Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.2 9/5/84; site anasazi.UUCP Path: utzoo!watmath!clyde!burl!ulysses!mhuxr!mhuxn!ihnp4!qantel!lll-crg!seismo!hao!noao!terak!anasazi!steve From: steve@anasazi.UUCP (Steve Villee) Newsgroups: net.puzzle Subject: Re: Winning 1/3 of the Lottery Message-ID: <377@anasazi.UUCP> Date: Mon, 25-Nov-85 20:38:22 EST Article-I.D.: anasazi.377 Posted: Mon Nov 25 20:38:22 1985 Date-Received: Fri, 29-Nov-85 21:38:29 EST References: <25@bbncc5.UUCP> Organization: Anasazi, Phoenix Az. Lines: 44 > 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? The following tickets will do it, although there may be a smaller set. #1: 1, 2, 3, 4, 5, 6 #2: 1, 2, 3, 7, 8, 9 #3: 1, 2, 3, 10, 11, 12 #4: 1, 2, 3, 13, 14, 15 . . #10: 1, 2, 3, 31, 32, 33 #11: 1, 2, 3, 34, 35, 36 #12: 4, 5, 6, 7, 8, 9 #13: 4, 5, 6, 10, 11, 12 . . #20: 4, 5, 6, 31, 32, 33 #21: 4, 5, 6, 34, 35, 36 #22: 7, 8, 9, 10, 11, 12 #23: 7, 8, 9, 13, 14, 15 . . #64: 28, 29, 30, 31, 32, 33 #65: 28, 29, 30, 34, 35, 36 #66: 31, 32, 33, 34, 35, 36 The number of tickets here is 11+10+9+8+7+6+5+4+3+2+1 = 66. I suspect that the prize for getting just two matching numbers is less than 66 dollars. --- Steve Villee (ihnp4!terak!anasazi!steve) International Anasazi, Inc. 7500 North Dreamy Draw Drive, Suite 120 Phoenix, Arizona 85020 (602) 870-3330