Podcast: Play in new window | Download

In this month's WBU spectacular:

- Big MathsJam is coming up - book quickly!
- The Relatively Prime Series 2 Kickstarter closes today. Donate quickly!
- Dave's got a chapter in a book - order quickly!
- Colin sails into the wind (virtually)
- Dave's moving house over half term: what maths are the movers doing?
- When will the first two-hour marathon be run? (Dave says the world record is currently 2:02:55, although it's
*actually*2:02:57). - @chrishazell72 got the last puzzle:

WBUPuzzle solution: Alphabetically Begin Counting - Disregard Eight Forwards, Gale

- This month's puzzle: Show that $n^4 + 4$ is not prime for integer $n \ge 2$
- What Dave Would Like To Know More About: shuffling

## Stephen Morris

On shuffling. With 2N cards lable the cards from 0 to 2N-1 from bottom to the top of the pack. Suppose a perfect shuffle leaves 0 and 2N in place, moves 1 to 2, 2 to 4, … N to 1, N+1 to 3, …, 2N-1 to 2N-2. Ignoring the top card (which doesn’t move) each card, c, moves to 2c mod 2N-1. The number of shuffles to bring it back to the start is s where 2^s = 1 mod 2N-1.

Thre is an alternative riffle shuffle does move the top and bottom cards. Then we have 2^s = 1 mod 2N+1.

## Dave Gale

Hi Stephen,

Is it as simple as that? I was under the impression that we didn’t know a lot about it yet. (Sadly, all my maths books are packed up at present so I can’t find where I got that from.)

I think I’d go with the ‘IN’ shuffle as an ‘Out’ shuffle can appear suspicious. Thanks for your comment.

Pingback: A nice little thought puzzle | cavmaths

## Johan Strandberg

On the first MathsJam, apparently everybody gave a talk. What percentage of the participants gave a talk at the zeroth MathsJam?