Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.3 4.3bsd-beta 6/6/85; site elsie.UUCP Path: utzoo!watmath!clyde!burl!ulysses!gamma!epsilon!zeta!sabre!petrus!bellcore!decvax!decwrl!pyramid!ut-sally!seismo!elsie!ado From: ado@elsie.UUCP (Arthur David Olson) Newsgroups: net.puzzle Subject: Re: Mass Lottery 3 number match (spoiler) Message-ID: <5313@elsie.UUCP> Date: Tue, 17-Dec-85 10:47:25 EST Article-I.D.: elsie.5313 Posted: Tue Dec 17 10:47:25 1985 Date-Received: Fri, 20-Dec-85 01:39:26 EST References: <13200001@faust.UUCP> Organization: NIH-LEC, Bethesda, MD Lines: 63 Here's a 150-ticket solution. If there are at least three winning numbers between 1 and 12, then at least one of these twenty tickets has at least three winning numbers: 1 2 3 4 5 6 | 1 2 3 4 7 8 | 1 2 3 4 9 10 | 1 2 3 4 11 12 1 2 5 6 7 8 | 1 2 5 6 9 10 | 1 2 5 6 11 12 | 1 2 7 8 9 10 1 2 7 8 11 12 | 1 2 9 10 11 12 | 3 4 5 6 7 8 | 3 4 5 6 9 10 3 4 5 6 11 12 | 3 4 7 8 9 10 | 3 4 7 8 11 12 | 3 4 9 10 11 12 5 6 7 8 9 10 | 5 6 7 8 11 12 | 5 6 9 10 11 12 | 7 8 9 10 11 12 If there are at least three winning numbers between 13 and 24, then at least one of these twenty tickets has at least three winning numbers: 13 14 15 16 17 18 | 13 14 15 16 19 20 | 13 14 15 16 21 22 | 13 14 15 16 23 24 13 14 17 18 19 20 | 13 14 17 18 21 22 | 13 14 17 18 23 24 | 13 14 19 20 21 22 13 14 19 20 23 24 | 13 14 21 22 23 24 | 15 16 17 18 19 20 | 15 16 17 18 21 22 15 16 17 18 23 24 | 15 16 19 20 21 22 | 15 16 19 20 23 24 | 15 16 21 22 23 24 17 18 19 20 21 22 | 17 18 19 20 23 24 | 17 18 21 22 23 24 | 19 20 21 22 23 24 If there are at least three winning numbers between 25 and 36, then at least one of these twenty tickets has at least three winning numbers: 25 26 27 28 29 30 | 25 26 27 28 31 32 | 25 26 27 28 33 34 | 25 26 27 28 35 36 25 26 29 30 31 32 | 25 26 29 30 33 34 | 25 26 29 30 35 36 | 25 26 31 32 33 34 25 26 31 32 35 36 | 25 26 33 34 35 36 | 27 28 29 30 31 32 | 27 28 29 30 33 34 27 28 29 30 35 36 | 27 28 31 32 33 34 | 27 28 31 32 35 36 | 27 28 33 34 35 36 29 30 31 32 33 34 | 29 30 31 32 35 36 | 29 30 33 34 35 36 | 31 32 33 34 35 36 If there aren't any winners in the above tickets, then there are exactly two winning numbers between 1 and 12, exactly two winning numbers between 13 and 24, and exactly two winning numbers between 25 and 36. Here, we'll rely on the fact that there are two winning numbers between 1 and 12 and at least one winning number between 13 and 24; this being so, then at least one of these ninety tickets has three (or four) winning numbers: 1 2 3 4 13 14 | 1 2 3 4 15 16 | 1 2 3 4 17 18 | 1 2 3 4 19 20 1 2 3 4 21 22 | 1 2 3 4 23 24 | 1 2 5 6 13 14 | 1 2 5 6 15 16 1 2 5 6 17 18 | 1 2 5 6 19 20 | 1 2 5 6 21 22 | 1 2 5 6 23 24 1 2 7 8 13 14 | 1 2 7 8 15 16 | 1 2 7 8 17 18 | 1 2 7 8 19 20 1 2 7 8 21 22 | 1 2 7 8 23 24 | 1 2 9 10 13 14 | 1 2 9 10 15 16 1 2 9 10 17 18 | 1 2 9 10 19 20 | 1 2 9 10 21 22 | 1 2 9 10 23 24 1 2 11 12 13 14 | 1 2 11 12 15 16 | 1 2 11 12 17 18 | 1 2 11 12 19 20 1 2 11 12 21 22 | 1 2 11 12 23 24 | 3 4 5 6 13 14 | 3 4 5 6 15 16 3 4 5 6 17 18 | 3 4 5 6 19 20 | 3 4 5 6 21 22 | 3 4 5 6 23 24 3 4 7 8 13 14 | 3 4 7 8 15 16 | 3 4 7 8 17 18 | 3 4 7 8 19 20 3 4 7 8 21 22 | 3 4 7 8 23 24 | 3 4 9 10 13 14 | 3 4 9 10 15 16 3 4 9 10 17 18 | 3 4 9 10 19 20 | 3 4 9 10 21 22 | 3 4 9 10 23 24 3 4 11 12 13 14 | 3 4 11 12 15 16 | 3 4 11 12 17 18 | 3 4 11 12 19 20 3 4 11 12 21 22 | 3 4 11 12 23 24 | 5 6 7 8 13 14 | 5 6 7 8 15 16 5 6 7 8 17 18 | 5 6 7 8 19 20 | 5 6 7 8 21 22 | 5 6 7 8 23 24 5 6 9 10 13 14 | 5 6 9 10 15 16 | 5 6 9 10 17 18 | 5 6 9 10 19 20 5 6 9 10 21 22 | 5 6 9 10 23 24 | 5 6 11 12 13 14 | 5 6 11 12 15 16 5 6 11 12 17 18 | 5 6 11 12 19 20 | 5 6 11 12 21 22 | 5 6 11 12 23 24 7 8 9 10 13 14 | 7 8 9 10 15 16 | 7 8 9 10 17 18 | 7 8 9 10 19 20 7 8 9 10 21 22 | 7 8 9 10 23 24 | 7 8 11 12 13 14 | 7 8 11 12 15 16 7 8 11 12 17 18 | 7 8 11 12 19 20 | 7 8 11 12 21 22 | 7 8 11 12 23 24 9 10 11 12 13 14 | 9 10 11 12 15 16 | 9 10 11 12 17 18 | 9 10 11 12 19 20 9 10 11 12 21 22 | 9 10 11 12 23 24 -- UUCP: ..decvax!seismo!elsie!ado ARPA: elsie!ado@seismo.ARPA DEC, VAX and Elsie are Digital Equipment and Borden trademarks