game of No Thanks!, with its interesting game theoretic strategy – you have to try to collect the optimal hand, and each card can be directly picked up or offered round the table, which is often worth doing, as it results in winning more tokens (I didn’t play – I only had it explained to me – but I’d like to next time!). On the other table, a game of MathsJam staple SET took place, followed by what’s quickly becoming a staple – 6 Nimmt!, a German card game involving placing your cards without overfilling a stack, in which case you have to take the whole stack.

We also tried out someone’s new Christmas present – a dice game called Farkel. While it can be played using a regular set of dice, the Farkel dice that came with instructions had a different symbol (‘Farkel’, or ⌘) in place of the number 5 (but were otherwise just normal dice). This resulted in a group decision to replace the word ‘five’ with the word ‘farkel’ in conversation, and hilarity ensued (especially for the person scoring the game, who had to often say things like ‘you have farkel hundred and farkelty points’, written ⌘⌘0). We’re such wags.

The game involves trying to roll certain combinations to score points, and on each roll you choose which of your dice you want to score, and have the option of re-rolling the rest – although if none of them score anything, you lose all the points you’ve earned so far that turn. The game’s initial barrier of needing to score at least 500 points (⌘00 points) to be ‘in’, much like the mechanic in Rummikub, meant that it took us a while for all 7 players to be scoring points. Mostly, we just complained that all the scores were multiples of 10 (indeed, multiples of farkelty) so we could have divided the whole thing through, and instead of trying to score 10,000 points to finish, we’d only need 200, which would… be quicker?

We also had a crack at some of the puzzles posed by other MathsJams on Twitter, including a square-based teaser from Leeds – but it was mostly good to see everyone, and to have such a good turnout (with a few new faces too!). We’re all looking forward to February 201⌘!

]]>

For those not able to read the language of diagram fluently, the puzzle goes as follows. The king of the octopuses has four servants, and the servants have either 6,7 or 8 legs. Servants with 7 legs always lie, and servants with 6 or 8 legs always tell the truth. The king asks ‘How many legs do you four have in total?’, and the four octopus servants (who are standing behind a table, so you can’t see their legs) answer 25, 26, 27 and 28 respectively. Who is telling the truth?

Inspired by this puzzle, and how well it went down, we moved onto other similar logic puzzles. A recent blog post by Tanya Khovanova discusses a selection of such problems, and in fact our MathsJam attendees complained about each puzzle in precisely the way that each next puzzle was an improvement on the previous, which sort of freaked me out a bit. We had fun with the last one, but we think we have it figured!

We had a few new attendees this month, who got stuck in to some of the puzzles, and once more the magnificent Sam brought cake (which had fruit on it, so it was healthy). We played around with Tantrix tiles, including this quite nice puzzle (right) where you lay out the numbered tiles and then flip them over in place, resulting in a layout which can be made to all connect correctly when the tiles are rotated in place.

We also played with a couple of puzzles recently posted on Futility Closet:

An efficiency-minded pharmacist has just received a shipment of 10 bottles of pills when the manufacturer calls to say that there’s been an error — nine of the bottles contain pills that weigh 5 grams apiece, which is correct, but the pills in the remaining bottle weigh 6 grams apiece. The pharmacist could find the bad batch by simply weighing one pill from each bottle, but he hits on a way to accomplish this with a single weighing. What does he do?

The follow-up puzzle:

Suppose there are six bottles of pills, and more than one of them may contain defective pills that weigh 6 grams instead of 5. How can we identify the bad bottles with a single weighing?

There were a few nice puzzles floating around on Twitter, which we didn’t quite get round to.

```
```EDB: Take a 2^nx2^n grid & delete 1 square. Can the rest be tiled by L shapes of 3 squares?

— Maths Jam (@MathsJam) February 18, 2014

```
```A good puzzle from a very squashed London @mathsjam #mathsJam pic.twitter.com/gVO992Besn

— Matthew Scroggs (@mscroggs) February 18, 2014

We also got wound up by this voucher, which prompted a short exchange on Twitter with Thornton’s, and a discussion about previous examples of poor units discipline from companies (including the classic Verizon $0.02/0.02¢ debacle):

```
```MAN: We are mostly being annoyed at this ambiguous and dimensionally impossible offer from @thorntonschocs. pic.twitter.com/k6RBVuv0SF

— Maths Jam (@MathsJam) February 18, 2014

We also gave the NorthWest Python members in attendance some programming to do, in order to calculate some facts about the digits of Pi, which resulted in some nice discussion of ways to program things to solve puzzles – Robie brought along his copy of One Tough Puzzle, and showed us the code his brother had written to calculate the solution.

We had a fairly early finish (around 10pm), and we all left happy in the knowledge that at least we weren’t drunk by 7pm, unlike Cardiff:

```
```CDF: WOO BABY CARDIFF IS HERE BRING ON TEH SEXY MATHS WOO BABY YEAH #youknowit

— Maths Jam (@MathsJam) February 18, 2014

]]>

December’s MathsJam meetings were moved forward a week, since we thought people might not turn up to one held on Christmas Eve (since they’d all be at midnight maths anyway) so we met on 17th – still sufficiently near Christmas to be Christmassy, and so people brought along mince pies and various other baked goods, including some Mars bar and marshmallow rice crispie cakes, which disappeared mysteriously quickly.

The main focus of the evening was the building of a fractal Christmas tree, based on the worksheets from the Think Maths website. The worksheets allow you to print nets of a Sierpinski tetrahedron, Menger sponge and Koch snowflake, which can be repeated to whatever extent you deem necessary and then assembled into a festive-looking tree. Our effort was a decent size, and the @MathsJam twitter feed from around then contains some photos of the tree as well as a video of it zooming outwards like a true fractal.

We printed the worksheets at A5 size, which meant the tetrahedra and Menger sponge weren’t quite the right size relative to each other that the hole in the base of the tetrahedron wasn’t bigger than the face of the cube – it meant the top part balanced quite precariously, but I’m not completely sure we changed the relative scales by printing them both with the area scaled down, and if anyone can work out whether it’d be different using A4 versions, let me know.

We wondered how the next scale up would work – making $64 \times 4 = 256$ tetrahedra would leave a huge hole in the base, and would this be able to balance on a Menger sponge made from 20 of the Menger sponges (3 times as long on each side)? I’ve seen it done using three sponges, one under each smaller tree, but one big one would be better. It also just occurred to me that the really hardcore way to scale up the Koch snowflake on the top would be to cut 20 and staple them into an icosahedron. We did not do that.

Extreme props to Mark, who spent a good chunk of time cutting out the Koch snowflake for the top of the tree. He cut the tiny triangles out, where the other two faces were cut by people who cut them off, so we nominated this the front of the tree. Around that time, Leeds MathsJam were discussing on Twitter how to fold a piece of paper so as to make a Koch snowflake with a single cut. That would certainly have saved some time – unless you wanted an infinitely detailed snowflake, in which case it might take longer to do the folding. Than the life of the universe.

Afterwards, we donated our completed tree to the pub, which they were immensely pleased with. We spent a small fraction of our MathsJam being jealous of Leeds MathsJam, whose pub had not only decorated the blackboard (blackboard!!) to welcome them, but also provided them with crackers and mince pies.

We moved on to some other puzzles, including a coins/knight’s moves puzzle tweeted by a mystery MathsJam, which later turned out to be Nottingham. Given the layout of board and coins shown in the photo, what’s the minimum number of knight’s moves needed to switch the two silver coins for the copper ones?

Another discussion centred around this probability puzzle: Two people take turns to roll a dice, and on each roll, if they roll a 6 they win and if not the game continues. Is this game fair, and if not which player has the advantage?

There’s a nice way to show this using probability trees, but some of us managed without even drawing one. We then discussed the further question: if the game isn’t fair (which the existence of this further question slightly implies), what would you need the probability of winning on each go to be in order to make it fair? Is it even possible to do that? We hacked around at it and convinced ourselves of an answer.

We also spent a while discussing the five card trick (another explanation) by mathematician William Fitch Cheney, Jr., where a spectator randomly chooses five cards from a deck, and two magicians have agreed a system whereby if one magician passes the other four of the cards, the other can name the fifth. It’s a lovely trick, and several variations have been developed, many of which are discussed in Colm Mulcahy’s recent book.

According to Twitter, we also discussed Doctor Who, and the best way to teach coding (we concluded people should be able to pseudocode well, as a priority over knowing a load of syntax). I can’t find anything else illuminating from December’s Jam, but here are some other puzzles I found lurking in the scrap paper pile (apologies if these aren’t correctly stated, but I’m reconstructing the questions from someone’s scribbled solutions):

- Given a cube made from smaller cubelets ($n \times n \times n$), if you remove all the cubelets along one edge, prove that the number of cubelets remaining will be divisible by six.
- Given a pile of 105 rocks split into piles of 51, 49 and 5, you’re allowed to either combine two piles or split an even pile in half. Can you achieve 105 piles of size 1?
- Can you arrange 11 trees on a field to maximise the number of possible lines which pass through three or more trees? What’s the most lines you can make?
- Given a $3 \times 3$ grid of squares, and a cube whose face is the same size as one of the small squares, can you cut the grid along some of the gridlines and use it to wrap the cube so all the faces are covered?
- The Hadwiger-Nelson problem: what’s the minimum number of colours needed to colour the whole plane so that no two points which are distance 1 apart are the same colour?

That’s all for this month – the next MathsJam is on Tuesday 21st January, at a pub near your house. Go and join in!

]]>It turned out John also has a copy of *Is Maths Inevitable?*. It’s a good book!

I have written down this question:

How many sets of

Mad Abelrules are there for decks of 52 cards?

And then I’ve written down a reference to OEIS sequence A000001, the number of groups of order $n$.

Some teachers from the RGS came to ask if they could send their students. They were a little bit rude! (For reference, the answer was: “we’re sitting in a pub.”)

I brought in some books I’d bought from Barter Books. They were: *MATHEMATICS*, which has some lovely colour plates; *Practical Geometry and Graphics*; and an unloved book of logarithms which has had an unfinished flickbook animation of a train drawn in it.

The best magic-ish square of all time!

I asked if there are more people with the title ‘Professor’ than ‘Sir’. I quickly added in Dames to the right-hand side, but it was a losing battle from the start. We reckon there are way more Professors than members of the Order of the British Empire of any sort.

I then asked how many different things there are on sale in the UK priced less than 5p, and whether I have enough money to buy one of each. I haven’t written down our answers, but thinking about it now I reckon I could do it.

Next, we talked about Australian Aboriginal kinship rules. They’re fascinating! We worked out a few of the possible permutations of intermarriages, and saw that they do a pretty good job of preventing inbreeding if you stick to them.

We looked at the book Mathographics, which Edmund Harriss recommended to me.

Here’s a dubious method from *Mathographics*:

Is my battered old Rubik’s cube deliberately set up with the pattern of a Conway’s Life glider in this photo?

Here’s a puzzle:

Write the numbers 1 to 14 around a circle so that the sum and difference of every pair of adjacent numbers is prime.

And here’s a solution:

1 – 12 – 5 – 2 – 9 – 14 – 3 – 8 – 11 – 6 – 13 – 10 – 7 – 4 – …

We played Mastermind with the other MathsJams over Twitter. It was a bit of a mess. I got one of my answers wrong, which confused everybody.

I might have mentioned my obsession with interesting times before. We realised that there’s a good stretch of really interesting numbers between 12:33 and 12:37.

**12:33**$12^2 + 33^2 = 1233$ (mentioned months ago)**12:34**yes.**12:35**Fibonacci sequence**12:36**$1+2+3 = 6$; $1 \times 2 \times 3 = 6$; $12 \mid 36$. (best time)**12:37**$1,2,3,7$ are the first four Heegner numbers, as well as the first four record trajectory lengths for the Collatz problem.

If you can extend the happy moment in either direction with an interesting fact about 12:32 or 12:38, please tell me.

John said that Gauss invented the fast Fourier transform two years before Fourier invented the Fourier transform.

We drew a five point egg (page 10 of *Mathographics*).

We tried to work out the best deal for a second-hand maths book, prompted by the fact I bought *MATHEMATICS *for £1.80 and my lovely 1811 arithmetic textbook for £5. We decided you should try to maximise

\[ \frac{\text{Goodness}}{\text{Price}} \left( \times \text{ age} \right) \text ? \]

We agreed that the best possible deal would be an original Euclid parchment for 1p.

June was a busy month!

John has Khinchin’s book!

Context: David and I reviewed Khinchin’s constant as part of the Integer Sequence Review Mêlée Hyper-Battle DX 2000 and we thought it was the best (disregard the subsequent rounds of the competition).

A puzzle:

I talked about the Matula-Goebel bijection between natural numbers and rooted trees.

We did puzzles 22 and 100 from *Mathematical Quickies *by the excellently-named Charles Trigg.

I brought in my Buckyballs again. I made everyone angry by insisting on arranging them into a cube before leaving, and failing repeatedly.

John said that $n!$ can always be written as the sum of $n$ distinct divisors of $n!$.

A final puzzle:

Write down the numbers $1$ to $n$. Remove a number. The mean of the remaining numbers is $20 \frac{1}{3}$. What’s $n$?

Leeds tweeted that $n = 40$, and you take away $27$.

I missed August. I was tired from having a nice time in Wales. Sorry!

There were loads of us in September! Good ol’ back to school times.

Mike showed us his blue and red relativity graphs. The idea is that you see a time-distance graph from different reference frames by wearing different pairs of colour-filter glasses.

Eamonn brought in his MiQube, and a wooden magic square.

We did puzzle 260 from *Mathematical Quickies**.*

David asked what sets of numbers $A$ have the property that $\lvert A + A \rvert = 2 \lvert A \rvert$. He’s since expanded this thought into a ruddy great paper with lots of mentions of Terence Tao.

John asked:

What’s the lowest possible degree of a regular graph of diameter 12?

I tried to instigate some Mad Abel, but people weren’t feeling it.

We reckon that Cantor’s tartan (link goes to some slides; I couldn’t find a good reference) is the solution to the Simon the snake problem if he only bends at right angles. (I think. I should take better notes.)

We talked about the Wieferich primes, which went on to be crowned Integest Sequence 2013.

I have written down “spiral cake”. Maybe I was planning on making one. That didn’t happen.

I showed everyone pictures of the art I commissioned from Edmund Harriss for Newcastle Uni’s maths building.

David showed us a limit that makes no sense:

\[ \frac{1}{2}^{\,\frac{1}{3}^{\,\frac{1}{4}^{\,\dots}}} \]

I mentioned the toast formula.

We played a few games of *Set*.

Mike posed this problem:

I have a biased coin. $\Pr(\text{heads})$ was picked at random from $U(0,1)$ when it was made. I toss it twice. What’s the probability of the second toss being heads, given that the first toss came up heads?

Here’s a game:

Draw $n$ vertices on the plane. Players take turns to draw an edge. The first to complete a triangle loses.

I’ve written down that on six vertices, we reckoned that the first player loses.

How many magmas are there of order $n$? I have a feeling that a couple of people looked this up later, but I can’t remember what the answer was.

John 3D-printed the Herschel enneahedron!

It’s very nice to hold. When I held it in my hand, the thought occurred to me that you could use it as a die. I asked what probabilities the different faces would have. We realised that there’s a way of constructing the enneahedron so that each face had the same probability of landing facing downwards, but our proof was non-constructive.

I’ve written down “Herschel graph – Stiglitz”. Any ideas what that means, anybody?

The MathsJam twitter account passed $\lfloor 1000 \pi \rfloor$ tweets.

Mike showed us his “magic” coins. They were: 1 HH, 1 TT, 4 TH. Apparently they give the closest approximation to a uniform 50-50 distribution of faces of any bag of mixed coins, if you take one out at random and toss it.

Mike also showed us *The Fractionator*:

We talked about searching for things in $\pi$. We decided it was too hard.

It was Martin Gardner’s 99th anniversary, or close to it. Most people present didn’t know very much about him.

Here’s a code:

What’s going on?

I brainstormed ideas for the MathsJam conference cake-baking contest. I decided to attempt a series of cakes each containing a mix of brown and white sponge, so that any random slice would have a 50% chance of having purely white edges. The most fiddly solution would’ve required baking a circular Cantor set.

The last Newcastle MathsJam of 2013! Unlike some of the other MathsJams, we’re not hardcore enough to meet on Christmas Eve, and too stubborn to reschedule to the week before.

I had thought about my enneahedron-as-a-fair-die idea. I decided I needed to get some money to 3D-print a load of different-sized enneahedra to find the one closest to a fair die.

I’ve written down “Zina’s shape thing”. That’s a reference to David’s supervisor, who has described a 3D shape mathematically but has no idea what it looks like, and wants to 3D print it to find out.

A puzzle, from Stephen?

Arrange seven points in the plane such that there are exactly three lines with exactly two points on them.

Much drawing of Fano planes and so on ensued. Stephen (or whoever) then asked for thirteen points and six lines with exactly two points on each. Then we found out about the Sylvester-Gallai theorem.

We decided we’d like to make a mug with the heat equation printed on the side in thermal ink so it only appears when the mug is hot.

A puzzle from one of the other MathsJams:

Wrap a 1×1×1 cube with a 3×3 square of paper.

We found the really easy solution where you place the cube diagonally in the middle of the paper, before finding out that the puzzle insisted you can only fold on grid-lines, and cutting is allowed. We found that solution too, so we’re still clever.

Which is best plane? John said the projective plane, Stephen voted for the complex plane, and I was shouted down when I promoted the sphere.

Pick a sequence of moves on the Rubik’s cube. What’s its period? (The number of repetitions needed to get back to the solved state)

91 is the smallest number that passes the easy divisibility tests but isn’t prime. (This was a tweet from another MathsJam, or another mathematician, I think.)

It looks like that’s everything I’ve written down at MathsJam since May. See you in January!

By the way, previous MathsJam recaps have been published at my old mathem-o-blog. I decided I preferred The Aperiodical’s layout so I’ll be publishing them here from now on.

]]>We covered a few nice puzzles, found on the blog Futility Closet:

- This puzzle about piles of rocks, from the Moscow Olympiad
- This triangle in a circle in a triangle, which took me back to a holiday I once went on where nobody else could see the easy solution
- This cube puzzle, which was discussed without me and I don’t even know if anyone got an answer, but it looks nice

We also played some good games, including Tantrix, which we all recommend heartily to anyone who’s looking to invest in maths games – it can be played as a multiplayer competitive tabletop game, but it also includes endless layers of puzzles, using different subsets of the pieces and trying to create closed loops. Plus, it’s good for making pretty patterns. Insider tip: Pocket Tantrix is half the price, and does exactly the same thing but is a bit smaller.

We also had a quick game of meta-noughts and crosses (listed on the tic-tac-toe Wikipedia page as ‘super tic-tac-toe’, and marketed as ‘Tic-tac-toe-ten’), inspired by some of the other MathsJams who were playing it. We realised halfway through we didn’t have a full grasp of the rules (if the board you’re required to go in next is full, where do you go?) but good fun was had by all.

Chris, who’s a survivor from the recently hiatused Northampton MathsJam (he was the organiser, but he moved to Manchester) came along and brought, among other things, a deck of cards for the game Skat. It’s a German game, which uses only the cards 7, 8, 9, 10, J, Q, K, A in each of the four suits. Firstly, props to whichever marketing genius realised you could sell people a special deck for this, rather than just using an existing deck and leaving some of the cards in the box. The game (as far as we could work out, using the rules from the Wikipedia page) is similar to bridge, in that there’s an auction and then cards are played in tricks, but the order in which cards beat each other is not the same as the number of points you get for that card, nor is either of these the natural ordering of the cards. There are several other ways in which it was confusing, but I think one hand was successfully played (at least one of the players had bridge experience, but apparently that didn’t help).

In order to have a less confusing card game experience, we moved on to the game of Mad Abel. Having been asked by an attendee ‘What’s the mathsiest card game you know?’, I was obliged to show everyone this game, which has previously been a favourite at Newcastle MathsJam. It’s fairly simple in that you have to take it in turns to lay cards from your hand, and the first person to place down all their cards wins. You must lay down one or more cards which sum to the same total as the top two cards on the pile of cards on the table, and the main mathematical twist in the game comes in the way you ‘add’ the cards together.

It’d be a great game to learn if you want to improve your finite group theory: the cards are thought of as group elements, where you ‘add’ the suit and rank separately, modulo four and thirteen respectively, to get the sum. Hearts is 0, spades is 1, diamonds is 2 and clubs is 3 (cue brilliant mnemonics, including my favourite ‘hearts is love’), but you only consider the remainder after division by four, and so if you add a diamond to a club you get a spade, and if you add a heart to a club you get a club. Then you add the ranks of the cards, where king is 13 (which equals zero) and then ace is one, two is two and so on up to queen is 12 (or -1), again considering only the remainder on division by 13.

Each turn is accompanied by a long pensive stare at your cards, repeatedly asking what the sum of the top two cards on the table is again to kill some time, and occasionally someone works out they can go (and everyone checks it’s right). If you can’t go (we noticed this was often more because you couldn’t figure out whether you had a valid move than that you didn’t have the cards) you have to pick up two cards. There’s a full explanation of the rules by its author Smarí McCarthy, which also goes into prime number variants.

That’s all for this month, but next month the students will be back, so we’ll lose our nice quietness and be back to a noisy pub – although this may bring fresh attendees and boost our numbers! Hope to see you then.

]]>First, we looked at the lovely puzzle of which numbers can be written as a sum of consecutive integers – some can, and some can’t, and you can use a pile of counters of size n to determine whether n can be done, by trying to build some kind of truncated triangle of rows whose lengths increase by one. The group all had a good crack at this, and after initially noticing a pattern, which was quickly confirmed by others having found the same pattern, we all had a go at a proof. I explained the proof I’d seen of this, which hinges on divisors, and there was also quite a nice one posted on Twitter (spoilers).

We then moved on to a second counter-based investigation, which involved splitting a row or pile of n counters into two parts, at which point you write down the product of the sizes of the two groups (e.g if you split a row of 5 counters into 2 and 3, you’d write down $2\times 3=6$). Then repeat this for any section of the coins which is in a group of size more than one; e.g. take the new set of 3, split it into 1 and 2 and write down $1 \times 2=2$. When you’ve split the entire set into singles, take the sum of the products you’ve written down. We determined that this value will be the same for any value of n, and the numbers form a pleasing sequence, of which Paul wrote a quite nice proof by induction.

It was at this point that @robiebasak arrived with a large cake, which we promptly demolished (having already eaten @diffractionman‘s flapjacks and crisps) and had a crack at a cube assembly puzzle brought by @samheadleand, which involved each piece having a different colour of faces when viewed from each of the six directions, and the cube had to be assembled keeping all the pieces in the right orientation so all the colours pointed the same way, even inside the cube. I’m not sure if anyone actually solved it, but it was a lovely puzzle. According to its box, it can also be played as a board game in five different ways.

We also saw Sam’s amazing homemade version of SET, which she’d made as a present for Robie, a maths/Python fan:

Playing fake set @MathsJam Manc :) pic.twitter.com/BymLVw9Lpp

— Sam Headleand (@samheadleand) July 23, 2013

Then we carried on with counter puzzles – next up, coin fountains. The rules are defined as follows: you have to arrange n coins (or in our case, counters) so that they form one block which has a flat base, and any counter higher up in the arrangement is supported by two below it. The number of possible distinct fountains for n coins follows the familiar pattern $1, 1, 2, 3, 5 \ldots$ but then dives off into a controversial 9, and anyone who was thinking Fibonacci numbers gets a smack in the maths-face. The actual sequence, for integer sequence fans, is OEIS A005169. We prodded at this for a while, but didn’t manage to come up with a proof.

At this point, the counters were co-opted for a game of Hex – the blockbusters-style game invented by game theorist John Nash, and discussion continued. We also discussed the nice proof that the alternating sum of reciprocal powers of two sums to a third, which I saw David Bedford give in a recent talk on infinite series.

That’s about all we got to this month – see you next month for more MathsJam recapping!

]]>