From: Robin Chapman Subject: Re: Lottery Problem Date: Mon, 12 Jul 1999 07:15:01 GMT Newsgroups: sci.math Keywords: application of Steiner systems! In article , "Steyer Michael" wrote: > I am looking for the solution for an apparently well known problem. It is > asked for the minimum number of tickets in a 49/6 lottery that guarantees > you at least a 3-match. The CRC handbook of combinatorial design tells 174 > at most (solution is given) and 86 at least. The solution for 174 is derived > from two Steiner systems S(3,6,22) which is a sort of waste since you don't > need to have a design that includes every combination of 3 numbers. The > absolute minimum of tickets you can think of is even 46: There is a total of > (49 choose 3) = 18424 3-combinations, and with every ticket you cover (6 > choose 3)=20. Since every draw results in the same number (20) of > 3-combinations, 18242/(20*20) = 46 is the theoretical minimum of tickets > required.Does anyone know the real minimum ?? No. But 174 has been bettered. Uenal Mutlu has an example with 168 tickets. See http://lottery.merseyworld.com/Wheel/Wheel.html -- Robin Chapman http://www.maths.ex.ac.uk/~rjc/rjc.html "They did not have proper palms at home in Exeter." Peter Carey, _Oscar and Lucinda_ Sent via Deja.com http://www.deja.com/ Share what you know. Learn what you don't.