Mathematical headaches? Problem solved!
Hi, I'm Colin, and I'm here to help you make sense of maths
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In this month's WBU spectacular:
WBUPuzzle solution: Alphabetically Begin Counting - Disregard Eight Forwards, Gale
Colin is a Weymouth maths tutor, author of several Maths For Dummies books and A-level maths guides. He started Flying Colours Maths in 2008.
He lives with an espresso pot and nothing to prove.
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.
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
On the first MathsJam, apparently everybody gave a talk. What percentage of the participants gave a talk at the zeroth MathsJam?
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I teach in my home in Abbotsbury Road, Weymouth.
It's a 15-minute walk from Weymouth station, and it's on bus routes 3, 8 and X53. On-road parking is available nearby.
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