14
| New Scientist | 5 August 2023
News
YOU can guarantee a win in every
draw of the UK National Lottery by
buying just 27 tickets, say a pair of
mathematicians – but you won’t
necessarily make a profit.
Players of the UK “Lotto” choose
six numbers from 1 to 59, paying
£2 per ticket. Prizes are awarded
for tickets matching two or more
of six randomly drawn numbers.
David Cushing and David
Stewart at the University of
Manchester, UK, claim that
despite there being 45,057,474
combinations of numbers, it
is possible to guarantee a win
with just 27 specific tickets.
The proof of their idea relies
on a field called finite geometry
and involves placing each of the
numbers from 1 to 59 in pairs or
triplets on a point within one of
five geometrical shapes, then
using these to generate lottery
tickets based on the lines within
the shapes. The five shapes offer 27
such lines, meaning that 27 tickets
bought using those numbers, at a
cost of £54, will hit every possible
winning combination of two
numbers (arXiv, doi.org/kmcw).
The work yielded a specific
list of 27 tickets, but the pair say
subsequent work shows there
are two other combinations of
27 tickets that also guarantee a win.
Looking at the winning
numbers from the 21 June Lotto
draw, the pair found their method
would have won £1810. But the
same numbers played on 1 July
would have matched just two balls
on three of the tickets – still a
technical win, but giving just three
“lucky dip” tries in the next draw,
each of which came to nothing.
Stewart says proving that
27 tickets could guarantee a win
was relatively easy, but proving
it is impossible to guarantee a
win with 26 was far trickier. He
estimates that the number of
calculations needed to verify that
would be 10
16
5, far more than the
number of atoms in the universe.
The solution was a computer
programming language called
Prolog. Unlike conventional
computer languages where a
coder sets out what a machine
should do, step by step, Prolog
takes a list of facts relating to a
problem and whittles down an
array of possible solutions.
Cushing says the work shouldn’t
be taken as a reason to gamble,
Dostları ilə paylaş: |