ado@elsie.UUCP (Arthur David Olson) (12/23/85)
And now for the 123-ticket solution. The first sixty tickets are as before. One or more of these twenty tickets have three or more winning numbers if there are three or more winning numbers between 1 and 12: 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 One or more of these twenty tickets have three or more winning numbers if there are three or more winning numbers between 13 and 24: 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 One or more of these twenty tickets have three or more winning numbers if there are three or more winning numbers between 25 and 36: 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 none of the above tickets is a winner, then there are exactly two winners 1 and 12, exactly two winners between 13 and 24, and exactly two winners between 25 and 36. If there are two winners between 1 and 6, then at least one of these 18 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 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 If there aren't two winners between 1 and 6, then there is at least one winner between 7 and 12, and at least one of these 45 tickets will have three or four winners: 7 8 13 14 15 16 | 9 10 13 14 15 16 | 11 12 13 14 15 16 7 8 13 14 17 18 | 9 10 13 14 17 18 | 11 12 13 14 17 18 7 8 13 14 19 20 | 9 10 13 14 19 20 | 11 12 13 14 19 20 7 8 13 14 21 22 | 9 10 13 14 21 22 | 11 12 13 14 21 22 7 8 13 14 23 24 | 9 10 13 14 23 24 | 11 12 13 14 23 24 7 8 15 16 17 18 | 9 10 15 16 17 18 | 11 12 15 16 17 18 7 8 15 16 19 20 | 9 10 15 16 19 20 | 11 12 15 16 19 20 7 8 15 16 21 22 | 9 10 15 16 21 22 | 11 12 15 16 21 22 7 8 15 16 23 24 | 9 10 15 16 23 24 | 11 12 15 16 23 24 7 8 17 18 19 20 | 9 10 17 18 19 20 | 11 12 17 18 19 20 7 8 17 18 21 22 | 9 10 17 18 21 22 | 11 12 17 18 21 22 7 8 17 18 23 24 | 9 10 17 18 23 24 | 11 12 17 18 23 24 7 8 19 20 21 22 | 9 10 19 20 21 22 | 11 12 19 20 21 22 7 8 19 20 23 24 | 9 10 19 20 23 24 | 11 12 19 20 23 24 7 8 21 22 23 24 | 9 10 21 22 23 24 | 11 12 21 22 23 24 Total tickets: 20 + 20 + 20 + 18 + 45 = 123. -- UUCP: ..decvax!seismo!elsie!ado ARPA: elsie!ado@seismo.ARPA DEC, VAX and Elsie are Digital Equipment and Borden trademarks