Euromillions Wheels, Reduced Lotto Systems
By Ion Saliu, Millions Wheeler At-Large
LexicoWheels, generator of lotto wheels based on lexicographical indexing; applies to any lotto, Keno, Powerball, Mega Millions, CA SuperLotto, Euromillions.
The following is a collection of special Euromillions lotto wheels: Balanced and randomized. The reduced Euromillions systems are created by Ion Saliu's lotto wheeling software based on lexicographical order. See the links on this page for more Euromillions wheeling software and other resources. Evidently, the function in the lotto wheeling software is E = Euromillions '5+2'.
This is a collection of unique loto wheels applicable to the Euro Millions game. The wheels are created under the restriction of balanced lexicographical indexing AND the hypergeometric odds. These lottery wheels do not assure the minimum guarantee 100% in every winning drawing. Nevertheless, if the winning condition (i.e. correctly selecting the 5 winners in the first ball set and/or the 2 Star Numbers in the second ballset) is reached 10 times, the Euromillions wheels will assure an average of 10 hits. In fact, we do not treat the lottery as a one-shot deal!
This type of lottery wheels has a tremendous cost advantage: Their size is equal to the number of lottery combinations (lines) according to the odds for the respective category. Also, in my research, I detected the clear tendency for this kind of lotto wheels to offer better results, especially when the first and second prizes are concerned.
The first Euro Millions wheel only deals with the 9 numbers in the second ball set. The condition is '1 of 2', even though four of the nine numbers are missing. Again, in 10 successful tries the wheel will yield 10 combinations with at least '1 of 2 in 9'.
Two other wheels deal with regular Euromillions numbers in the first set of 5 from 50. These wheels are applicable to 5-number regular lotto games. One of the wheels is wheeling all 50 regular Euromillions numbers in the first ball set for the '3 of 5' minimum guarantee. The other wheel is a '4 of 5', 25-number wheel (also the first ball-set).
Finally, there is a Euromillions wheel that combines both sections of the game: '4 of 5', 15-number first set, plus '1 of 2', 5-number, second ball set.
Euromillions Wheel #1: 9 numbers second set = 1 of 2; 3 combinations
1 5
3 6
6 8
Euromillions Wheel #2: 15 numbers first ball set = '4 of 5'; 5 numbers second ball set = '1 of 2'; 122 combinations
1 2 3 4 5 1 3
1 2 3 4 5 3 4
1 2 3 9 15 1 3
1 2 3 9 15 3 4
1 2 4 9 10 1 3
1 2 4 9 10 3 4
1 2 5 9 15 1 3
1 2 5 9 15 3 4
1 2 6 13 15 1 3
1 2 6 13 15 3 4
1 2 8 14 15 1 3
1 2 8 14 15 3 4
1 3 4 6 11 1 3
1 3 4 6 11 3 4
1 3 5 7 8 1 3
1 3 5 7 8 3 4
1 3 6 8 15 1 3
1 3 6 8 15 3 4
1 3 8 9 10 1 3
1 3 8 9 10 3 4
1 3 11 13 15 1 3
1 3 11 13 15 3 4
1 4 5 14 15 1 3
1 4 5 14 15 3 4
1 4 7 10 11 1 3
1 4 7 10 11 3 4
1 4 9 14 15 1 3
1 4 9 14 15 3 4
1 5 6 11 15 1 3
1 5 6 11 15 3 4
1 5 8 12 13 1 3
1 5 8 12 13 3 4
1 6 7 9 12 1 3
1 6 7 9 12 3 4
1 6 9 12 14 1 3
1 6 9 12 14 3 4
1 7 9 10 15 1 3
1 7 9 10 15 3 4
1 8 10 12 13 1 3
1 8 10 12 13 3 4
1 12 13 14 15 1 3
1 12 13 14 15 3 4
2 3 4 12 13 1 3
2 3 4 12 13 3 4
2 3 5 14 15 1 3
2 3 5 14 15 3 4
2 3 7 10 11 1 3
2 3 7 10 11 3 4
2 3 9 14 15 1 3
2 3 9 14 15 3 4
2 4 5 9 15 1 3
2 4 5 9 15 3 4
2 4 6 13 15 1 3
2 4 6 13 15 3 4
2 4 8 14 15 1 3
2 4 8 14 15 3 4
2 5 6 8 15 1 3
2 5 6 8 15 3 4
2 5 8 9 10 1 3
2 5 8 9 10 3 4
2 5 11 13 15 1 3
2 5 11 13 15 3 4
2 6 8 12 14 1 3
2 6 8 12 14 3 4
2 7 8 10 15 1 3
2 7 8 10 15 3 4
2 8 9 10 15 1 3
2 8 9 10 15 3 4
2 9 13 14 15 1 3
2 9 13 14 15 3 4
3 4 5 10 15 1 3
3 4 5 10 15 3 4
3 4 7 8 12 1 3
3 4 7 8 12 3 4
3 4 9 10 15 1 3
3 4 9 10 15 3 4
3 5 6 9 14 1 3
3 5 6 9 14 3 4
3 5 8 9 15 1 3
3 5 8 9 15 3 4
3 5 13 14 15 1 3
3 5 13 14 15 3 4
3 6 9 10 11 1 3
3 6 9 10 11 3 4
3 7 8 12 13 1 3
3 7 8 12 13 3 4
3 8 9 12 13 1 3
3 8 9 12 13 3 4
3 10 11 13 15 1 3
3 10 11 13 15 3 4
4 5 7 8 12 1 3
4 5 7 8 12 3 4
4 5 9 10 15 1 3
4 5 9 10 15 3 4
4 6 7 11 13 1 3
4 6 7 11 13 3 4
4 6 10 12 14 1 3
4 6 10 12 14 3 4
4 7 9 14 15 1 3
4 7 9 14 15 3 4
4 8 11 13 15 1 3
4 8 11 13 15 3 4
5 6 7 9 12 1 3
5 6 7 9 12 3 4
5 6 9 12 14 1 3
5 6 9 12 14 3 4
5 7 9 10 15 1 3
5 7 9 10 15 3 4
5 8 10 12 13 1 3
5 8 10 12 13 3 4
5 12 13 14 15 1 3
5 12 13 14 15 3 4
6 7 11 13 14 1 3
6 7 11 13 14 3 4
6 9 10 13 15 1 3
6 9 10 13 15 3 4
7 8 10 13 15 1 3
7 8 10 13 15 3 4
8 9 10 11 15 1 3
8 9 10 11 15 3 4
10 11 13 14 15 1 3
10 11 13 14 15 3 4
Euromillions Wheel #3: 25 numbers first ball set = '4 of 5'; 532 combinations
1 2 3 4 19
1 2 3 10 14
1 2 3 19 24
1 2 4 9 19
1 2 4 18 20
1 2 5 10 14
1 2 5 19 24
1 2 6 12 16
1 2 7 8 21
1 2 7 16 21
1 2 8 13 15
1 2 9 11 20
1 2 10 11 15
1 2 10 23 25
1 2 12 13 21
1 2 13 16 25
1 2 15 16 25
1 2 17 24 25
1 3 4 7 12
1 3 4 13 25
1 3 5 7 22
1 3 5 14 24
1 3 6 9 18
1 3 6 18 19
1 3 7 12 23
1 3 8 10 14
1 3 8 19 24
1 3 9 16 25
1 3 10 16 20
1 3 11 17 21
1 3 12 20 25
1 3 14 17 22
1 3 16 20 23
1 4 5 6 10
1 4 5 12 17
1 4 6 7 21
1 4 6 14 23
1 4 7 10 20
1 4 7 20 25
1 4 8 15 24
1 4 9 13 25
1 4 10 13 20
1 4 11 14 18
1 4 12 16 21
1 4 13 21 25
1 4 15 21 25
1 4 19 21 25
1 5 6 11 19
1 5 7 8 11
1 5 7 15 20
1 5 8 12 17
1 5 9 10 24
1 5 9 21 25
1 5 10 20 24
1 5 11 23 24
1 5 13 15 24
1 5 14 23 25
1 5 17 20 25
1 6 7 10 11
1 6 7 19 21
1 6 8 14 25
1 6 9 13 16
1 6 10 12 23
1 6 11 13 20
1 6 12 15 21
1 6 13 19 25
1 6 15 19 25
1 6 18 24 25
1 7 8 13 20
1 7 9 11 25
1 7 10 11 20
1 7 11 12 16
1 7 12 14 15
1 7 13 17 22
1 7 15 17 22
1 7 18 19 24
1 8 9 13 20
1 8 10 13 15
1 8 11 13 24
1 8 12 15 25
1 8 13 20 24
1 8 15 20 24
1 8 19 20 24
1 9 10 16 25
1 9 11 18 19
1 9 12 22 23
1 9 14 18 20
1 9 16 21 24
1 10 11 12 21
1 10 12 14 20
1 10 13 18 20
1 10 15 18 20
1 10 18 20 24
1 11 12 18 22
1 11 14 15 25
1 11 16 18 20
1 11 20 24 25
1 12 14 17 22
1 12 16 20 23
1 13 14 15 19
1 13 16 17 21
1 13 20 21 25
1 14 17 18 21
1 15 16 19 23
1 15 22 24 25
1 17 18 21 25
1 20 21 23 24
2 3 4 9 24
2 3 4 18 25
2 3 5 10 19
2 3 5 20 24
2 3 6 12 21
2 3 7 9 10
2 3 7 17 18
2 3 8 13 20
2 3 9 11 25
2 3 10 11 20
2 3 11 12 16
2 3 12 14 15
2 3 13 17 22
2 3 15 17 22
2 3 18 19 24
2 4 5 8 20
2 4 5 16 20
2 4 6 10 18
2 4 6 20 23
2 4 7 14 15
2 4 8 11 15
2 4 8 23 25
2 4 9 18 25
2 4 10 18 20
2 4 11 19 23
2 4 13 14 19
2 4 14 19 24
2 4 17 18 21
2 5 6 8 9
2 5 6 15 18
2 5 7 10 25
2 5 7 22 23
2 5 8 16 20
2 5 9 14 19
2 5 10 13 25
2 5 11 14 23
2 5 12 17 18
2 5 13 23 25
2 5 15 23 25
2 5 19 23 25
2 6 7 13 17
2 6 8 10 20
2 6 8 20 25
2 6 9 17 23
2 6 10 17 18
2 6 11 18 20
2 6 12 22 24
2 6 14 18 21
2 6 16 21 25
2 7 8 9 19
2 7 8 18 20
2 7 9 15 24
2 7 10 15 19
2 7 11 16 19
2 7 12 19 20
2 7 14 16 20
2 7 16 18 24
2 7 21 23 24
2 8 9 18 20
2 8 10 17 22
2 8 11 18 24
2 8 12 24 25
2 8 14 18 25
2 8 16 23 24
2 9 10 11 25
2 9 11 12 21
2 9 12 14 20
2 9 13 18 20
2 9 15 18 20
2 9 18 20 24
2 10 11 16 24
2 10 12 19 25
2 10 14 16 25
2 10 16 19 23
2 10 22 24 25
2 11 13 15 25
2 11 14 24 25
2 11 17 21 22
2 12 13 17 22
2 12 15 17 22
2 12 18 19 24
2 13 14 21 25
2 13 17 19 25
2 14 15 19 24
2 14 18 23 25
2 15 17 24 25
2 16 18 22 23
2 18 19 20 24
3 4 5 7 22
3 4 5 14 24
3 4 6 9 18
3 4 6 18 19
3 4 7 12 23
3 4 8 10 14
3 4 8 19 24
3 4 9 16 25
3 4 10 16 20
3 4 11 17 21
3 4 12 20 25
3 4 14 17 22
3 4 16 20 23
3 5 6 7 11
3 5 6 13 24
3 5 7 9 25
3 5 7 19 20
3 5 8 14 24
3 5 9 13 15
3 5 10 12 22
3 5 11 13 19
3 5 12 15 20
3 5 13 19 24
3 5 15 19 24
3 5 18 23 25
3 6 7 12 14
3 6 8 9 20
3 6 8 18 21
3 6 9 15 25
3 6 10 15 20
3 6 11 16 20
3 6 12 19 21
3 6 14 16 21
3 6 16 18 25
3 6 21 23 25
3 7 8 16 20
3 7 9 14 19
3 7 10 13 25
3 7 11 14 23
3 7 12 17 18
3 7 13 23 25
3 7 15 23 25
3 7 19 23 25
3 8 9 16 20
3 8 10 15 24
3 8 11 16 24
3 8 12 19 25
3 8 14 16 25
3 8 16 19 23
3 8 22 24 25
3 9 10 21 25
3 9 12 13 16
3 9 13 16 20
3 9 15 16 20
3 9 17 22 23
3 10 11 15 18
3 10 12 17 23
3 10 14 15 19
3 10 16 17 21
3 10 20 21 25
3 11 13 14 20
3 11 14 19 25
3 11 17 18 22
3 12 13 15 24
3 12 14 23 25
3 12 17 20 25
3 13 14 18 25
3 13 16 23 24
3 14 15 17 22
3 14 18 19 24
3 15 17 19 25
3 16 18 19 20
3 17 20 23 25
4 5 6 8 9
4 5 6 15 18
4 5 7 10 25
4 5 7 22 23
4 5 8 16 20
4 5 9 14 19
4 5 10 13 25
4 5 11 14 23
4 5 12 17 18
4 5 13 23 25
4 5 15 23 25
4 5 19 23 25
4 6 7 13 17
4 6 8 10 20
4 6 8 20 25
4 6 9 17 23
4 6 10 17 18
4 6 11 18 20
4 6 12 22 24
4 6 14 18 21
4 6 16 21 25
4 7 8 9 19
4 7 8 18 20
4 7 9 15 24
4 7 10 15 19
4 7 11 16 19
4 7 12 19 20
4 7 14 16 20
4 7 16 18 24
4 7 21 23 24
4 8 9 18 20
4 8 10 17 22
4 8 11 18 24
4 8 12 24 25
4 8 14 18 25
4 8 16 23 24
4 9 10 11 25
4 9 11 12 21
4 9 12 14 20
4 9 13 18 20
4 9 15 18 20
4 9 18 20 24
4 10 11 16 24
4 10 12 19 25
4 10 14 16 25
4 10 16 19 23
4 10 22 24 25
4 11 13 15 25
4 11 14 24 25
4 11 17 21 22
4 12 13 17 22
4 12 15 17 22
4 12 18 19 24
4 13 14 21 25
4 13 17 19 25
4 14 15 19 24
4 14 18 23 25
4 15 17 24 25
4 16 18 22 23
4 18 19 20 24
5 6 7 10 11
5 6 7 19 21
5 6 8 14 25
5 6 9 13 16
5 6 10 12 23
5 6 11 13 20
5 6 12 15 21
5 6 13 19 25
5 6 15 19 25
5 6 18 24 25
5 7 8 13 20
5 7 9 11 25
5 7 10 11 20
5 7 11 12 16
5 7 12 14 15
5 7 13 17 22
5 7 15 17 22
5 7 18 19 24
5 8 9 13 20
5 8 10 13 15
5 8 11 13 24
5 8 12 15 25
5 8 13 20 24
5 8 15 20 24
5 8 19 20 24
5 9 10 16 25
5 9 11 18 19
5 9 12 22 23
5 9 14 18 20
5 9 16 21 24
5 10 11 12 21
5 10 12 14 20
5 10 13 18 20
5 10 15 18 20
5 10 18 20 24
5 11 12 18 22
5 11 14 15 25
5 11 16 18 20
5 11 20 24 25
5 12 14 17 22
5 12 16 20 23
5 13 14 15 19
5 13 16 17 21
5 13 20 21 25
5 14 17 18 21
5 15 16 19 23
5 15 22 24 25
5 17 18 21 25
5 20 21 23 24
6 7 8 15 23
6 7 9 13 24
6 7 10 13 19
6 7 11 14 17
6 7 12 16 20
6 7 13 21 24
6 7 15 21 24
6 7 19 21 24
6 8 9 15 23
6 8 10 15 18
6 8 11 16 18
6 8 12 18 25
6 8 14 16 19
6 8 16 18 23
6 8 21 22 25
6 9 10 20 23
6 9 11 22 25
6 9 13 15 23
6 9 14 23 24
6 9 17 20 24
6 10 11 14 22
6 10 12 16 25
6 10 13 23 24
6 10 15 23 24
6 10 19 23 24
6 11 12 24 25
6 11 14 18 25
6 11 16 23 24
6 12 13 15 18
6 12 14 21 24
6 12 17 19 24
6 13 14 18 19
6 13 16 21 23
6 14 15 16 24
6 14 17 23 25
6 15 17 18 25
6 16 17 22 23
6 17 20 21 24
7 8 9 10 23
7 8 9 21 24
7 8 10 20 23
7 8 11 22 25
7 8 13 15 23
7 8 14 23 24
7 8 17 20 24
7 9 10 13 19
7 9 11 14 17
7 9 12 16 20
7 9 13 21 24
7 9 15 21 24
7 9 19 21 24
7 10 11 19 22
7 10 13 14 18
7 10 14 19 23
7 10 17 18 20
7 11 12 14 20
7 11 13 18 20
7 11 15 18 20
7 11 18 20 24
7 12 13 20 23
7 12 15 20 23
7 12 19 20 23
7 13 15 17 21
7 13 18 19 23
7 14 16 17 20
7 14 20 21 24
7 15 18 23 24
7 16 19 23 25
7 18 20 23 24
8 9 10 15 18
8 9 11 16 18
8 9 12 18 25
8 9 14 16 19
8 9 16 18 23
8 9 21 22 25
8 10 12 13 15
8 10 13 16 19
8 10 15 16 19
8 10 17 21 25
8 11 12 16 21
8 11 13 21 25
8 11 15 21 25
8 11 19 21 25
8 12 14 15 23
8 12 16 17 25
8 12 20 23 24
8 13 15 20 23
8 13 19 20 23
8 14 16 20 22
8 15 16 17 20
8 15 20 21 24
8 16 22 24 25
8 19 20 23 24
9 10 11 19 22
9 10 13 14 18
9 10 14 19 23
9 10 17 18 20
9 11 12 14 20
9 11 13 18 20
9 11 15 18 20
9 11 18 20 24
9 12 13 20 23
9 12 15 20 23
9 12 19 20 23
9 13 15 17 21
9 13 18 19 23
9 14 16 17 20
9 14 20 21 24
9 15 18 23 24
9 16 19 23 25
9 18 20 23 24
10 11 12 18 21
10 11 14 15 24
10 11 16 18 19
10 11 20 23 25
10 12 14 17 21
10 12 16 20 22
10 13 14 15 18
10 13 16 17 20
10 13 20 21 24
10 14 17 18 20
10 15 16 19 22
10 15 22 23 25
10 17 18 21 24
10 20 21 22 25
11 12 14 17 20
11 12 16 20 21
11 13 14 15 17
11 13 16 17 19
11 13 20 21 23
11 14 17 18 19
11 15 16 19 21
11 15 22 23 24
11 17 18 21 23
11 20 21 22 24
12 13 15 20 22
12 13 19 20 22
12 14 16 20 21
12 15 16 17 19
12 15 20 21 23
12 16 22 23 25
12 19 20 22 25
13 14 16 21 22
13 15 16 17 24
13 15 20 22 25
13 17 18 19 22
13 19 21 22 24
14 15 18 21 23
14 16 19 21 24
14 18 20 21 23
15 16 18 23 24
15 18 19 21 23
16 17 20 21 22
17 18 19 22 24
19 20 21 24 25
Euromillions Wheel #4: 50 numbers first ball set = '3 of 5'; 215 combinations
1 2 3 5 39
1 2 14 31 45
1 3 6 22 41
1 3 21 38 39
1 4 12 16 36
1 5 6 39 48
1 5 22 34 45
1 6 15 30 40
1 7 11 40 48
1 8 9 35 49
1 8 32 40 45
1 9 28 37 42
1 10 28 38 50
1 11 32 42 49
1 13 14 45 49
1 14 20 24 44
1 15 31 38 49
1 17 25 26 50
1 19 26 35 48
1 22 23 26 30
1 25 30 46 50
1 31 44 49 50
2 3 10 24 44
2 3 37 43 46
2 4 17 34 35
2 5 10 48 50
2 6 7 8 27
2 6 22 40 46
2 7 17 25 40
2 8 14 30 34
2 9 13 24 39
2 10 13 25 34
2 11 14 31 36
2 12 17 22 23
2 13 21 38 39
2 14 31 48 49
2 16 22 25 26
2 18 20 39 49
2 20 24 31 50
2 23 24 34 44
2 27 29 30 49
2 39 40 43 45
3 4 17 25 50
3 5 10 32 37
3 5 40 43 45
3 6 22 29 46
3 7 17 19 40
3 8 14 23 30
3 9 13 18 45
3 10 13 19 34
3 11 14 24 25
3 12 16 41 44
3 13 21 28 39
3 14 31 32 36
3 16 21 35 44
3 18 20 29 39
3 20 23 45 49
3 23 24 26 35
3 27 28 33 40
3 38 40 43 45
4 5 19 20 49
4 6 13 18 41
4 7 9 39 49
4 7 32 49 50
4 8 25 36 45
4 9 23 28 50
4 10 23 29 49
4 11 25 38 41
4 12 32 36 46
4 14 17 19 50
4 15 25 27 37
4 17 20 40 49
4 19 21 46 49
4 21 29 33 41
4 24 36 45 48
4 30 34 43 50
5 6 12 24 41
5 7 9 17 27
5 7 30 31 50
5 8 24 26 35
5 9 22 23 26
5 10 22 23 46
5 11 24 27 33
5 12 29 38 40
5 14 16 21 24
5 15 23 33 50
5 17 19 35 49
5 19 20 36 45
5 21 27 30 41
5 24 32 39 50
5 30 31 35 48
6 7 13 16 19
6 8 10 39 43
6 8 43 46 49
6 9 33 34 48
6 10 33 36 39
6 11 44 48 50
6 13 16 24 32
6 14 22 26 35
6 15 39 40 48
6 17 28 29 48
6 19 30 32 36
6 22 25 36 44
6 25 37 41 50
6 32 45 48 49
7 8 19 32 46
7 9 18 20 33
7 10 18 21 24
7 11 19 33 50
7 12 23 28 39
7 13 31 38 48
7 15 19 24 48
7 16 32 37 38
7 18 29 36 49
7 20 42 43 50
7 23 44 45 48
7 28 36 47 50
8 9 12 46 50
8 10 13 14 28
8 11 14 18 25
8 12 16 29 47
8 13 20 46 49
8 14 30 32 36
8 16 21 26 44
8 18 20 22 36
8 20 23 31 39
8 22 40 44 48
8 26 41 48 49
8 37 41 45 47
9 10 33 35 43
9 11 44 45 49
9 13 16 23 48
9 14 22 25 49
9 15 38 48 49
9 17 28 29 38
9 19 30 31 44
9 22 25 35 48
9 25 37 40 49
9 32 44 48 49
10 11 25 43 50
10 12 32 41 45
10 14 17 21 45
10 15 25 29 48
10 17 21 22 30
10 19 22 24 44
10 21 29 36 50
10 24 37 41 50
10 30 35 38 44
11 12 21 27 49
11 13 27 46 49
11 15 17 35 48
11 16 28 35 48
11 18 26 33 47
11 20 32 48 49
11 23 33 36 48
11 28 31 33 47
12 13 16 25 41
12 14 22 27 46
12 15 39 45 47
12 17 28 31 43
12 19 30 34 37
12 22 25 39 42
12 25 37 48 49
12 33 34 36 43
13 14 38 39 47
13 16 24 25 43
13 18 22 33 39
13 20 26 40 41
13 23 26 46 47
13 27 32 45 48
14 15 16 24 31
14 16 25 35 43
14 18 23 47 50
14 20 28 41 43
14 23 29 30 32
14 27 37 40 48
15 16 18 25 38
15 17 32 45 48
15 19 36 44 46
15 22 29 33 43
15 26 29 36 49
15 34 37 41 44
16 18 24 39 41
16 20 30 31 42
16 23 30 34 36
16 27 42 45 47
17 18 21 24 45
17 20 24 41 47
17 23 25 26 32
17 27 29 39 46
17 39 45 47 49
18 21 24 40 42
18 24 28 45 46
18 29 34 39 46
19 20 33 37 44
19 23 33 41 47
19 28 31 37 43
20 21 26 36 42
20 24 31 39 50
20 29 41 47 48
21 23 25 38 41
21 27 30 42 48
21 42 43 44 45
22 26 42 44 47
22 37 41 48 50
23 28 31 32 37
24 25 32 42 44
24 32 35 37 43
25 29 36 48 50
26 29 31 34 48
27 29 43 45 49
28 32 36 43 49
30 31 35 40 50
32 35 43 45 48
42 44 46 47 48
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