Ion Saliu
2018-01-03 19:20:42 UTC
Positional Lotto Wheels from Groups of Numbers I
Axiomatics:
One year and one day ago, I started a thread in this glorious newsgroup:
https://groups.google.com/forum/#!topic/rec.gambling.lottery/E-aM_zUsQFY
(Hottest-24 lotto numbers in the 6-59 UK Lottery).
One string of consisted of the most frequent 24 numbers regardless of position. Another groups consisted of the top 24 numbers position by position. I chose for this thread only the top 12 elelements for each position.
Top-24 lotto numbers regardless of position
14 2 41 10 29 34 37 38 40 11 46 54 57 58 8 26 12 39 31 51 52 17 55 19
Top-12 lotto numbers in ech position
2 1 10 11 4 8 5 7 13 3 9 12
14 17 12 3 13 11 8 22 7 15 16 2
30 31 26 18 25 16 20 29 21 22 35 27
32 34 37 46 38 39 42 28 40 41 19 24
40 51 44 41 53 48 49 43 52 47 54 37
58 57 59 54 52 55 56 50 51 49 42 46
The non-positional system generates a total of C(24, 6) = 134,596 combosnations (a favorite of my lottery-speak, mind you!) The positional system generated a total of 1,067,772 combinations (there is no formula for that as some numbers overlap randomly).
I stressed in another thread that the positional systems always perform better than non-positional systems based on frequency/skips. Granted, the positional system amount to a larger number of combinations.
At any rate, these types of lottery strategies are impractical. Nobody can generate that many combosnations and print them on tickets... and then go to a lottery terminal! So, many lottery players think of wheeling the combinations and the results are so-called 'reduced lottery systems (wheels)'.
I generated all possible combinations from the two systems above. Software: SkipSystem.exe, menu II of the Bright / Ultimate grandiose lottery applications. Functions: 'S = Lotto 6', then 'G = Generate Combinations from Systems'. We enter the systems above, one at a time, paying attention to the names of the output files.
In the next step, we are going to wheel the output files created at the first step. Software: SoftwareLotto6.exe. It is listed as 'Super Utilities' on the main menu of the Bright / Ultimate grand lottery packages. The super pack has many functions. We'll use the function D = Duplicates: Strip and Wheel'. I chose the '3 of 6' minimum guarantee to get the minimal amount of combinations to be published here.
The non-positional system ended up as a 74-line lotto wheel:
2 8 10 11 12 14
2 8 17 19 26 29
2 8 31 34 37 38
2 8 39 40 41 46
2 8 51 52 54 55
2 10 17 31 39 51
2 10 19 34 40 52
2 10 26 37 41 54
2 10 29 38 46 55
2 11 17 34 41 55
2 11 19 31 46 54
2 11 26 38 39 52
2 11 29 37 40 51
2 12 17 37 46 52
2 12 19 38 41 51
2 12 26 31 40 55
2 12 29 34 39 54
2 14 17 38 40 54
2 14 19 37 39 55
2 14 26 34 46 51
2 14 29 31 41 52
8 10 17 34 46 54
8 10 19 31 41 55
8 10 26 38 40 51
8 10 29 37 39 52
8 11 17 31 40 52
8 11 19 34 39 51
8 11 26 37 46 55
8 11 29 38 41 54
8 12 17 38 39 55
8 12 19 37 40 54
8 12 26 34 41 52
8 12 29 31 46 51
8 14 17 37 41 51
8 14 19 38 46 52
8 14 26 31 39 54
8 14 29 34 40 55
10 11 17 19 37 38
10 11 26 29 31 34
10 11 39 40 54 55
10 11 41 46 51 52
10 12 17 26 57 58
10 12 31 38 52 54
10 12 34 37 51 55
10 14 19 29 51 54
10 14 31 37 40 46
10 14 34 38 39 41
11 12 19 29 52 55
11 12 31 37 39 41
11 12 34 38 40 46
11 14 17 29 39 46
11 14 19 26 40 41
11 14 31 38 51 55
11 14 34 37 52 54
12 14 17 19 31 34
12 14 26 29 37 38
12 14 39 40 51 52
12 14 41 46 54 55
17 19 39 41 52 54
17 19 40 46 51 55
17 26 31 38 41 46
17 26 34 37 39 40
17 29 31 37 54 55
17 29 34 38 51 52
19 26 31 37 51 52
19 26 34 38 54 55
19 29 31 38 39 40
19 29 34 37 41 46
26 29 39 41 51 55
26 29 40 46 52 54
31 34 39 46 52 55
31 34 40 41 51 54
37 38 39 46 51 54
37 38 40 41 52 55
The positional system ended up as a 370-line lotto wheel:
1 2 16 19 37 42
1 2 18 24 40 46
1 2 20 28 41 49
1 2 21 32 43 50
1 2 22 34 44 51
1 2 25 38 47 52
1 2 26 39 48 54
1 3 16 24 41 50
1 3 18 19 43 49
1 3 20 32 37 46
1 3 21 28 40 42
1 3 22 38 48 55
1 3 25 34 53 54
1 3 27 39 44 52
1 7 16 28 43 46
1 7 18 32 41 42
1 7 20 24 44 54
1 7 21 34 37 49
1 7 22 39 40 50
1 7 26 38 51 56
1 8 16 32 40 49
1 8 18 28 37 50
1 8 20 34 43 52
1 8 21 24 47 51
1 8 22 41 53 56
1 8 25 42 44 46
1 8 27 38 54 57
1 11 16 34 47 55
1 11 18 38 44 58
1 11 20 39 51 57
1 11 21 41 48 52
1 11 22 24 37 59
1 11 25 40 43 56
1 11 26 42 49 50
1 12 16 38 53 59
1 12 18 34 48 56
1 12 20 40 47 58
1 12 21 46 54 55
1 12 22 28 52 57
1 12 25 37 41 51
1 13 18 39 47 59
1 13 20 42 53 55
1 13 22 32 54 58
1 13 26 34 40 57
1 13 27 28 48 51
1 13 29 37 44 56
1 13 30 38 41 46
1 14 21 39 53 58
1 14 22 46 47 49
1 14 25 32 48 57
1 14 26 28 44 55
1 14 27 34 41 59
1 14 29 40 51 52
1 14 30 37 43 54
1 15 25 39 49 55
1 15 26 32 52 59
1 15 27 42 43 58
1 15 29 41 47 54
1 15 31 37 53 57
1 15 35 46 48 50
1 17 27 32 47 56
1 17 29 42 48 59
1 17 31 40 41 55
1 17 35 37 52 58
2 3 16 28 44 54
2 3 18 32 47 51
2 3 20 24 43 55
2 3 21 34 41 46
2 3 22 37 40 49
2 3 25 42 48 50
2 3 26 38 53 57
2 7 16 24 47 49
2 7 18 19 44 50
2 7 20 32 40 52
2 7 21 28 48 55
2 7 22 38 41 54
2 7 25 34 43 57
2 7 27 37 51 58
2 7 29 39 53 56
2 8 16 34 48 58
2 8 18 38 43 56
2 8 20 37 44 57
2 8 21 39 40 59
2 8 22 42 47 55
2 8 26 28 51 52
2 8 27 46 49 50
2 8 30 32 53 54
2 11 16 32 41 56
2 11 18 28 53 59
2 11 20 42 54 58
2 11 21 38 49 51
2 11 22 39 43 46
2 11 27 40 44 55
2 11 29 34 37 50
2 12 16 39 51 55
2 12 18 37 52 54
2 12 20 46 48 59
2 12 21 24 44 56
2 12 25 32 49 58
2 12 26 40 41 42
2 13 16 38 40 50
2 13 18 34 49 55
2 13 21 42 52 57
2 13 25 28 37 46
2 13 29 41 43 51
2 13 30 39 44 58
2 14 18 39 41 57
2 14 20 34 47 56
2 14 22 24 48 52
2 14 29 32 44 46
2 14 30 42 49 59
2 14 31 40 43 58
2 14 35 37 53 55
2 15 25 40 51 54
2 15 26 46 47 58
2 15 30 37 48 56
2 15 31 38 44 59
2 17 26 37 43 59
2 17 29 40 47 57
2 17 30 46 52 55
2 17 31 42 51 56
3 7 16 19 40 51
3 7 18 24 37 56
3 7 20 28 47 50
3 7 21 32 44 57
3 7 22 34 52 58
3 7 25 38 49 59
3 7 26 39 41 55
3 7 27 46 48 54
3 8 16 37 47 52
3 8 18 34 44 59
3 8 20 38 41 42
3 8 22 39 51 54
3 8 25 28 43 58
3 8 26 32 48 56
3 8 29 40 53 55
3 11 16 39 48 49
3 11 18 40 41 54
3 11 22 42 44 56
3 11 25 32 52 55
3 11 26 34 43 51
3 11 27 28 37 57
3 11 29 46 47 59
3 12 16 42 43 57
3 12 18 46 53 58
3 12 22 32 41 59
3 12 25 39 47 56
3 12 26 37 44 50
3 12 30 38 40 52
3 13 21 24 48 58
3 13 26 42 47 54
3 13 27 40 43 59
3 13 29 32 49 50
3 13 30 37 51 55
3 13 31 41 52 56
3 14 21 38 54 56
3 14 29 37 41 58
3 14 31 34 49 57
3 14 35 39 40 46
3 15 18 28 48 52
3 15 20 39 53 59
3 15 22 24 47 57
3 15 27 41 49 51
3 15 31 32 43 54
3 17 25 46 51 57
3 17 30 39 43 50
3 17 31 38 47 58
3 17 35 42 49 55
4 7 16 32 37 50
4 7 18 28 40 49
4 7 20 34 41 51
4 7 21 24 43 52
4 7 22 42 48 57
4 7 25 39 54 58
4 7 26 46 53 59
4 7 27 38 47 55
4 8 16 19 41 46
4 8 18 24 48 54
4 8 20 32 47 59
4 8 21 28 53 57
4 8 22 38 40 58
4 8 25 34 37 55
4 8 26 39 43 49
4 8 27 42 52 56
4 11 16 24 40 42
4 11 18 19 37 51
4 11 20 28 44 46
4 11 21 34 54 59
4 11 22 41 47 50
4 11 27 32 48 58
4 11 29 38 43 57
4 11 30 39 53 55
4 12 16 34 44 49
4 12 18 32 43 55
4 12 20 37 53 56
4 12 21 38 48 50
4 12 27 28 41 54
4 12 29 39 52 59
4 12 30 42 47 51
4 13 16 28 47 56
4 13 20 24 49 57
4 13 21 32 40 46
4 13 25 38 44 51
4 13 26 37 48 52
4 13 29 34 53 58
4 13 31 42 43 50
4 14 20 40 48 55
4 14 22 28 43 51
4 14 25 41 49 52
4 14 31 39 44 56
4 15 16 38 52 54
4 15 21 37 41 42
4 15 22 32 49 56
4 15 27 34 40 50
4 15 29 46 51 55
4 17 18 34 47 52
4 17 22 24 44 55
4 17 26 32 41 57
4 17 29 37 49 54
4 17 35 39 48 51
5 7 16 34 54 56
5 7 18 38 52 57
5 7 20 42 43 49
5 7 21 40 41 58
5 7 22 28 44 59
5 7 29 32 48 51
5 8 16 24 43 59
5 8 18 19 40 42
5 8 20 28 54 55
5 8 25 32 41 50
5 8 26 37 53 58
5 8 29 34 47 49
5 8 30 39 48 52
5 8 35 46 51 56
5 11 16 19 44 52
5 11 18 46 48 55
5 11 20 38 40 59
5 11 21 37 47 56
5 11 22 32 53 57
5 11 27 39 41 42
5 12 16 37 40 46
5 12 18 24 41 49
5 12 21 34 51 52
5 12 25 38 43 54
5 12 29 42 44 55
5 13 16 41 48 57
5 13 20 34 44 50
5 13 21 39 43 55
5 13 22 24 40 51
5 13 27 38 49 56
5 13 29 46 52 54
5 13 31 32 37 59
5 14 16 28 49 50
5 14 22 34 37 42
5 14 25 39 51 59
5 14 26 32 40 54
5 14 30 41 47 55
5 14 35 38 48 58
5 15 18 39 44 54
5 15 20 24 37 52
5 15 21 46 49 57
5 15 25 28 53 56
5 15 35 42 47 59
5 16 22 39 47 58
5 17 18 28 51 58
5 17 21 24 53 54
5 17 22 41 43 52
5 17 25 40 44 49
5 17 27 37 48 50
7 8 29 41 44 52
7 8 30 34 40 46
7 8 31 39 47 57
7 8 35 37 48 59
7 11 30 32 43 59
7 11 31 37 41 46
7 11 35 42 51 52
7 12 27 40 53 57
7 12 31 42 54 59
7 12 35 38 44 46
7 13 35 40 54 55
7 14 16 42 44 58
7 14 26 34 48 50
7 14 35 41 43 56
7 15 22 37 43 55
7 15 26 28 54 57
7 15 29 38 40 42
7 17 30 41 48 49
8 11 30 41 51 58
8 11 31 40 48 50
8 12 27 32 44 51
8 12 31 38 49 55
8 13 21 41 49 54
8 14 18 32 52 58
8 14 30 38 44 50
8 15 35 40 41 57
8 17 20 24 40 56
8 22 31 46 52 59
9 11 16 37 43 58
9 11 18 39 52 56
9 11 22 28 48 54
9 11 25 41 44 57
9 11 30 40 47 49
9 12 16 19 47 50
9 12 18 40 51 59
9 12 20 32 54 57
9 12 21 28 43 49
9 12 22 34 53 55
9 12 29 38 41 56
9 12 31 39 48 58
9 13 16 24 44 46
9 13 18 19 41 58
9 13 20 28 52 59
9 13 25 39 40 42
9 13 27 34 37 54
9 13 35 38 47 57
9 14 16 40 53 56
9 14 18 24 43 50
9 14 20 37 49 51
9 14 26 46 52 57
9 14 27 28 47 58
9 14 29 39 54 55
9 15 16 28 41 55
9 15 20 38 43 46
9 15 21 32 51 58
9 15 22 40 44 52
9 15 25 34 48 59
9 16 18 42 49 54
9 16 29 34 51 57
9 17 21 41 47 59
9 17 22 38 49 50
9 17 26 34 44 56
9 17 30 32 37 42
10 11 16 46 51 54
10 11 18 42 47 57
10 11 21 39 44 50
10 11 26 28 40 58
10 11 27 34 49 52
10 11 31 38 53 56
10 12 16 24 52 58
10 12 20 41 43 50
10 12 22 40 54 56
10 12 26 34 47 59
10 12 29 37 48 57
10 13 16 19 49 59
10 13 18 28 43 54
10 13 20 32 51 56
10 13 31 46 47 55
10 14 16 38 43 55
10 14 21 24 37 46
10 14 25 40 47 50
10 14 27 42 53 54
10 14 31 41 48 51
10 15 18 19 53 55
10 15 21 34 43 56
10 15 25 37 44 58
10 15 26 38 48 49
10 16 25 34 41 42
10 16 30 39 40 57
10 17 18 41 44 46
10 17 20 34 48 54
10 17 22 37 47 51
10 17 25 32 53 59
10 22 27 39 48 59
10 22 29 41 49 55
11 13 35 46 49 58
11 17 26 38 54 55
12 15 30 34 54 58
12 17 27 34 43 46
13 16 31 39 53 54
13 17 22 46 48 56
.... to be continued ....
Axiomatics:
One year and one day ago, I started a thread in this glorious newsgroup:
https://groups.google.com/forum/#!topic/rec.gambling.lottery/E-aM_zUsQFY
(Hottest-24 lotto numbers in the 6-59 UK Lottery).
One string of consisted of the most frequent 24 numbers regardless of position. Another groups consisted of the top 24 numbers position by position. I chose for this thread only the top 12 elelements for each position.
Top-24 lotto numbers regardless of position
14 2 41 10 29 34 37 38 40 11 46 54 57 58 8 26 12 39 31 51 52 17 55 19
Top-12 lotto numbers in ech position
2 1 10 11 4 8 5 7 13 3 9 12
14 17 12 3 13 11 8 22 7 15 16 2
30 31 26 18 25 16 20 29 21 22 35 27
32 34 37 46 38 39 42 28 40 41 19 24
40 51 44 41 53 48 49 43 52 47 54 37
58 57 59 54 52 55 56 50 51 49 42 46
The non-positional system generates a total of C(24, 6) = 134,596 combosnations (a favorite of my lottery-speak, mind you!) The positional system generated a total of 1,067,772 combinations (there is no formula for that as some numbers overlap randomly).
I stressed in another thread that the positional systems always perform better than non-positional systems based on frequency/skips. Granted, the positional system amount to a larger number of combinations.
At any rate, these types of lottery strategies are impractical. Nobody can generate that many combosnations and print them on tickets... and then go to a lottery terminal! So, many lottery players think of wheeling the combinations and the results are so-called 'reduced lottery systems (wheels)'.
I generated all possible combinations from the two systems above. Software: SkipSystem.exe, menu II of the Bright / Ultimate grandiose lottery applications. Functions: 'S = Lotto 6', then 'G = Generate Combinations from Systems'. We enter the systems above, one at a time, paying attention to the names of the output files.
In the next step, we are going to wheel the output files created at the first step. Software: SoftwareLotto6.exe. It is listed as 'Super Utilities' on the main menu of the Bright / Ultimate grand lottery packages. The super pack has many functions. We'll use the function D = Duplicates: Strip and Wheel'. I chose the '3 of 6' minimum guarantee to get the minimal amount of combinations to be published here.
The non-positional system ended up as a 74-line lotto wheel:
2 8 10 11 12 14
2 8 17 19 26 29
2 8 31 34 37 38
2 8 39 40 41 46
2 8 51 52 54 55
2 10 17 31 39 51
2 10 19 34 40 52
2 10 26 37 41 54
2 10 29 38 46 55
2 11 17 34 41 55
2 11 19 31 46 54
2 11 26 38 39 52
2 11 29 37 40 51
2 12 17 37 46 52
2 12 19 38 41 51
2 12 26 31 40 55
2 12 29 34 39 54
2 14 17 38 40 54
2 14 19 37 39 55
2 14 26 34 46 51
2 14 29 31 41 52
8 10 17 34 46 54
8 10 19 31 41 55
8 10 26 38 40 51
8 10 29 37 39 52
8 11 17 31 40 52
8 11 19 34 39 51
8 11 26 37 46 55
8 11 29 38 41 54
8 12 17 38 39 55
8 12 19 37 40 54
8 12 26 34 41 52
8 12 29 31 46 51
8 14 17 37 41 51
8 14 19 38 46 52
8 14 26 31 39 54
8 14 29 34 40 55
10 11 17 19 37 38
10 11 26 29 31 34
10 11 39 40 54 55
10 11 41 46 51 52
10 12 17 26 57 58
10 12 31 38 52 54
10 12 34 37 51 55
10 14 19 29 51 54
10 14 31 37 40 46
10 14 34 38 39 41
11 12 19 29 52 55
11 12 31 37 39 41
11 12 34 38 40 46
11 14 17 29 39 46
11 14 19 26 40 41
11 14 31 38 51 55
11 14 34 37 52 54
12 14 17 19 31 34
12 14 26 29 37 38
12 14 39 40 51 52
12 14 41 46 54 55
17 19 39 41 52 54
17 19 40 46 51 55
17 26 31 38 41 46
17 26 34 37 39 40
17 29 31 37 54 55
17 29 34 38 51 52
19 26 31 37 51 52
19 26 34 38 54 55
19 29 31 38 39 40
19 29 34 37 41 46
26 29 39 41 51 55
26 29 40 46 52 54
31 34 39 46 52 55
31 34 40 41 51 54
37 38 39 46 51 54
37 38 40 41 52 55
The positional system ended up as a 370-line lotto wheel:
1 2 16 19 37 42
1 2 18 24 40 46
1 2 20 28 41 49
1 2 21 32 43 50
1 2 22 34 44 51
1 2 25 38 47 52
1 2 26 39 48 54
1 3 16 24 41 50
1 3 18 19 43 49
1 3 20 32 37 46
1 3 21 28 40 42
1 3 22 38 48 55
1 3 25 34 53 54
1 3 27 39 44 52
1 7 16 28 43 46
1 7 18 32 41 42
1 7 20 24 44 54
1 7 21 34 37 49
1 7 22 39 40 50
1 7 26 38 51 56
1 8 16 32 40 49
1 8 18 28 37 50
1 8 20 34 43 52
1 8 21 24 47 51
1 8 22 41 53 56
1 8 25 42 44 46
1 8 27 38 54 57
1 11 16 34 47 55
1 11 18 38 44 58
1 11 20 39 51 57
1 11 21 41 48 52
1 11 22 24 37 59
1 11 25 40 43 56
1 11 26 42 49 50
1 12 16 38 53 59
1 12 18 34 48 56
1 12 20 40 47 58
1 12 21 46 54 55
1 12 22 28 52 57
1 12 25 37 41 51
1 13 18 39 47 59
1 13 20 42 53 55
1 13 22 32 54 58
1 13 26 34 40 57
1 13 27 28 48 51
1 13 29 37 44 56
1 13 30 38 41 46
1 14 21 39 53 58
1 14 22 46 47 49
1 14 25 32 48 57
1 14 26 28 44 55
1 14 27 34 41 59
1 14 29 40 51 52
1 14 30 37 43 54
1 15 25 39 49 55
1 15 26 32 52 59
1 15 27 42 43 58
1 15 29 41 47 54
1 15 31 37 53 57
1 15 35 46 48 50
1 17 27 32 47 56
1 17 29 42 48 59
1 17 31 40 41 55
1 17 35 37 52 58
2 3 16 28 44 54
2 3 18 32 47 51
2 3 20 24 43 55
2 3 21 34 41 46
2 3 22 37 40 49
2 3 25 42 48 50
2 3 26 38 53 57
2 7 16 24 47 49
2 7 18 19 44 50
2 7 20 32 40 52
2 7 21 28 48 55
2 7 22 38 41 54
2 7 25 34 43 57
2 7 27 37 51 58
2 7 29 39 53 56
2 8 16 34 48 58
2 8 18 38 43 56
2 8 20 37 44 57
2 8 21 39 40 59
2 8 22 42 47 55
2 8 26 28 51 52
2 8 27 46 49 50
2 8 30 32 53 54
2 11 16 32 41 56
2 11 18 28 53 59
2 11 20 42 54 58
2 11 21 38 49 51
2 11 22 39 43 46
2 11 27 40 44 55
2 11 29 34 37 50
2 12 16 39 51 55
2 12 18 37 52 54
2 12 20 46 48 59
2 12 21 24 44 56
2 12 25 32 49 58
2 12 26 40 41 42
2 13 16 38 40 50
2 13 18 34 49 55
2 13 21 42 52 57
2 13 25 28 37 46
2 13 29 41 43 51
2 13 30 39 44 58
2 14 18 39 41 57
2 14 20 34 47 56
2 14 22 24 48 52
2 14 29 32 44 46
2 14 30 42 49 59
2 14 31 40 43 58
2 14 35 37 53 55
2 15 25 40 51 54
2 15 26 46 47 58
2 15 30 37 48 56
2 15 31 38 44 59
2 17 26 37 43 59
2 17 29 40 47 57
2 17 30 46 52 55
2 17 31 42 51 56
3 7 16 19 40 51
3 7 18 24 37 56
3 7 20 28 47 50
3 7 21 32 44 57
3 7 22 34 52 58
3 7 25 38 49 59
3 7 26 39 41 55
3 7 27 46 48 54
3 8 16 37 47 52
3 8 18 34 44 59
3 8 20 38 41 42
3 8 22 39 51 54
3 8 25 28 43 58
3 8 26 32 48 56
3 8 29 40 53 55
3 11 16 39 48 49
3 11 18 40 41 54
3 11 22 42 44 56
3 11 25 32 52 55
3 11 26 34 43 51
3 11 27 28 37 57
3 11 29 46 47 59
3 12 16 42 43 57
3 12 18 46 53 58
3 12 22 32 41 59
3 12 25 39 47 56
3 12 26 37 44 50
3 12 30 38 40 52
3 13 21 24 48 58
3 13 26 42 47 54
3 13 27 40 43 59
3 13 29 32 49 50
3 13 30 37 51 55
3 13 31 41 52 56
3 14 21 38 54 56
3 14 29 37 41 58
3 14 31 34 49 57
3 14 35 39 40 46
3 15 18 28 48 52
3 15 20 39 53 59
3 15 22 24 47 57
3 15 27 41 49 51
3 15 31 32 43 54
3 17 25 46 51 57
3 17 30 39 43 50
3 17 31 38 47 58
3 17 35 42 49 55
4 7 16 32 37 50
4 7 18 28 40 49
4 7 20 34 41 51
4 7 21 24 43 52
4 7 22 42 48 57
4 7 25 39 54 58
4 7 26 46 53 59
4 7 27 38 47 55
4 8 16 19 41 46
4 8 18 24 48 54
4 8 20 32 47 59
4 8 21 28 53 57
4 8 22 38 40 58
4 8 25 34 37 55
4 8 26 39 43 49
4 8 27 42 52 56
4 11 16 24 40 42
4 11 18 19 37 51
4 11 20 28 44 46
4 11 21 34 54 59
4 11 22 41 47 50
4 11 27 32 48 58
4 11 29 38 43 57
4 11 30 39 53 55
4 12 16 34 44 49
4 12 18 32 43 55
4 12 20 37 53 56
4 12 21 38 48 50
4 12 27 28 41 54
4 12 29 39 52 59
4 12 30 42 47 51
4 13 16 28 47 56
4 13 20 24 49 57
4 13 21 32 40 46
4 13 25 38 44 51
4 13 26 37 48 52
4 13 29 34 53 58
4 13 31 42 43 50
4 14 20 40 48 55
4 14 22 28 43 51
4 14 25 41 49 52
4 14 31 39 44 56
4 15 16 38 52 54
4 15 21 37 41 42
4 15 22 32 49 56
4 15 27 34 40 50
4 15 29 46 51 55
4 17 18 34 47 52
4 17 22 24 44 55
4 17 26 32 41 57
4 17 29 37 49 54
4 17 35 39 48 51
5 7 16 34 54 56
5 7 18 38 52 57
5 7 20 42 43 49
5 7 21 40 41 58
5 7 22 28 44 59
5 7 29 32 48 51
5 8 16 24 43 59
5 8 18 19 40 42
5 8 20 28 54 55
5 8 25 32 41 50
5 8 26 37 53 58
5 8 29 34 47 49
5 8 30 39 48 52
5 8 35 46 51 56
5 11 16 19 44 52
5 11 18 46 48 55
5 11 20 38 40 59
5 11 21 37 47 56
5 11 22 32 53 57
5 11 27 39 41 42
5 12 16 37 40 46
5 12 18 24 41 49
5 12 21 34 51 52
5 12 25 38 43 54
5 12 29 42 44 55
5 13 16 41 48 57
5 13 20 34 44 50
5 13 21 39 43 55
5 13 22 24 40 51
5 13 27 38 49 56
5 13 29 46 52 54
5 13 31 32 37 59
5 14 16 28 49 50
5 14 22 34 37 42
5 14 25 39 51 59
5 14 26 32 40 54
5 14 30 41 47 55
5 14 35 38 48 58
5 15 18 39 44 54
5 15 20 24 37 52
5 15 21 46 49 57
5 15 25 28 53 56
5 15 35 42 47 59
5 16 22 39 47 58
5 17 18 28 51 58
5 17 21 24 53 54
5 17 22 41 43 52
5 17 25 40 44 49
5 17 27 37 48 50
7 8 29 41 44 52
7 8 30 34 40 46
7 8 31 39 47 57
7 8 35 37 48 59
7 11 30 32 43 59
7 11 31 37 41 46
7 11 35 42 51 52
7 12 27 40 53 57
7 12 31 42 54 59
7 12 35 38 44 46
7 13 35 40 54 55
7 14 16 42 44 58
7 14 26 34 48 50
7 14 35 41 43 56
7 15 22 37 43 55
7 15 26 28 54 57
7 15 29 38 40 42
7 17 30 41 48 49
8 11 30 41 51 58
8 11 31 40 48 50
8 12 27 32 44 51
8 12 31 38 49 55
8 13 21 41 49 54
8 14 18 32 52 58
8 14 30 38 44 50
8 15 35 40 41 57
8 17 20 24 40 56
8 22 31 46 52 59
9 11 16 37 43 58
9 11 18 39 52 56
9 11 22 28 48 54
9 11 25 41 44 57
9 11 30 40 47 49
9 12 16 19 47 50
9 12 18 40 51 59
9 12 20 32 54 57
9 12 21 28 43 49
9 12 22 34 53 55
9 12 29 38 41 56
9 12 31 39 48 58
9 13 16 24 44 46
9 13 18 19 41 58
9 13 20 28 52 59
9 13 25 39 40 42
9 13 27 34 37 54
9 13 35 38 47 57
9 14 16 40 53 56
9 14 18 24 43 50
9 14 20 37 49 51
9 14 26 46 52 57
9 14 27 28 47 58
9 14 29 39 54 55
9 15 16 28 41 55
9 15 20 38 43 46
9 15 21 32 51 58
9 15 22 40 44 52
9 15 25 34 48 59
9 16 18 42 49 54
9 16 29 34 51 57
9 17 21 41 47 59
9 17 22 38 49 50
9 17 26 34 44 56
9 17 30 32 37 42
10 11 16 46 51 54
10 11 18 42 47 57
10 11 21 39 44 50
10 11 26 28 40 58
10 11 27 34 49 52
10 11 31 38 53 56
10 12 16 24 52 58
10 12 20 41 43 50
10 12 22 40 54 56
10 12 26 34 47 59
10 12 29 37 48 57
10 13 16 19 49 59
10 13 18 28 43 54
10 13 20 32 51 56
10 13 31 46 47 55
10 14 16 38 43 55
10 14 21 24 37 46
10 14 25 40 47 50
10 14 27 42 53 54
10 14 31 41 48 51
10 15 18 19 53 55
10 15 21 34 43 56
10 15 25 37 44 58
10 15 26 38 48 49
10 16 25 34 41 42
10 16 30 39 40 57
10 17 18 41 44 46
10 17 20 34 48 54
10 17 22 37 47 51
10 17 25 32 53 59
10 22 27 39 48 59
10 22 29 41 49 55
11 13 35 46 49 58
11 17 26 38 54 55
12 15 30 34 54 58
12 17 27 34 43 46
13 16 31 39 53 54
13 17 22 46 48 56
.... to be continued ....