It's that time of year when little messages reveal just how important you are (or aren't)

I never quite know what to do about Christmas cards. Some years I send them, some years I don't. The result is a strange sort of fractured, dislocated correspondence from year to year. People cross me off their Christmas card lists ("well, he didn't send us one"). Then suddenly they get one from me and either I get this rushed card back the following day or, more likely, they put me back on the list for next year, by which time I've opted out again.

It's never quite emotionally satisfactory. A piece of paper with somebody's signature on it (sometimes, even, a signature you don't recognise) and no message except the implicit one: we haven't seen you since the last time we sent you a piece of paper with our signature on, we have nothing to say to you except that you are in our address book. And a happy new year as well.

Then there are the people who went to all the trouble back in the summer to have specially taken photographs showing their children dressed up as Santa's elves or decorating the tree. Worse still are those parents (eg, Tony Blair, Prince Charles) who are there with their children, grinning and cuddling away. Not just that, but they send the result to dozens of people in the expectation that they will be delighted to put this image on their mantelpiece and keep it there throughout Christmas. Family touchy-feeliness is like those men who have their scrotums nailed to wooden boards: enjoyable for those who like that sort of thing, but they induce symptoms of nausea in onlookers, and so should be carried on in the privacy of the home with the blinds drawn. Or they send you those round-robin accounts of what they've been up to, to show 1) that they are so important that you will want to know every detail of their lives and 2) you are so unimportant that you don't deserve an individual letter. You know the sort of thing: "Cindy was awfully good as Goneril in the school play, Juliet got second prize in the country gymkhana and they switched off Clive's life-support machine."

Except that they don't have that last bit. It's all about how wonderfully their children have done. Paul Theroux has a bit of that in his extraordinary new book about V S Naipaul. He describes a scene in which one of Theroux's young sons tells Naipaul that for his homework he is reading a biography of Ivan the Terrible in French in order to write an essay in Russian. It's as if Theroux, having tried to make you hate both Naipaul and Naipaul's dead brother, Shiva, and having established himself in most readers' minds as the most unsympathetic author since the New York Times published the manifesto of the Unabomber, now wants to make you loathe his sons as well.

But stay, this is meant to be a festive time. I always plan in advance to do something special for the Christmas issue. A parodic pantomime perhaps, or a crossword of my own devising, an amusing Christmas carol containing incongruous satirical elements ("Hark the herald spin-doctors sing . . .", something like that), but I never quite get around to it.

Instead, I'll do what I did last year, which is to pose a brief yuletide quiz.

First an easy one. 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?

Second: I have bought lots and lots of sheets of stamps to send out my Christmas parcels, but unfortunately I have only two kinds: 5p stamps and 17p stamps. What is the largest postage that I won't be able to manage exactly with a combination of those two 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"?

Answers can either be sent via the Statesman or straight to my e-mail address: seanicci@dircon.co.uk. The first couple of correct answers may even get a prize. We've been clearing out in preparation for moving and have found boxes of remaindered copies of old books of mine . . . I mean, valuable modern first editions, some of which I may deign to share with a couple of lucky readers. And I'll sign them, so you can't even take them out and sell them.