This month was a small group, but MathsJam is serious business so we got through loads of fun in the time allotted for fun. To start with, we hacked away at Leeds’ tweeted starter for ten:

LDS : As I am alone, starting w/ simple one ; don’t know the answer yet.Is it possible to cut unit square into 3 triangles w/ areas in GP?

— Maths Jam (@MathsJam) August 21, 2012

This resulted in a large amount of paper with quadratics and surds scribbled on, and I still don’t know if we got an answer (but we probably did).

We looked at quite a few things from Futility Closet, a blog which posts regularly interesting bits of lexicon, chess problems, anecdotes and quite frequently maths puzzles. Here are some of the ones we played with:

- This puzzle, in which neither diameter nor circumference of a carousel’s outer and inner circles are known, but the length of a chord touching the inner circle is, and the amount of paint needed to cover the annulus between is then calculable;
- Two concentric roulette wheels are each divided into 100 sectors and 50 randomly chosen sectors on each are painted black, and the rest white. Prove that it’s possible to orient the wheels so at least 50 sectors on the two wheels match up;
- A proof that all horses are the same colour, which we eventually found a flaw in but it’s nice.

Having been stood around with a Rubik’s cube (my default setting) at a recent festival, a colleague there had set me the following puzzle, which we tweeted and then tried to solve:

MAN: Can a worm enter the surface of a Rubik’s cube shaped apple, eat every segment (once) and finish in the centre?

— Maths Jam (@MathsJam) August 21, 2012

Again, sheets of scrap filled up with diagrams and lots of pointing, staring and slowly turning over of my convenient nearby Rubik’s cube took place. Twitter replied with one YES and one NO, and I won’t tell you which is right, but there’s a nice proof of whichever it is.

As I and Paul Taylor (and Andrew Taylor) are regular Puzzlebomb setters, I decided to devote a little MathsJam time to working on puzzles for this month’s Puzzlebomb. The main puzzle this month will consist of many smaller puzzles, and I collected some nice ideas for numerical puzzles to fit in with that. Watch out for them in the next issue!

We also spent a little time discussing Matt Parker‘s exciting domino-related forthcoming Manchester Science Festival event, for which we’ll be contributing some volunteers and time. We drew lots of diagrams of domino logic gates and got a bit excited.

That’s about all for this month, although we also enjoyed the fact that the first Bombay MathsJam had happened that day, and were deeply moved by the photo of people doing a MathsJam in a cafe in India and it’s OUR FAULT.