MADRID, (EUROPA PRESS) – Mathematicians from the University of Manchester have answered the question: How many lottery tickets do you need to buy to guarantee winning something in the UK National Lottery?
Focusing on the flagship “Lotto” game, which draws six random numbers from 1 to 59, Dr. David Stewart and Dr. David Cushing discovered that 27 is the lowest possible number of tickets needed to guarantee a prize, although, what What is more important, with no guarantee of making the initial expense profitable.
They describe the solution using a mathematical system called finite geometry, which is centered around a triangle-like structure called the Fano plane. Each point of the structure is drawn with pairs of numbers and connected with lines: each line generates a set of six numbers, which is equal to one ticket.
Three Fano planes and two triangles are needed to cover all 59 numbers and generate 27 sets of tickets.
Choosing tickets in this way guarantees that no matter which of the 45,057,474 possible draws occurs, at least one of the tickets will have at least two numbers in common. Of any draw of six, two numbers must appear in one of five geometric structures, ensuring that they appear on at least one ticket.
But Dr. Stewart and Dr. Cushing say the hard work is actually showing that you can’t achieve the same result with 26 tickets.
Dr David Stewart, Reader in Pure Mathematics at the University of Manchester, said in a statement: “Fundamentally, there is a tension that comes from the fact that there are only 156 entries in 26 tickets. This means that many numbers cannot appear one time”. many times. Eventually you will see that you will be able to find six numbers that do not appear on any ticket together. In terms of graph theory, we ended up proving the existence of an independent set of size six.”
Although a win is guaranteed, the researchers say the chances of winning are highly unlikely and should not be used as a reason to gamble.
The 27 lottery tickets would cost you £54. And Peter Rowlett, a mathematician at The Aperiodical website, has shown that in almost 99% of cases, he would not get that money back.
By testing the theory in the lottery draw on July 1, 2023; the researchers hit just two balls on three of the tickets, the reward being three lucky guesses in a subsequent lottery, each resulting in nothing.
The researchers say the finding is computationally interesting. They use a fifty-year-old programming language called Prolog, which they say makes it one of the oldest examples of real artificial intelligence.
