Thursday, 17 December 2009


A small prize will be offered for the best solution emailed to by a Greenwich student before 5pm on Monday 18 January 2010 (deadline extended because of the bad weather). In the event of a tie, a winner will be chosen randomly. The judges' decision is final. For obvious reasons, the source of these questions won’t be revealed until afterwards. The quiz has seven questions.

Q1. Identify the mathematicians whose names are given below as anagrams. Accents and punctuation marks such as hyphens are omitted, and spellings are taken from the MacTutor History of Mathematics website


Q2. What is the smallest two-digit integer?

Q3. Is 10^2010 + 1 prime? Justify your answer.

Q4. On average, how many times do you need to toss a fair coin before you have seen a run of an odd number of heads followed by a tail?

Consider a chessboard – an 8x8 grid of squares in which each row and column is alternately black and white. You have 31 2x1 rectangles each the size of two adjacent squares of the chessboard. Remove the top left and bottom right corner squares. Is it possible to cover the 62 remaining squares with your 31 rectangles? Provide a solution or show that it can’t be done.

Q6. A, B and C are candidates in an election. There is an odd number of voters. The votes are counted and there is a three-way tie. As a tie-breaker the voters’ are asked for their second choices, and again there is a three-way tie. A suggests that, to break the tie, there be a two-way election between B and C, with the winner then facing A in another two-way election. Is this fair? And what is the probability that A would win the election if it were held in this way, assuming no voter changes their mind?

Q7. Here are two hidden messages. What do they say?



Wednesday, 16 December 2009

GMC2 Solution

Congratulations again to Nic Mortimer, who wins the prize for the first corrrect solution to the second Greenwihc Maths Challenge. He deciphered the encrypted passage from G.H. Hardy's A Mathematician's Apology (which is given below). The substitution cipher was based on the word CHRISTMAS with A mapping to C, B to H, C to R and so on. But to make it harder, half the Es in the plaintext were treated as Ys, so the mapping was not one-to-one.

The next Greenwich Maths Challenge will be launched on or after Monday 11 January.

Meanwhile, you can do the Christmas Quiz, which will be posted here shortly!

Here is the passage from Hardy:

Greek mathematics is ‘permanent’, more permanent even than Greek literature. Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. “Immortality” may be a silly word, but probably a mathematician has the best chance of whatever it may mean... Nor need he fear very seriously that the future will be unjust to him.
No other subject has such clear-cut or unanimously accepted standards, and the men who are remembered are almost always the men who merit it. Mathematical fame, if you have the cash to pay for it, is one of the soundest and steadiest of investments.

Thursday, 10 December 2009

One in a million

Picture of a mathea]mstician at a blackboard
Yesterday's radio play "One in a million" presented some interestingn examples in applied probability (although the image on the BBC website, reproduced here, seems to show some quantum mechanics!) If you want to hear a play in which Bayes' Theorem plays a key role, you have another few days while its available on BBC iPlayer.
(Thanks to Steve Baker for this)

Tuesday, 8 December 2009

Greenwich Maths Challenge 2 - Winner

Greenwich Maths Challenge 2 has been won by Nic Mortimer! The solution won't be published for a couple of weeks to allow the rest of you the fun of solving.

Sunday, 6 December 2009


GMC2Here is the second Greenwich Maths Challenge, posted on Monday 7 December at 8pm. There will be a prize of a £10 token for the first correct solution received from a Greenwich student or a group of Greenwich students. Collaboration is encouraged. Your answers should be sent to The judges' decision is final.

We have taken a quotation from a book by a famous mathematician (the views expressed are those of the mathematician in question and not ours!) and encrypted it using a substitution cipher. Your task is to decrypt the ciphertext below. (Line breaks are inserted uniformly after every 40 characters and have no other significance.) The cipher tools on Simon Singh's Code Book CD-rom may (or may not) be useful - this can be downloaded free from



(And yes, the quotation in some ways reflects the period in which it was written!)

Greenwich Maths Challenge 1

A number of answers were submitted to this problem (see below). The winner is Alex Cole, with commendations to Khadija Khairoun and Steve Baker. All of the competitors identified that the issue lies in the combination of probabilities that are not independent. Unfortunately Alex's answer, which used Bayes's Theorem, has too much mathematics to be easily turned into HTML so I'm not posting it here. The problem was taken from Raymond Smullyan's book The Riddle of Sheherazade and Other Amazing Puzzles.

Greenwich Maths Challenge 2 will be published here on Monday 7 December at 8pm (or as soon after as I remember).

Sunday, 8 November 2009


GMC logo
Here is what you've all been waiting for - the inaugural Greenwich Maths Challenge. The intention is that a new question will be posted monthly during the University session. There will be a prize of a £10 token for the best answer received from a Greenwich student or a group of Greenwich students. Collaboration is encouraged. Your answers should be sent to The judges' decision is final.

The first challenge is this. What is wrong with Scheherazade's argument in the following story by Raymond Smullyan? The clearest explanation submitted before midnight on Sunday November 29 by a Greenwich student or students will win the prize.

"And now" said Scheherazade, "I have a paradox for you. There are three boxes labeled A, B and C. One and only one of the three boxes contains a gold coin; the other two are empty. I will prove to you that regardless of which of the three boxes you pick, the probability that it contains the gold coin is one in two."
"That's ridiculous!" said the king. "Since there are three boxes the probability is clearly one in three."
"Of course it's ridiculous," said Scheherazade, "and that's what makes it a paradox. 1 will give you proof that the probability is one in two, and your problem is to find the error in the proof, since the proof must obviously contain an error."
"All right," said the king.
"Let's suppose you pick Box A. Now, the coin is with equal probability in any of the three boxes, so if Box B should be empty, then the chances are fifty-fifty that the coin is in Box A."
"Right," said the king.
"Also, if Box C is empty, then again the chances are fifty-fifty that the coin is in Box A."
"That's right," said the king.
"But at least one of the boxes, B or C, must be empty, and whichever one is empty, the chances are fifty-fifty that the coin is in Box A. Therefore the chances are fifty-fifty, period!"
"Oh, my!" said the king.

Friday, 6 November 2009

Coming Soon - Greenwich Maths Challenge!

We're about to introduce the Greenwich Maths Challenge! Each month, a tough maths question will be posed on this site. There will be a prize for the best (or, sometimes, first) solution received from a Greenwich student or group of students before the deadline specified. Others are welcome to submit solutions but won't be eligible for the prize. The problems will be varied but they will all be demanding. The first problem will be posted on this blog on the evening of Sunday 8 November. Are you ready for the Greenwich Maths Challenge?

More on the THE Award

Chris BaileyProfessor Chris Bailey, leader of the Greenwich team which has just won the Times Higher Education Award for the Outstanding Engineering Research Team of 2009, writes about the work of his team:

The field of Computational Mechanics and Reliability uses mathematical techniques and software to predict how products (i.e. laptops, aircraft engines, automobiles, ships, etc) will behave when subjected to different environmental conditions and most importantly how long they will survive. This area of research within the school has aided many companies design and maintain reliable products from aerospace electronics to heritage structures.

Saturday, 24 October 2009

Award triumph for Greenwich mathematicians!

Chris Bailey and his team Chris Bailey and his team at Greenwich have won the Times Higher Award for 'Outstanding Engineering Research Team of the Year" for 2009. This is wonderful news for the University and the Department of Mathematical Sciences!

Wednesday, 14 October 2009

Greenwich podcasts!

A number of Greenwich mathematicians have made podcasts about their work which you can download from Travels in a Mathematical World. (This site, maintained by Peter Rowlett of the Institute of Mathematics and its Applications, has many fascinating podcasts about mathematics and mathematicians.)

A new podcast is added every week: this week's one (Number 41) is by Professor Ed Galea of the Fire Safety Engineering Group at Greenwich. Earlier podcasts by Greenwich people about their work at Greenwich are numbers 16 (Professor Chris Bailey), 20 (Professor Choi-Hong Lai), and 29 (Noel-Ann Bradshaw). In addition Noel-Ann Bradshaw has recorded a series of podcasts on the history of mathematics - these are numbers 2 (Newton and Leibniz), 6 (Galois), 11 (Euler), 13 (Nightingale), 17 (Al-Khwarizmi), 21 (Turing), 25 (Fibonacci) and 30 (Ramanujan).

Sunday, 11 October 2009

The great Tom Lehrer

Mathematicians of my generation were brought up on the records of Tom Lehrer, who sang satirical songs as a sideline to his maths career. I'm grateful to Sandy Galbraith for sending this link to Lehrer singing about maths: some of these I didn't know!

Friday, 2 October 2009

Keith Moffatt awarded 2009 David Crighton Medal

Keith Moffatt
Professor Keith Moffatt FRS of Cambridge University has been awarded the 2009 David Crighton Medal by the LMS and the IMA. You can read about Professor Moffatt's work on the LMS website (follow the link "Prizes").

Two colleagues at Greenwich have expressed particular pleasure at the announcement.
Professor Ed Galea of our Fire Safety Engineering Group says "This is wonderful news. Much of my PhD was based around the work of Keith Moffatt. I can remember spending months trying to understand some of the work in his papers on magnetohydrodynamics and star formation. And when I finally did understand it I thought how elegant and simple it was, which made me feel both immensely pleased and immensely stupid at the same time!"

Valdis Bojarevics, Reader in our Computational Science and Engineering Group, says, "Good news indeed! This jiggles my memory to one of the first encounters with this remarkable man back in 1981 when I was demonstrating to the prominent visitor, Prof. Keith Moffatt, a rotating vortex generation in a mercury experiment passing a thousand amperes current. As usual the so called 'generals' effect happened, and the thing did not work initially as expected: the 'pinch' effect with a loud bang and splashing of the weak acid solution on top of the mercury. We ended both hiding at the bottom of the experimental table... Keith was so impressed, that we were invited to publish this in the Journal of Fluid Mechanics ( he was the editor at that time), [V.Bojarevics, E.Shcherbinin. Azimuthal rotation in the axisymmetric meridional flow due to an electric current source. - Journal of Fluid Mechanics, (1983) vol. 126, 413.] I met him on several occasions, his talks are always the top attraction at the conferences. His publications are available online at"

Wednesday, 30 September 2009

Turtles all the way down

A frame from Logicomix From Logicomix: an epic search for truth by Apostolos Doxiadis and Christos H. Papadimitriou, art by Alecos Papadatos and Annie Di Donna. More about this when I find time to read it!

Sunday, 27 September 2009

The three jars problem

Here is a relatively well known puzzle (it appears, for example, in the film Fermat's Room.

"You are given three closed tins of sweets that are labelled "Lemon Sherbet", "Toffees" and "Mixture". One contains lemon sherbets, one contains toffees and the third contains a mixture of the two, and they are all wrongly labelled. What is the minimum number of sweets that you have to remove in order to ascertain which jar contains which variety?"

If you don't know the problem, work out the answer now before reading any more. So that you can't immediately see the answer I give below, I'm interposing a totally irrelevant image:

Sherbet powder (Bottles of sherbet powder in Goodies Sweet Shop, Steep Hill, Lincoln: photograph by Andy Dingley from Wikipedia Commons.)

The book answer is one. If you take one from the tin labelled "mixture" it tells you what is in that tin, since it isn't the mixture. You can then easily identify the other two, knowing that neither is correctly labelled.

I think this answer is wrong. The true answer is zero. (And this is not because of any issue with the wording, that you might be able to feel or smell what is in the mixture tin without actually removing anything.)

You don't actually have to remove a whole sweet. You could open the mixture tin and break one of the sweets into two, remove half a sweet and work out the answer. You could take a smaller piece than a half - it could be a third, or a quarter, or a fifth, or even smaller.

In fact, for any epsilon greater than zero, you could remove a piece smaller than that size and it would give you the solution. So the number of pieces you have to examine is smaller than any positive number. The only such number is zero, so zero pieces suffice.

Maths puzzle competition result

The entries for the freshers' maths puzzle competition on Friday have been marked and we can now announce the winner. It was very close, with all teams scoring well, but Adam's group scored 78/100 to beat Andrew and Daniel's group by a single point.

Congratulations to the winners. And, while some of the expositions could have been clearer, remarkably, every script submitted was easily legible. Keep that up, please!

Saturday, 26 September 2009

Greenwich Scavenger Hunt Result

Winners: Jodie, Chris, Kieron, Corin etc.
(Note: I'll act as middleman and get you all a discounted membership of the OR Society for only £150 a month each)
Highly commended: Roxy
Finding out the hard way that rebels don't win anything: Nic and his group

Friday, 25 September 2009

Games in Greenwich Park with new students

A very successful afternoon of mathematical games in Greenwich Park with new first year students and their mentors. Naturally the staff team, with superior knowledge of the mathematics of statics and dynamics, scored a decisive victory at Jenga.

Thursday, 24 September 2009

iSquared special issue

iSquared magazine The latest issue of the excellent maths magazine iSquared is a special issue about "Women in maths". It contains a number of thought-provoking articles, interviews, reviews and quotes, from Emilie du Chatelet on the prejudice which excluded women from the sciences in the eighteenth century to Julia Robinson wishing to be remembered as a mathematician regardless of her sex.

iSquared has been nominated for the Maggies awards for the best magazine covers of the past year. A tip - if you are thinking of subscribing to iSquared (which I recommend), if you vote for the awards you get a voucher which gives you a discount on a subscription.

Wednesday, 23 September 2009

Science Museum

A visit to the Science Museum is always fun. Highlights today were seeing the original book with Kepler's view of the planets fitting into the Platonic solids, Henry Perigal's geometric pen, ome Indian weights and measures (the same object being both), a model of Kelvin's tide-predicting machine, Alan Bennett's blown glass Klein Bottles, and the wonderful range of polyhedra models.

Any visit to the Science Museum reminds me of previous visits, from my first visit to London when I was 11, a later visit with my father when I finished my sixth form, visits during my undergraduate days and ever since. And of course my favourite object of all, Bill Phillips's water-powered economic computer Moniac, which I remember admiring with my father on that first visit forty years ago. It's a false memory - the Museum didn't have the object then - but it's still part of my personal story of how I became interested in mathematics, mathematical modelling and computing: the areas in which I have spent my entire working life.

Moniac hydraulic computer

Tuesday, 22 September 2009


One of the freakest random events ever seems to have occurred in the Bulgarian national lottery, when the same six winning numbers were selected on two consecutive draws on 6 and 10 September. An investigation has apparently found no evidence of wrong-doing: it was just a remarkable coincidence. I find that hard to believe. What do you think?

Thursday, 17 September 2009

Ian Stewart coming to Greenwich!

Ian Stewart
I'm thrilled to hear that Ian Stewart has accepted an invitation to give the keynote speech at the Undergraduate Mathematics Conference which the maths department at Greenwich is organising, with support from the IMA, next February. (For more details of the conference contact the organiser Noel-Ann Bradshaw.)

Ian Stewart is the author of many wonderful books including Why beauty is truth: a history of symmetry, Letters to a young mathematician, Professor Stewart's Cabinet of Mathematical Curiosities and Taming the Infinite: The Story of Mathematics. This summer he was awarded the Christopher Zeeman Medal, awarded jointly by the LMS and the IMA for his work on promoting mathematics. He is a brilliant speaker, and it will be wonderful to hear him at Greenwich again.

(Photo by Avril Stewart from Wikipedia Commons.)

Thursday, 10 September 2009

A fascinating novel

Cover of David Leabvitt's novel 'The Indian Clerk' I've only just got around to reading this fascinating novel, published last year. It fictionalises the relationship between the mathematicians Hardy, Littlewood and Ramanujan almost a hundred years ago. Historians may object to some of the liberties taken by the novelist, but it is a loving examination of a mathematical world, not ar removed in time, but now almost unthinkable. It deals with the characters' dilemmas sympathetically. As one who was brought up on the story of Hardy and Ramanujan as it has become part of mathematical folklore, I was particularly interested to see a non-mathematician's take. A thought-provoking novel which I strongly recommend.

Simon Singh at the British Science Festival

Simon Singh - photo by Steve Trigg from Wikipedia Commons
A wonderfully entertaining and thought-provoking lecture by Simon Singh at the British Science Festival on "Why journalists love stupid equations and other problems in the media". The issue of how to promote maths is not straightforward and Simon brought out the complexities through a range of examples ranging from the blatant commercial creation of an equation designed solely to gather press coverage for a PR company's client. to serious research which appealed to the press: Simon showed that it's not always easy to distinguish these. In my opinion (for what it's worth) we have to live with the media we have and it's not worth getting worried about the appeal of stupid equations. Much more serious is the second issue Simon raised: that of the way the libel laws are constraining scientific debate and suppressing the expression of serious scientific comment. For more about this see the Sense about Science campaign.

Wednesday, 22 April 2009

The London Mathematical Society

Readers of this blog may be aware of the controversial proposal to form a New Unified Mathematical Society in the UK and consequently to disband the London Mathematical Society and the Institute of Mathematics and its Applications. Yesterday I attended the first of the necessary two Special General Meetings of the LMS which passed by a narow majority the motion to proceed with the winding up of the Society.

For such a historic event it was all rather low-key. There was an hour of procedural wrangles before the vote, but no discussion of the substantive issue.

I suppose the vote of the Scottish Parliament in January 1707 for the Treaty of Union must have been rather similar.

Thursday, 5 March 2009

Maths and making fun of Arsenal

I rather regret doing this now: Arsenal supporters are having such a tough time that it seems a bit unfair to have mocked poor Marcus in this way. In my defence, at the time I named the Bentley group, it wasn't obvious just how poor Arsenal were going to be this season.

Monday, 23 February 2009


An exciting evening for MathSoc with Peter Rowlett leading a session on exploring Newtonian dynamics with a Wii. Peter explained the mechanics behind pool and then had us playing the game to see how it works in practice. We then moved onto doubles matches in tennis, with perhaps slightly less maths in evidence, but I'm proud of saving three match points against Justin.

Sunday, 8 February 2009

Royal Institution Masterclasses

We're running our annual series of sixth-form Royal Institution masterclasses once again. We've had two so far - Chris Walshaw on how abstract algebra made the founders of Google very rich, and Graham Hoare on the joys of number theory. I am amazed yet again at the enthusiasm of the students who participate. Having people arrive an hour early for a Saturday morning maths lecture is rather remarkable (and rather different from my own early-morning lectures where students tend to stumble in sleepily after I've started). But each year I'm also impressed by our undergraduate helpers who always manage to be enthusiastic, welcoming, willing to do whatever may be required, and totally reliable. All of the speakers really enjoy doing these classes, and that's a wonderful reflection on the Greenwich students who help and the sixth-formers from all over London who attend.

Thursday, 8 January 2009

A new symmetry object

This is to report that Ameli Gottstein, who won the Christmas Maths Quiz, has chosen as her prize to have a new mathematical structure, a group of symmetries in multi-dimensional space, named after her. (Others similarly honoured include the footballers Jermain Defoe and David Bentley.)

A description of Ameli's group will shortly appear. If you want to name one of these amazing mathematical structures after someone, all you have to do is make a donation to Marcus du Sautoy's favourite charity and Marcus will name a group for you. This makes an excellent present (I think) and is in a very good cause.

Tuesday, 6 January 2009

Christmas maths quiz - solution

Here are the answers to the Christmas Maths Quiz posted last month. The best entry received from a Greenwich undergraduate came from Ameli Gottstein, who wins the prize. Well done Ameli!

Many of the questions (2, 3, 4, 5 and 6) were taken from Peter Winkler's Mathematical Puzzles: A Connoisseur's Collection (A.K. Peters).

The answers were:

Q1. Identify the mathematicians whose names have been shuffled so that the letters are in alphabetical order.
a) AEHLST - Thales
b) AAHIPTY - Hypatia
c) AAHKMYY - Khayyam
d) DEE - Dee
e) AEFMRT - Fermat
f) AHILLOPT - L'Hopital
g) EELRU - Euler
h) ADEGMNOR - De Morgan
i) AAAJMNNRU - Ramanujan
j) ACDIR - Dirac
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?
Peter Rowlett wrote a computer programme to address this and provided a list of all mathematicians in the St Andrews website whose names have this property. The longest such name waa that of Edwin Abbott (author of the classic mathematical novel Flatland). Peter also found mathematicians whose names are in reverse alphabetical order - the longest this time was Rolle.

Q2. Can you find English words containing the following letters consecutively? a) WKW b) HIPE c) ZV d) HQ e) NSW
The answers I was expecting were AWKWARD, ARCHIPELAGO, RENDEZVOUS, EARTHQUAKE and ANSWER. Alternatives proposed included (c) JAZZVOCALIST and (d) MATHQUIZ, which I liked.

Q3. Which of the United States is closest to Africa?
Maine. (If you don't believe this, have a look at a globe! Map projections distort distances!)

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?
One for Americans, I think. Florida is an east coast state and part of Florida (for example Pensacola) is in the Central Time Zone, while parts of Oregon (including Ontario) observe Mountain Time, so Ontario, Oregon and Pensacola are only an hour apart. The trick now is to call from Pensacola to Ontario between 2 and 3am on the morning in October when Daylight Saving Time ends, so that the clock has gone back an hour in Pensacola but has not yet done so in Ontario, and the time in each is the same.

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?
The ones which are left are exactly the perfect squares: 1, 4, 9, 16, ...

Q6. On average, how many times would you have to roll a fair die before all six numbers have appeared?
If we have already thrown n of the six numbers, then the expected number of rolls before a new number is thrown is 6/(6-n). So the answer to the question is 6/6 + 6/5 + 6/4 + 6/3 + 6/2 + 6/1 which is about 14.7.

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?
They are triplets.

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.
We use the famous Pigeon-Hole Principle (PHP). Consider the integers 1, 11, 111, 1111, 11111 ... up to the integer with (n+1) ones. There are n+1 such integers and only n possible remainders when you divide by n, so two of these integers have the same remainder. If they were 11111111 and 1111, for example, then the difference would be 11110000 which is a multiple of n of the required form.

Q9. Can you decipher this message? SZKKBSLORWZBGLBLFZOO
HAPPY HOLODAY TO YOU ALL - this used the Atbash cipher.