A Christmas maths quiz

A small prize will be awarded for the best answers submitted to A.Mann@gre.ac.uk by a University of Greenwich maths undergraduate by midnight on Sunday 4 January 2009. The rest of you are doing it for fun only!

Q1. Identify the mathematicians whose names have been shuffled so that the letters are in alphabetical order. (Some are easier than others!) As extra help, they are given in chronological order. Accents and punctuation marks such as hyphens are omitted, and spellings are taken from the MacTutor History of Mathematics website
http://www-groups.dcs.st-and.ac.uk/~history/

a) AEHLST
b) AAHIPTY
c) AAHKMYY
d) DEE
e) AEFMRT
f) AHILLOPT
g) EELRU
h) ADEGMNOR
i) AAAJMNNRU
j) ACDIR

As a tie-break, can you suggest a candidate for the mathematician with the longest name in which the letters are in alphabetical order, so that (like one of the above) they would appear unchanged if their name were included in the above list? (My best so far is five letters long.)

Q2. Can you find English words containing the following letters consecutively?
a) WKW
b) HIPE
c) ZV
d) HQ
e) NSW

Q3. Which of the United States is closest to Africa?

Q4. There are several different time zones in the United States. New York on the east coast is normally three hours ahead of Los Angeles on the west coast. A phone call is made from an East Coast state to a West Coast state and it is the same time at both ends. How can this be?

Q5. There are 100 lightbulbs and switches, numbered 1 – 100, and 100 students. Initially each bulb is off. The first student switches on every light. The second then switches off every second light. The third student now changes the state of every third bulb, so 3, 9, 15,… are switched off and 6, 12, 18, … are switched back on. The fourth student changes the state of every fourth bulb, and so on. After the 100th student has done this, which bulbs are left on?

Q6. On average, how many times would you have to roll a fair die before all six numbers have appeared?

Q7. Sasha and Siobhan are in the same class. They look alike, have the same birthday, were born in the same year, and have the same parents. Yet they are not twins. Can you explain this?

Q8. Let n be a natural number. Show that there is an integer (non-zero) multiple of n which (in base 10) contains only 1s and 0s.

Q9. Can you decipher this message?

SZKKBSLORWZBGLBLFZOO

Q10. And can you decipher this one?

JUTZ JU ZNOY WAOF ATZOR EUA NGBK JUTK GRR EUAX IUAXYKCUXQ!

Ingenious

Noel-Ann and I have been playing a new board game (or at least, one new to us) called "Ingenious". Tiles, in the shape of two coloured hexagons joined domino-style are placed on a hexagonal grid and one scores points for each hexagon of the same colour in an unbroken line from the ones one has placed. The catch is that the loser is the one whose lowest-scoring colour has the lower total, regardless of how many points one has for one's other five colours. The game in the photo is typical - I have won because Noel-Ann's score for yellow is less than mine for green and red, my joint worst-scoring colours.

I have found this an unusually difficult game in which to plan strategically. If anyone has any tips please email me privately.

9th IMA Younger Mathematicians Conference

What a truly inspirational day.......

So many eye-opening talks including, the importance of eigenvalues and eigenvectors within Google's framework for ranking the search results, the future plans for preserving the Cutty Sark as a national treasure and the use of the Monte Carlo Simulation methods for calculating the most likely ruin event within the financial industry.
Noel-Ann Bradshaw (University of Greenwich) gave a brilliant talk on how multi-objective evolutionary algorithms can be used within portfolio optimisation in the financial markets.
Gareth Howell (Cardiff University) gave us a sneak preview into the life of a PhD student and talked about research he's conducting on Theoretical Statistics, including the Farey Series for finding all rational fractions between 0 and 1.

David Youdan also told us about the possible merge between the IMA and LMS into a more unified mathematical society.
All in all, it was a stimulating day and one I certainly will never forget.

My favourite Quote of the day:

"The openness to keep learning is as important as the subject itself" - Andrew Smith (Deloitte)

Maths Inspiration

Lovely to see Rob Eastaway's Maths Inspiration going so well, as shown on the BBC morning news yesterday. When Rob set this up a couple of years ago, one of the first venues was the Greenwich Theatre and we organised an outing for students - we even cancelled a Discrete Maths lecture for the day! And I suspect Rob's event, which featured Claire Ellis, Hugh Hunt and Colin Wright as well as Rob himself, was almost as entertaining as my class would have been.

Mark Haddon - Proof-reading at the Royal Society

A fascinating discussion at the Royal Society this week between the novelist Mark Haddon, author of The Curious Incident of the Dog in the Night-time, and the mathematician Marcus du Sautoy. It was full of fascinating insights into the nature of creativity, artistic and mathematical: it was a remarkably stimulating evening (and there is a webcast available (click on "Physics and Mathematics" and look for "Proof-reading: Telling stories with numbers, telling stories with words"). I was left excited by illuminating ideas which emerged in the interview. It also inspired me to investigate Haddon's website.

"A webcomic of romance, sarcasm, math and language"

One of many from http://xkcd.com/. Thanks to Ian for telling me about this!

Blanc Mange, bags and stick goblins – Math Lecture with John Mason

It’s 1 o’clock on a windy Wednesday. We wait for the lecture, enjoying a free lunch, socializing and solving problems for each other, or just causing more. Then the time comes, we enter the room, crowding in the middle, waiting again for a speech to start.

We are asked to fill the front rows so we move. We are asked to participate in conversation so we try. Short introduction: Who? Why? What? (John Mason to educate us holds a lecture on thinking mathematically.) Then he walks to the middle fires up his Mac and soon we stare at the blue screen filled with circles, numbers and colour. The lecture is called Thinking Mathematically. So the circles – at least for me – bring up memories of Maths and stick figures (And stick figures make me - like a dog of Pavlov - to associate with a giant in the playground. Hence the goblins in the header.) Of course they should mean numbers and addition and powers and laws but that’s why we have this lecture. Not to train our strictly meant mathematical knowledge but to make us better understand what we already should now.

We are sorting colourful objects, putting them in bags and then generating functions like wings of angels

All this to learn something most people would think impossible to learn. But we do, and we like it.

After all this is what maths about. Understanding what you already know to make something entirely new and astonishing. Or help someone else make it.

A MathSoc event

Greenwich maths staff and students took part in a MathSoc field trip to Thorpe Park today:

One from the Independent

"The art of mathematics"

Thanks to Tony Ackroyd for this one

http://news.bbc.co.uk/1/hi/sci/tech/7617191.stm

Newton discovers Surrealism

from Private Eye no. 1218, 5 September 2008

Darth Vader explains the Pythagorean Theorem

Thanks to Don Cook and the Philomathes list for this one.

Mathematical Chat-up Lines

Try these at your own risk (and report the results here):

• "If I were sin^2 and you were cos^2 together we would be 1."
• "I wish I were your derivative sp that I could lie tangent to your curves."
• "That dress would look even better at 32 feet per second per second."

(My thanks to Daniel for sending me these, from a letter to the Times from Dom Rowland and Ed Smith of Trinity College, Cambridge.)

Maths at the Edinburgh Fringe

In a rather warm studio at the top of several flights of stairs sat a girl, Rachel, reading Ian Stewart’s From Here to Infinity and a man, Colwyn, strumming a rather out-of-tune guitar. This was the opening scene of the Edinburgh Fringe production of the play ‘The root of minus 1’ performed by Hartshorn-Hook Productions in association with Angel and Virgins Theatre Company.

The play unfolded into a poignant insight into this couple’s struggle to come to terms with the death of their sister / sister-in-law. The sister, Michelle, had been a budding mathematician at university but had met with a fatal accident before completing her degree. She had developed a very close and possibly intimate relationship with her lecturer, Karen, who helped Rachel and Colwyn find out more about the maths in Michelle’s life. Discussions with Karen covered a wide variety of mathematical issues: certain historical mathematics topics such as counting, infinity and the Pythagoreans and other mathematical areas such as topology, calculus and as the title suggests – imaginary numbers.
The actress playing the part of Karen also cleverly played the character Emily the counsellor who, without giving her own opinion, helped the couple to understand their own fears and feelings.

The mathematical content came over with a passion that I hope would inspire others to take more than a passing interest in the subject as well as a number of amusing insights about mathematicians. If the theatre company ever staged a production in London it would make a great trip for maths students – I would enjoy seeing it again.

What is 7 times 13?

http://www.youtube.com/watch?v=7WMi5TUJDso

(Thanks to Don Cooke and Udai Venedem of the Philomathes email group for this.)

How many socks make a pair?

Last night I was at the launch party for Rob Eastaway's new book, How many socks make a pair? Like Rob's previous books, including Why do buses come in threes? and How long is a piece of string?, this presents interesting mathematics from everyday life. It contains a number of gems. I was pleased to learn the name of Penney Ante, which I came across as a scholboy wihtout ever knowing its origins, and to discover the Saddam Puzzle.

"The Football Stadium" puzzle asks whether, if 101 metres of bunting is laid along a 100-metre touchline, pinned to each corner spot, is there enough play to allow someone to pass underneath the bunting at the centre line? The answer is surprisingly counter-intuitive (well, counter-my-intuition, anyway).

Strongly recommended!

The statistics of sex in your 70s

A Swedish study of attitudes to sex among the older generation provoked some interesting correspondence in the Independent over the last couple of weeks. The survey showed that 68% of men and 54% of women were continuing to have sex into their old age. Some readers jumped to the conclusion that 14% of men must either be lying or being unfaithful to their partners. But of course that superficial conclusion is wrong. Since women live longer than men, there were many more women than men in the age group, so it turns out that it's the women who are lying or being unfaithful (or having younger partners).

A neat illustration of how easy it is to misinterpret statistics?