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This paper develops and deploys a set of constraints for the purpose ofcalculating minimal sizes of lottery designs, with an application to the UKNational Lottery: in case there are n = 59 balls, the minimum number of ticketsof size six which are needed to match at least two balls on any draw of sizesix is precisely 27. In fact, we calculate this minimum value for all n at most70.

You need 27 tickets to guarantee a win on the UK National Lottery