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

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.

This article first appeared in the 01 January 1999 issue of the New Statesman, An earthquake strikes new Labour

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Q&A: What are tax credits and how do they work?

All you need to know about the government's plan to cut tax credits.

What are tax credits?

Tax credits are payments made regularly by the state into bank accounts to support families with children, or those who are in low-paid jobs. There are two types of tax credit: the working tax credit and the child tax credit.

What are they for?

To redistribute income to those less able to get by, or to provide for their children, on what they earn.

Are they similar to tax relief?

No. They don’t have much to do with tax. They’re more of a welfare thing. You don’t need to be a taxpayer to receive tax credits. It’s just that, unlike other benefits, they are based on the tax year and paid via the tax office.

Who is eligible?

Anyone aged over 16 (for child tax credits) and over 25 (for working tax credits) who normally lives in the UK can apply for them, depending on their income, the hours they work, whether they have a disability, and whether they pay for childcare.

What are their circumstances?

The more you earn, the less you are likely to receive. Single claimants must work at least 16 hours a week. Let’s take a full-time worker: if you work at least 30 hours a week, you are generally eligible for working tax credits if you earn less than £13,253 a year (if you’re single and don’t have children), or less than £18,023 (jointly as part of a couple without children but working at least 30 hours a week).

And for families?

A family with children and an income below about £32,200 can claim child tax credit. It used to be that the more children you have, the more you are eligible to receive – but George Osborne in his most recent Budget has limited child tax credit to two children.

How much money do you receive?

Again, this depends on your circumstances. The basic payment for a single claimant, or a joint claim by a couple, of working tax credits is £1,940 for the tax year. You can then receive extra, depending on your circumstances. For example, single parents can receive up to an additional £2,010, on top of the basic £1,940 payment; people who work more than 30 hours a week can receive up to an extra £810; and disabled workers up to £2,970. The average award of tax credit is £6,340 per year. Child tax credit claimants get £545 per year as a flat payment, plus £2,780 per child.

How many people claim tax credits?

About 4.5m people – the vast majority of these people (around 4m) have children.

How much does it cost the taxpayer?

The estimation is that they will cost the government £30bn in April 2015/16. That’s around 14 per cent of the £220bn welfare budget, which the Tories have pledged to cut by £12bn.

Who introduced this system?

New Labour. Gordon Brown, when he was Chancellor, developed tax credits in his first term. The system as we know it was established in April 2003.

Why did they do this?

To lift working people out of poverty, and to remove the disincentives to work believed to have been inculcated by welfare. The tax credit system made it more attractive for people depending on benefits to work, and gave those in low-paid jobs a helping hand.

Did it work?

Yes. Tax credits’ biggest achievement was lifting a record number of children out of poverty since the war. The proportion of children living below the poverty line fell from 35 per cent in 1998/9 to 19 per cent in 2012/13.

So what’s the problem?

Well, it’s a bit of a weird system in that it lets companies pay wages that are too low to live on without the state supplementing them. Many also criticise tax credits for allowing the minimum wage – also brought in by New Labour – to stagnate (ie. not keep up with the rate of inflation). David Cameron has called the system of taxing low earners and then handing them some money back via tax credits a “ridiculous merry-go-round”.

Then it’s a good thing to scrap them?

It would be fine if all those low earners and families struggling to get by would be given support in place of tax credits – a living wage, for example.

And that’s why the Tories are introducing a living wage...

That’s what they call it. But it’s not. The Chancellor announced in his most recent Budget a new minimum wage of £7.20 an hour for over-25s, rising to £9 by 2020. He called this the “national living wage” – it’s not, because the current living wage (which is calculated by the Living Wage Foundation, and currently a non-compulsory aspiration of campaigners) is already £9.15 in London and £7.85 in the rest of the country.

Will people be better off?

No. Quite the reverse. The IFS has said this slightly higher national minimum wage will not compensate working families who will be subjected to tax credit cuts; it is arithmetically impossible. The IFS director, Paul Johnson, commented: “Unequivocally, tax credit recipients in work will be made worse off by the measures in the Budget on average.” It has been calculated that 3.2m low-paid workers will have their pay packets cut by an average of £1,350 a year.

Could the government change its policy to avoid this?

The Prime Minister and his frontbenchers have been pretty stubborn about pushing on with the plan. In spite of criticism from all angles – the IFS, campaigners, Labour, The Sun – Cameron has ruled out a review of the policy in the Autumn Statement, which is on 25 November. But there is an alternative. The chair of parliament’s Work & Pensions Select Committee and Labour MP Frank Field has proposed what he calls a “cost neutral” tweak to the tax credit cuts.

How would this alternative work?

Currently, if your income is less than £6,420, you will receive the maximum amount of tax credits. That threshold is called the gross income threshold. Field wants to introduce a second gross income threshold of £13,100 (what you earn if you work 35 hours a week on minimum wage). Those earning a salary between those two thresholds would have their tax credits reduced at a slower rate on whatever they earn above £6,420 up to £13,100. The percentage of what you earn above the basic threshold that is deducted from your tax credits is called the taper rate, and it is currently at 41 per cent. In contrast to this plan, the Tories want to halve the income threshold to £3,850 a year and increase the taper rate to 48 per cent once you hit that threshold, which basically means you lose more tax credits, faster, the more you earn.

When will the tax credit cuts come in?

They will be imposed from April next year, barring a u-turn.

Anoosh Chakelian is deputy web editor at the New Statesman.