2023-08-10 04:00:15
Mathematicians from the University of Manchester have solved a mystery: how many lottery tickets to buy and how to fill them to guarantee a lottery win?
Image d’illustration Pixabay
David Stewart and David Cushing studied the flagship game of the British National Lottery, “Lotto”, which draws six random numbers from 1 to 59. They determined that 27 is the minimum number of tickets needed to guarantee a win, i.e. at minus two correct numbers in the same grid (A toaster is a small household appliance. A screen grid is an element of…). However, this does not guarantee a profit.
The solution relies on a mathematical system called finite geometry. At the heart of this system is a structure in the shape of a triangle (In Euclidean geometry, a triangle is a plane figure, formed by three points…), the Fano plane. Each point (Graphie) is associated with a pair (We say that a set E is a pair when it is formed of two distinct elements…) of numbers and connected by lines. Each line generates a combination (A combination can be:) of six numbers, ie a grid. Three Fano planes and two triangles are needed to cover all 59 numbers and produce 27 combinations.
Credit: University of Manchester
By filling in the grids in this way, it is guaranteed that at least one ticket will match at least two of the numbers drawn, regardless of the combination of the six numbers.
Even if a gain is guaranteed, the chances of making a profit remain slim. The 27 tickets would cost £54. Peter Rowlett, another mathematician, showed that in almost 99% of cases, this amount would not be recovered. The researchers tested their theory (The word theory comes from the Greek word theorein, which means “to contemplate, to observe,…) in the July 1, 2023 draw. They only managed to match two correct numbers out of three of the grids .
The 27 lottery number combinations.
Credit: University of Manchester
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