Help needed for my L(27,6,4,3) = 85 covering designPrev Topic Next Topic

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stivi19

?????
Bulgaria
Member #205,018
March 8, 2020
6 Posts
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Mar 8, 2020, 8:14 am

Hi, my name is Stanislav!
I have come up with a set of 85 6-tuples with the numbers from 1 to 27 which have the 3 if 4 guarantee for 17 543 out of 17 550 possible 4-tuples.
Can I please have a suggestion from you how can I improve on that?
Here is the current wheel:

1,3,7,19,20,27
1,2,4,5,19,25
1,7,8,20,23,24
1,15,21,23,24,27
1,10,13,17,23,26
1,5,8,9,21,24
1,2,10,21,22,23
1,7,15,17,20,22
1,2,12,13,16,19
1,6,21,22,24,25
1,7,12,14,20,26
1,3,8,10,17,22
1,2,6,9,11,19
1,7,13,16,18,20
1,2,14,18,19,26
1,10,12,15,17,18
1,10,14,16,17,27
1,3,4,11,21,24
2,7,8,10,21,27
2,15,17,20,23,27
2,7,13,23,24,26
2,10,12,14,21,26
2,10,13,16,18,21
2,5,8,9,17,20
2,6,17,20,22,25
2,7,12,15,18,24
2,3,4,11,17,20
2,3,10,15,20,21
2,7,14,16,24,27
2,8,15,17,19,24
2,3,7,8,22,24
3,9,12,16,23,25
3,9,18,25,26,27
3,5,6,12,13,27
3,17,19,21,23,24
3,9,13,14,15,25
3,5,6,15,16,26
3,8,13,16,22,27
3,5,6,14,18,23
3,4,11,14,18,23
3,8,19,20,21,22
3,8,12,15,22,26
3,4,7,10,11,19
3,5,8,9,11,22
4,5,13,16,25,26
4,9,12,13,22,27
4,5,6,7,17,21
4,7,9,17,21,25
4,9,14,18,22,23
4,6,8,14,22,25
4,5,12,15,25,27
4,6,8,12,16,23
4,9,15,16,22,26
4,6,8,18,26,27
4,6,8,13,14,15
4,6,9,10,20,24
4,5,10,20,24,25
5,11,12,16,22,23
5,7,11,17,21,25
5,11,13,14,15,22
5,7,8,9,10,19
5,8,9,14,18,23
5,6,10,11,20,24
5,11,18,22,26,27
6,9,11,12,13,26
6,7,9,11,17,21
6,7,10,19,22,25
6,9,11,15,16,27
6,12,18,22,23,25
7,13,14,17,18,21
7,12,16,17,21,26
7,10,15,19,23,27
8,11,12,13,25,27
8,11,14,18,23,25
8,11,15,16,25,26
9,10,11,20,24,25
10,12,13,14,20,24
10,17,19,22,24,27
10,16,18,20,24,26
12,14,17,19,24,26
12,15,18,19,20,21
13,16,17,18,19,24
13,19,20,21,23,26
14,16,19,20,21,27
14,15,16,18,23,27
stivi19

?????
Bulgaria
Member #205,018
March 8, 2020
6 Posts
Offline

Mar 11, 2020, 1:53 pm

There is a wheel with a coverage of 17 544:

1,6,21,22,24,25
1,10,13,17,23,26
1,2,4,5,19,25
1,7,15,17,20,22
1,2,12,13,16,19
1,2,10,21,22,23
1,10,12,15,17,18
1,7,13,16,18,20
1,3,7,19,20,27
1,3,8,10,17,22
1,7,8,20,23,24
1,5,8,9,21,24
1,2,6,9,11,19
1,3,4,11,21,24
1,10,14,16,17,27
1,7,12,14,20,26
1,2,14,18,19,26
1,15,21,23,24,27
2,8,15,17,19,24
2,3,7,8,22,24
2,3,4,11,17,20
2,7,8,10,21,27
2,15,17,20,23,27
2,7,13,23,24,26
2,3,10,15,20,21
2,7,14,16,24,27
2,5,8,9,17,20
2,10,12,14,21,26
2,6,17,20,22,25
2,10,13,16,18,21
2,7,12,15,18,24
3,9,12,16,23,25
3,4,11,12,14,18
3,5,6,15,16,26
3,8,19,20,21,22
3,6,8,14,22,25
3,8,13,16,22,27
3,5,6,12,13,27
3,4,8,11,22,23
3,5,6,14,18,23
3,17,19,21,23,24
3,9,13,14,15,25
3,9,18,25,26,27
3,4,7,10,11,19
4,5,6,7,17,21
4,6,9,10,20,24
4,6,8,12,16,23
4,6,8,13,14,15
4,7,9,17,21,25
4,5,9,15,25,27
4,9,14,18,22,23
4,9,15,16,22,26
4,6,8,18,26,27
4,5,10,20,24,25
4,9,12,13,22,27
4,5,13,16,25,26
5,8,9,14,18,23
5,11,13,14,15,22
5,6,9,11,13,26
5,6,10,11,20,24
5,7,8,9,10,19
5,11,18,22,26,27
5,7,11,17,21,25
5,11,12,16,22,23
6,12,18,22,23,25
6,7,10,19,22,25
6,9,11,15,16,27
6,7,9,11,17,21
7,13,14,17,18,21
7,12,16,17,21,26
7,10,15,19,23,27
8,12,15,18,22,26
8,11,12,13,25,27
8,11,14,18,23,25
8,11,15,16,25,26
9,10,11,20,24,25
10,17,19,22,24,27
10,12,13,14,20,24
10,16,18,20,24,26
12,15,18,19,20,21
12,14,17,19,24,26
13,19,20,21,23,26
13,14,15,16,23,27
13,16,17,18,19,24
14,16,19,20,21,27

But can anyone beat it?
stivi19

?????
Bulgaria
Member #205,018
March 8, 2020
6 Posts
Offline

Mar 11, 2020, 2:05 pm

I will give 1000 $ for any improvement > 17 544.
stivi19

?????
Bulgaria
Member #205,018
March 8, 2020
6 Posts
Offline

Mar 15, 2020, 3:49 pm

The UK National Lottery Wheeling Challenge is to find the smallest number of combinations in 6 from 49 that will guarantee at least one 2-match or 3-match. Am I the only person on the planet interested in breaking the current records of 163 combinations for a 3-match and 19 combinations for a 2-match?
stivi19

?????
Bulgaria
Member #205,018
March 8, 2020
6 Posts
Offline

Mar 16, 2020, 12:24 pm

Nobody interested in the theoretical part of the game...
lakerben

50

New Mexico
United States
Member #86,096
January 29, 2010
24,896 Posts
Offline

Apr 6, 2020, 10:48 pm

Quote: Originally posted by stivi19 on Mar 11, 2020
There is a wheel with a coverage of 17 544:

1,6,21,22,24,25
1,10,13,17,23,26
1,2,4,5,19,25
1,7,15,17,20,22
1,2,12,13,16,19
1,2,10,21,22,23
1,10,12,15,17,18
1,7,13,16,18,20
1,3,7,19,20,27
1,3,8,10,17,22
1,7,8,20,23,24
1,5,8,9,21,24
1,2,6,9,11,19
1,3,4,11,21,24
1,10,14,16,17,27
1,7,12,14,20,26
1,2,14,18,19,26
1,15,21,23,24,27
2,8,15,17,19,24
2,3,7,8,22,24
2,3,4,11,17,20
2,7,8,10,21,27
2,15,17,20,23,27
2,7,13,23,24,26
2,3,10,15,20,21
2,7,14,16,24,27
2,5,8,9,17,20
2,10,12,14,21,26
2,6,17,20,22,25
2,10,13,16,18,21
2,7,12,15,18,24
3,9,12,16,23,25
3,4,11,12,14,18
3,5,6,15,16,26
3,8,19,20,21,22
3,6,8,14,22,25
3,8,13,16,22,27
3,5,6,12,13,27
3,4,8,11,22,23
3,5,6,14,18,23
3,17,19,21,23,24
3,9,13,14,15,25
3,9,18,25,26,27
3,4,7,10,11,19
4,5,6,7,17,21
4,6,9,10,20,24
4,6,8,12,16,23
4,6,8,13,14,15
4,7,9,17,21,25
4,5,9,15,25,27
4,9,14,18,22,23
4,9,15,16,22,26
4,6,8,18,26,27
4,5,10,20,24,25
4,9,12,13,22,27
4,5,13,16,25,26
5,8,9,14,18,23
5,11,13,14,15,22
5,6,9,11,13,26
5,6,10,11,20,24
5,7,8,9,10,19
5,11,18,22,26,27
5,7,11,17,21,25
5,11,12,16,22,23
6,12,18,22,23,25
6,7,10,19,22,25
6,9,11,15,16,27
6,7,9,11,17,21
7,13,14,17,18,21
7,12,16,17,21,26
7,10,15,19,23,27
8,12,15,18,22,26
8,11,12,13,25,27
8,11,14,18,23,25
8,11,15,16,25,26
9,10,11,20,24,25
10,17,19,22,24,27
10,12,13,14,20,24
10,16,18,20,24,26
12,15,18,19,20,21
12,14,17,19,24,26
13,19,20,21,23,26
13,14,15,16,23,27
13,16,17,18,19,24
14,16,19,20,21,27

But can anyone beat it?

I used some of these numbers for tonight. Thr rr cash in NM is over 400k.

I'm sitting here listening to Merle Haggard sipping some coffee!
stivi19

?????
Bulgaria
Member #205,018
March 8, 2020
6 Posts
Offline

Apr 7, 2020, 2:24 am

The world record is 17 548 so I am looking for a wheel with 17 549 or 17 550 combinations coverage.

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Help needed for my L(27,6,4,3) = 85 covering designPrev TopicNext Topic

Help needed for my L(27,6,4,3) = 85 covering designPrev Topic Next Topic