Haven’t we all dreamt of winning the lottery and fulfilling our wishes of taking that expensive holiday or buying that grand sports car? Well, these dreams might just come true. You read that right! According to mathematicians at the University of Manchester, a person needs about 27 lottery tickets for a guaranteed win in the UK.
Mathematicians Explain The Lottery Ticket System
The team of mathematicians at the University of Manchester examined the UK National Lottery’s Lotto game, where players pick six numbers between 1 and 59 and aim to match the numbers drawn by the company. Prizes are awarded for correctly guessing pairs up to the jackpot (matching all six numbers), which is currently £7.8 million ($9.9 million).
To ensure a win in Lotto, Dr David Stewart and Dr David Cushing have devised a method to get at least two numbers right out of all 45,057,474 possible combinations, using only 27 tickets. They used Fano planes, geometrical constructions where pairs of numbers are plotted on or within triangles, and connected by straight lines or circles to describe the possible combinations. Each line passes through three pairs, producing one of the possible winning sextets.
The mathematical challenge was not winning the lottery, but determining the smallest possible number of tickets required. It proved quite challenging to show that you cannot win with 26 tickets. Stewart, a Reader in Pure Mathematics at the University of Manchester released the following statement–
“Fundamentally there is a tension which comes from the fact that there are only 156 entries on 26 tickets. This means a lot of numbers can’t appear a lot of times. Eventually, you see that you’ll be able to find six numbers that don’t appear on any ticket together. In graph theory terms, we end up proving the existence of an independent set of size six.”
According to mathematician Peter Rowlett, in 99% of cases, the investment won’t match the profit. You’ll win, but not much. However, the researchers put their theory into practice to see how it holds up.
Ahead of the July 1, 2023 draw, they purchased 27 lotto tickets at a cost of £54 ($68.61). Although three of the tickets had winning pairs, they did not win any additional prizes. This approach is more of an intriguing mathematical solution than a quick money-making scheme.
