# Time's up. Get your answers to the Sean French Christmas Quiz and start to live again

by Sean French Published

I'm a bit constrained in what I can write this week. My solicitor has said that I am absolutely not allowed to write about moving house. This is not because there is some problem with my mortgage, but because she feels I might write something that would cause offence and hence disaster somewhere along the chain.

This is understandable. I tempted fate two weeks ago by writing critically of certain kinds of Christmas cards, and fate responded as it tends to do when tempted. As soon as the magazine had gone to press and it was too late to do anything about it, cards of precisely those kinds arrived from very close friends. So it's rather lucky on the whole that we're going to be moving out of London because it looks like I'm soon going to need some new friends.

Did you spent the entire Christmas wrestling with the questions I posed in my last column? No? Oh well, here are the answers anyway.

I'm going to drive twice around a mile-long circular racetrack. I drive the first circuit at a steady 30 miles an hour. How fast do I have to drive on the second circuit so that my average speed for the two circuits is 60 miles an hour? One correspondent grumpily complained that this was too easy to be worth even asking. Well, try asking people the question, and most of them reply 90 (reckoning that if you add 30 and 90 together and divide them by two you will get 60). The snag is that an average speed of 60 miles an hour would take two minutes and you have already used the two minutes up going round once at 30 miles an hour, so the second lap would need to be driven at an infinite speed.

Second: I have bought an unlimited number of stamps with which to send out my Christmas parcels, but unfortunately I only have two kinds: five pence stamps and 17 pence stamps. What is the largest postage that I won't be able to manage exactly with a combination of those two stamps? Stephen Brierley pointed out that there is a simple formula, for two values a and b, if they haven't any common factors. It is ab - a - b. 85 - 5 - 17 equals 63, which is the answer. Peter Nicholls added that no parcel needs more than four 17 pence stamps.

And finally: what is the smallest number expressible as the sum of two cubes in two different ways? And who described that number as "rather dull"? And who described it as "very interesting"?

Here is how what is surely the most famous anecdote in the history of mathematics is recounted in Robert Kanigel's biography of Srinivasa Ramanujan, the extraordinary Indian number theorist. Ramanujan, who came to Britain from India in 1914, suffered wretchedly from the food and climate and became chronically ill. At one point, Ramanujan was in a nursing home in Putney, which Kanigel, an American science journalist, helpfully describes as "a few miles south-east of London on the south bank of the Thames". His friend, the Cambridge mathematician G H Hardy, went to visit him. Kanigel writes: "Putney was just a cab ride away. Once, in the taxi from London, Hardy noticed its number, 1729. He must have thought about it a little because he entered the room where Ramanujan lay in bed and, with scarcely a hello, blurted out his disappointment with it. It was, he declared, 'rather a dull number', adding that he hoped that wasn't a bad omen. 'No, Hardy,' said Ramanujan. 'It is a very interesting number. It is the smallest number expressible as the sum of two cubes in two different ways.' " Contrary to legend, Ramanujan hadn't worked it out on the spot. He had thought of it years before, recording it in his notebook.

But is the anecdote true? Peter Nicholls believes that Hardy made it up and suggests that "in typical Cambridge don fashion [he] used the taxi invention to test whether Ramanujan was still in possession of his faculties". Or maybe he pretended to think 1729 was a dull number to cheer Ramanujan up, to allow him to show off a bit. And then, in a donnish self-deprecating style, realised the anecdote would work better if he played the role of Dr Watson to Ramanujan's Sherlock Holmes.

So there we are, prizes are on their way, the decision of the judge is final, no correspondence will be entered into unless of a sexually provocative nature. And now it is 1999, only a year until the millennium bug reduces us to a Hobbesian state of tribal warfare while I write column after column explaining why the millennium doesn't start until 2001.