A couple of problems

Here’s a couple of problems that were shared with me recently, that I will be taking along to MathsJam this month.

1) Imagine 6 people standing in a row facing you, with numbers on their shirts: 1 2 3 4 5 6
They shuffle themselves in the following way: the person on the far left stands in the middle, and then the next person stands on his right, the next person stands on his left, the next person stands on the right end of the line, and so on, so you can now see the people in the order 6 4 2 1 3 5.

Then everyone repeats the shuffle again… and again… how long until they are back in the original order? What if we started with a different number of people?

2) Take a circle, and draw a chord AB. Then choose another point C on the circle to create the chord BC. Then choose another point D to create the chord CD. Then construct the line from D parallel to AB; this intersects the circle again at E. Then construct the line from E parallel to BC; this intersects the circle again at F. Finally, construct the line from F parallel to CD; this intersects the circle again at G. What can you say about point G?

October 2012

Well, it’s been a while, sorry about that. Unfortunately, Cambridge MathsJam did not meet in August or September, but we were back with a BANG this week. Our usual spot upstairs had been reserved by another group, so we squeezed around a couple of tables downstairs instead for a fun couple of hours of beer and maths.

We warmed up our brains with a simple problem from the NRICH website. It was nice to see the different approaches that people took, and it got people talking. We also played with a marble puzzle, an array of marbles where the object is to swap the two colours from one side of the board to the other using only the knight’s move from chess. At this point, completing the puzzle was our goal, and perhaps in future months we might work on reducing the number of moves – according to the box, 55 is average, and 45 is good, and it took me well over 60.

I did a trial run of something I’ve offered as a MathsJam talk at the MathsJam Conference next month to get some feedback from the people who are not going to be there. Then we rounded off the evening with a game of SET.

Next Cambridge MathsJam will be November 20th, upstairs in The Castle. Of course, there’s the MathsJam conference to look forward to between now and then though, looking forward to seeing lots of familiar faces again!

June 2012

I didn’t write an update for June 2012 because I spent most of the evening listening to the England game, and doing some origami. A MathsJam was happening around me, however, and if any of the participants wish to report on what they worked on, please get in touch. In particular, some of the non-football fans spent time working out how to make Euro 2012 more efficient in the hopes of reducing the amount of coverage!

May 2012

We had a slightly lower turnout this month than last month but still managed to do some good maths. I dug out some Martin Gardner books and we worked on some of the problems within. We also had a go at some matchstick puzzles, and one fiendishly difficult puzzle involving interlocking plastic pieces that none of us could do. One of our undergraduate members prepared for his finals by explaining the finer points of graph theory to me, which triggered a game of sprouts.

The gamblers in the group worked on a poker problem; I can’t remember the finer details so I hope one of them will come along and explain it in the comments.

It has become something of a tradition to present the bar staff with something mathematical at the end of the evening, so we made another type of cube from the Origami Polyhedra book. Next month I might try something big like an icosahedron.

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April 2012

April saw yet more games of SET and another post-it dodecahedron for the people who hadn’t made it to January’s mathsjam. Several mathsjammers chose to bring puzzle and problem books, and my favourite of the evening turned up a few days later as Richard Wiseman’s Friday Puzzle – what are the chances of that?!

We also explored some mathematical card tricks, including some that I’d picked up at the Mathematical Association conference earlier in the month.

March 2012

March 2012 was all about the games!
Learning to play SET:

Solving a variety of little puzzles:

We also made a start on some of the Origami polyhedra from this book:

These were so popular with the bar staff that they kept them behind the bar and insisted we made more in April!

Ian Stewart’s mathematical treasures column, cut out from the weekend papers, also provided a distraction, particularly this problem:

We also had a play with this set of cards which I’ve been working on for an upcoming NRICH problem. The idea is that you turn over two cards and have to find a number that satisfies both. I got lots of useful feedback, none of which I’ve had time to incorporate yet!