I need to preface this by saying: the maths relates to 27 lottery tickets required to win any lottery prize for the UK National Lottery. So don’t spend £54 expecting to win the jackpot each time. At best, you’ll get a free lucky dip for the next week. Sorry if the title got your hopes up! But if you’d like to hear the maths behind it, Matt Parker gave an overview of the paper that demonstrated the maths (you can also read the paper on Arxiv). Here’s the abstract:
In the UK National Lottery, players purchase tickets comprising their choices of six different numbers between 1 and 59. During the draw, six balls are randomly selected without replacement from a set numbered from 1 to 59. A prize is awarded to any player who matches at least two of the six drawn numbers. We identify 27 tickets that guarantee a prize, regardless of which of the 45,057,474 possible draws occurs. Moreover, we determine that 27 is the optimal number of tickets required, as achieving the same guarantee with 26 tickets is not possible.
I just thought: this might be good for syndicate organisers as, with this maths, they’ll need at least 27 members to guarantee a win amongst them. Splitting a tenner 27 ways (if you’re lucky!!) doesn’t sound as good though!