When the FIFA World Cup in Russia began earlier this month, a betting company launched a promotion offering a Â£100 million prize if entrants were able to correctly predict the outcome of all 64 matches in the tournament.
However according to Dr Fionntan Roukema, a University Teacher in Mathematics at the University of Sheffield, to guarantee success in predicting the correct outcome of all the matches, betting at a rate of one bet a second you'd have to have started placing bets more than a billion years before the universe existed
Dr Roukema suggests that guessing randomly, you'd need to make more than a million times the number of grains of sand on the planet worth of guesses to take home the cash.
He said: “I was a huge football fan during the golden era when Hristo Stoichkov won a golden boot, Ray Houghton lobbed Gianluca Pagliuca, and Gazza performed an outlandish chip over Colin Hendry! But that was the nineties and I hadn't found mathematics.
"Now I know some mathematics, but I've become 100 per cent ignorant of contemporary football. However, even though I have a complete lack of footballing knowledge, I'd like to explain to you how we can win the Â£100 million prize by only multiplying some numbers together, using a little imagination, and applying a modest amount of elbow grease.
“In order to guarantee a win, you need to bet on all possible outcomes. There more than five octillion different possible outcomes in the World Cup, where one octilion is a billion billion, billions - which is a lot of billions. To put the number five billion billion billion in context, this is about the same as the area of 10,000 planet earths put together and measured in millimeters squared!”
He added: “The mathematics of why there are so many choices boils down to there being a total of 64 games in the World Cup, which is large, and the incredibly fast growth of exponentiation means the number of possible options is outrageous. Almost as outrageous as the 1986 Argentinian handball or England’s record with penalties!”
The University of Sheffield's School of Mathematics and Statistics is placed in the world top 150 maths departments according to the Times Higher Education World Rankings for Physical Sciences.
It is home to experts in pure mathematics, applied mathematics, and probability and statistics. Their research is helping to bring new understanding to the complex, intricate mathematical structures that the modern world is built on, with applications in disciplines ranging from finance to healthcare.