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SUMMARY:David Stewart (Manchester)
DTSTART:20240213T140000Z
DTEND:20240213T150000Z
DTSTAMP:20260421T153817Z
UID:UEAPS/32
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UEAPS/32/">Y
 ou need 27 tickets to guarantee a win on the UK National Lottery (Jt with 
 David Cushing)</a>\nby David Stewart (Manchester) as part of ANTLR seminar
 \n\nLecture held in Queen 01.09.\n\nAbstract\nThe authors came across the 
 problem of finding minimal lottery design numbers j=L(n\,k\,p\,t)\; that i
 s\, 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\\c
 ap B_i with at least t elements. In the context of a lottery\, n represent
 s the. number of balls\, k the number of choices of balls on a ticket\, p 
 the size of a draw.\nFor the UK national lottery\, n=59\, k=p=6 and one ge
 ts a (rather meagre) prize as long as t is at least 2.\nUsing the constrai
 nt solving library in Prolog\, we calculated j for k=p=6\, t=2 and n all t
 he way up to 70. For example L(59\,6\,6\,2)=27. This is the second paper w
 here we have aimed to show the value of Prolog and constraint programming 
 in pure mathematics.\nI’ll give an overview of constraint programming\, 
 logic programming in Prolog\, and describe how we used these tools to solv
 e the problem described in the title.\n
LOCATION:https://researchseminars.org/talk/UEAPS/32/
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