Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: $Revision: 1.6.2.16 $; site ada-uts.UUCP Path: utzoo!watmath!clyde!burl!ulysses!mhuxr!mhuxn!ihnp4!qantel!lll-crg!ucdavis!ucbvax!decvax!cca!ada-uts!brianu From: brianu@ada-uts.UUCP Newsgroups: net.puzzle Subject: Re: Orphaned Response Message-ID: <11900001@ada-uts.UUCP> Date: Mon, 25-Nov-85 11:13:00 EST Article-I.D.: ada-uts.11900001 Posted: Mon Nov 25 11:13:00 1985 Date-Received: Fri, 29-Nov-85 08:58:28 EST References: <25@bbncc5.UUCP> Lines: 29 Nf-ID: #R:bbncc5:-2500:ada-uts:11900001:177600:1587 Nf-From: ada-uts!brianu Nov 25 11:13:00 1985 >***** ada-uts:net.puzzle / bbncc5!ldenenbe / 11:08 am Nov 19, 1985 >The Massachusetts State Megabucks Lottery works like this: A ticket costs >$1 and consists of six distinct numbers of your choosing between 1 and 36 >inclusive. You may buy as many tickets as you like. On Lottery Day >the Authorities choose six numbers. If those six are the same as your >six, you win! (There may be many winners, since other players may have >chosen the same set of six numbers. You split the Big Bucks equally.) >There are lesser prizes for matching five, four, and three numbers. > >What is the minimum number of tickets that you must buy to ensure that >at least one of your tickets matches two or more of the winning numbers? Well, there are 36*35/2 = 630 different combinations of two numbers 1-36. Suppose that they only choose 2 numbers rather than 6. Those 2 nuumbers must be one of the 630 combinations. To ensure that you have at least one ticket with this combination, you must buy enough tickets to cover all the pairs. Each ticket covers 15 pairs, so you must by at least 630/15=42 tickets. This is assuming you can find a covering without overlap. (this may or may not be possible) Since they draw 6 rather than 2 numbers, you will match all 15 pairs generated. So this method guarantees 15 pairs rather than the required 1. However, if there does not exist a non-overlapping covering of the 630 pairs, the nummber required can be reduced. So we have 42 tickets as the maximum that may be required. Brian Utterback Intermetrics Inc. UUCP:{cca,ihnp4}!ima!inmet!ada-uts!brianu