There will be a CIRCA lunchtime seminar on 28th March at 1pm in Theatre D of Maths.

David Stewart (University of Manchester) will speak.

**Title: **You need 27 tickets to guarantee a win on the UK National Lottery (Jt with David Cushing)

**Abstract:** The authors came across the problem of finding minimal lottery design numbers j=L(n,k,p,t); that is, a set B_1, …, B_j subsets of {1,..,n} each of size k, such that for any subset D of {1,..,n} of size p, one finds an intersection D\cap B_i with at least t elements. In the context of a lottery, n represents the. number of balls, k the number of choices of balls on a ticket, p the size of a draw.

For the UK national lottery, n=59, k=p=6 and one gets a (rather meagre) prize as long as t is at least 2.

Using the constraint solving library in Prolog, we calculated j for k=p=6, t=2 and n all the way up to 70. For example L(59,6,6,2)=27. This is the second paper where we have aimed to show the value of Prolog and constraint programming in pure mathematics.

I’ll give an overview of constraint programming, logic programming in Prolog, and describe how we used these tools to solve the problem described in the title.