# The numbers of the year 2012

What were the most significant numbers of 2012? BBC Radio's More or Less programme asked experts to explain which numbers were their favourites, and why.

## Sudoku

Dr James Grime, Millennium Mathematics Project, University of Cambridge

Number of clues needed to solve a Sudoku

On 1 January 2012, a paper was released which answered the question: "How many clues do you need to solve a Sudoku?" The answer is 17.

Sudoku fans had found puzzles that could be solved with 17 clues, but they couldn't find any that could be solved with 16 or fewer. So they thought maybe 17 was the minimum number - but to prove that would involve taking every possible Sudoku solution and checking each one to see whether it could be solved for every possible starting position of 16 clues.

## How Sudoku is played

• A Sudoku grid has 81 cells, divided into nine squares of nine cells
• When finished, each row, each column, and each nine-cell square has to contain numbers 1 to 9
• A certain number of cells are filled in to start with (the clues) the puzzle consists in filling in the rest

The total number of Sudoku solutions is 6,700 million, million, million. For each of those, the total number of 16-clue starting positions is 33 million billion.

So demonstrating that no Sudoku with 16 clues has a unique solution is a massive problem. Even with a computer it was thought it would take 300,000 years to check all the possibilities and to show that none of them work.

However, a mathematician called Gary McGuire at University College Dublin reduced the problem mathematically, then what he was left with he checked with a computer programme which ran for the whole of 2011. Then he released his result on 1 January 2012.

Not all Sudoku can be solved with just 17 clues but no Sudoku grids with 16 or fewer clues have just one unique solution.

See James Grime explain it on YouTube

### Gay footballers

Bill Edgar, football statistician at The Times

We are just reaching the 20th anniversary of the last time an openly gay football player played in England's the top four divisions - Justin Fashanu at Torquay United.

I wanted to work out what the chances were that no league footballer in that time has been gay, whether openly so or not, assuming that there was no reason for the proportion of gay footballers to differ from the proportion of gay people in society as a whole.

Many surveys have tried to decide what proportion of British men are gay. Answers have ranged wildly from 1.5% to 6% so I took the lowest figure of 1.5%.

Divide one by this - it's the chance of there having been no gay Premier League player since 1993

In those 20 years, 13,600 players have appeared in the league. The chance of picking 13,600 men randomly from the whole population and none of those being gay is one chance in five times 10 to the power of 90. That's one in five with 90 noughts. To make a slightly more understandable number, I then looked at Premier League players of which there have been 3,200 in the past 20 years.

The chances of there being no gay footballer among those is 1 in 10 to the power of 21, which is one and 21 noughts. To illustrate how unlikely that is - if the entire earth's surface was covered with drawing pins edge to edge, the chance of you picking up one specific drawing pin at random would be 200 times higher than the chance there being no gay player in the Premier League over the past 20 years.

No doubt there have been many gay players in the Premier League, but perhaps not as many as proportionally as in the country as overall - we don't really know.

### Higgs Boson

Dr Pippa Wells, physicist at CERN, the European Organisation for Nuclear Research

In the 1960s, several theorists proposed a mechanism to give mass to fundamental particles.

• Particle physics has an accepted definition for a "discovery": a five-sigma level of certainty
• The number of standard deviations, or sigmas, is a measure of how unlikely it is that an experimental result is simply down to chance, in the absence of a real effect
• For example, tossing a coin and getting a number of heads in a row may just be chance, rather than a sign of a "loaded" coin
• The "three sigma" level represents about the same likelihood of tossing nine heads in a row
• Five sigma, on the other hand, would correspond to tossing more than 21 in a row
• With independent confirmation by other experiments, five-sigma findings become accepted discoveries

Peter Higgs realised that the new field that they needed would actually produce a new particle, the Higgs Boson. Over the last decades people have been searching for the Higgs Boson and we were really hoping that this year we could confirm it and announce the discovery.

So my number for this year is five, because in July 2012, the two big teams hunting the Higgs Boson at the Large Hadron Collider both reported around a "5 sigma" level of certainty that they had found a new particle.

The formal threshold for claiming a discovery is a 5-sigma level - equivalent to a one-in-3.5 million probability that these results might actually be down to chance.

The two experiments also reported the discovery at the same mass value of around 125 gigaelectronvolts - about 125 times heavier than a hydrogen atom.

The fact that both experiments had seen it and with the same mass meant we were absolutely sure we had found something new.

### Eurozone crisis in two numbers

My statistic of the year was given to me by Jean Claude Trichet, the former president of the European Central Bank. He told me about the 80:20 ratio for Europe and the 20:80 ratio for the United States.

In Europe, 80% of business and household finance comes from banks. In US, it's 20%

What does that mean? It means that in Europe, roughly speaking, banks provide 80% of the finance needed by businesses and households. Whereas in the States banks provide only 20% of the finance required by businesses and households.

Why does this matter? This tells us a huge amount about the crisis in the eurozone and it also tells us a huge amount about why the economy of Britain and many economies in Europe in general have singularly failed to recover since the great crash of 2008, whereas although the American economy is not off to the races it has grown rather more strongly than the European economies.

Let's explain the significance of being so dependent on banks. When banks are weak, when they have a shortage of capital which is palpably true of many eurozone banks and arguably - according to the governor of the bank - true of British banks, they are reluctant to lend. What they try and do is actually shrink - to use the ghastly phrase, deleverage - and when banks deleverage and when money isn't going to households and businesses those households and businesses can't spend, they can't invest and frankly the economy can't grow.

And also when you have banks playing such an important role it turns out banks are enormous, they're so big that when they get into trouble even governments like the Spanish government find it very difficult to afford to bail them out.

So the 80:20 ratio tells you two fantastically important things. It tells you why the European economy has been so sluggish and also tells you why governments like Spain and Ireland have been on the brink of bankruptcy because their banks are so big they can't afford to rescue them.

### Car accidents

Jack Straw, MP for Blackburn, UK

My number is 1,901. That is the number of road fatalities in 2011 in the UK.

The number of road fatalities has dropped sharply

It's interesting, in my opinion, because it illustrates the dramatic improvement in road safety that has happened in the last 40 years and the last 80 years.

As a result of controversial measures like the breathalyser and seat belts, and the improved safety of vehicles and junctions, the number of fatalities has dropped from a peak of around 8,000 40 years ago to below 2,000, even though the number of vehicles has shot up.

### Young people

Jil Matheson, statistician

The population of England and Wales is 56.1 million, four million more than a decade earlier.

Record numbers of children in England and Wales

We know we are an ageing population with one in six of us are aged 65 or over.

But the other age of the age spectrum is interesting too - 10.6 million children in England and Wales.

That's more than there have ever been in the country before. There has been a big increase in the number of very young children - over 400,000 more than 10 years ago.

We were all talking in the office about the increase of the population who said they had no religion. It was 15% and now it's 25%. Norwich is the place the most people say that they have no religion.

### Brazil pensioners

Helen Joyce, Brazil correspondent, The Economist

The number that surprised me most this year is the average age of retirement of a Brazilian working in the private sector. It's 53. Now Brazilians don't die at 55, 58 or 60, they live well into their 70s.

Average age of retirement in Brazil's private sector

That means that Brazilians live about 20 years in their retirement on average - you can imagine how much their pension system costs.

The system I'm talking about is for private sector workers but it's run by the government. You pay in, it's compulsory and it's pay as you go, so it's current pensioners who are living off your contributions. The hope is that in the future you're going to live off other workers' contributions.

There is a similar system for public sector workers but the point is these are all run by the government and backed by the government. I looked into the numbers. The only country, big country in the world, that spends more on pensions than Brazil is Italy, and Italy is well known to be having a pensions crisis.

This has two big implications. It means all sorts of other government spending are starved. Children lose out in Brazil because the country spends this mountain on pensions.

The second implication is for the future. Calculations suggest that if they were to keep the current system, by about 2050 workers would have to put nearly their entire salary into pensions - not into their own pension, it's a pay-as-you-go system, but other people's pensions to support old people.

They would have nothing to keep for themselves.

### Olympic legacy

Gabriella Lebrecht, sports analyst at Decision Technology

As soon as a country is awarded an Olympics, they start to pump funding into sports. This means they have athletes that are better prepared, funded and have better equipment so have a better chance of doing well. Additionally there is a home advantage effect.

Number of years for Olympics legacy to fade

We wanted to see what the rate of decay, in medal terms, was after the home Olympics.

This involves looking at the time when they held the Olympics and afterwards and trying to fit an exponential function to it and then we can compare the different rates. This gives us a total medal decay rate and a gold medal decay rate.

The stand-out appalling performance has been Greece. Since Athens 2004, they have a decay rate of -1.04 which is double any of the previous decay rates. They have really fallen through the floor.

In Australia, their media got very upset about perceived poor performance in London, but in terms of total medals, it is perfectly in line with the average decay rate. However in gold medals they're slightly below.

We looked at two Olympics previously to hosting, which is before the host nation has been awarded the Olympics, so they have no idea and no special funding has already kicked in, and then compared that to three Olympics after, or however many you want.

The answer is that 12 years on, the probability of them winning that many medals is statistically significant but if you look 16 years on, it's not significant. Meaning statistically there's no significant legacy 16 years or more afterwards. You can't tell the difference between a nation that has or hasn't hosted the Olympics in their recent past.

### US election

Gillian Tett, Financial Times

In my opinion, the most eye-popping statistic in 2012 was the amount of money that the Americans spent on their election.

Dollars spent on US election, per American

They spent \$2.5bn (£1.54bn) on the direct presidential campaign but when you throw in all the money for the Senate races and the House of Representatives you end up with about \$6bn dollars of total spending on the campaigns.

If you work it out per person in the US, it's about \$18 (£11). The last general election in the UK was \$0.80 (50p) per person and the last Canadian election was about \$8 per person.

However there's a rather interesting catch. If you look at the sheer size of the US economy and the amount invested in elections, then the American number may not be so large after all.

My other eye-popping statistic of the year was that Americans spent \$7bn on potato chips this year and about \$8bn on the Halloween celebrations.

There are some people then who say that spending around \$6bn on an election is not that bad, especially when you compare it to the other things that Americans could spend money on in a consumer culture.

## Features & Analysis

• ### Foot loose Watch

How barefoot Indian tribe inspired a US fitness revolution

• ### Afrikaner agony

What is the future for white people in South Africa?

• ### America's Latino future

Mark Mardell assesses impact of growing immigrant community

• ### Hoops and dreams

The surprising life of a young multimillionaire

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