Home

 
What are Lotto Wheels

Lotto wheels or coverings are systems of lotto combinations, composed of a given set of selected numbers and containing conditional guarantees. E.g., the wheel, listed below, guarantees a prize of 4, provided that any 5 numbers out of 1 to 15 are drawn out. (Lotto player bets that he will have 5 winning numbers in his choice of 15, and only in such case, the wheel guarantees him a prize of 4 or more.) Each combination contains 6 numbers. In general, the choice can be any 15 (or other number of) numbers, not necessarily consecutive 1..15, but that is a trivial substitution into a template of 1..15.

In more mathematical texts (like Lotto Designs), you will find these parameters denoted as v,k,t,m. In the example: v=15, k=6, t=4, m=5. This wheel could also be classified as "Pick6 wheel, guarantee 4/5". (E.g. in collections like Peter's Wheels Page.) Variable b denotes the number of combinations or "blocks" in a wheel, or the "size" of the wheel. In the example below, b=44.

Wheels like the one below are also called "abbreviated wheels" because they do not contain all possible combinations of e.g. 6 numbers out of 15, but only as many as necessary to provide the required guarantee. In general, it is easy to compose lavishly big wheels to meet this condition, but the goal is to make them as small as possible. For lotto players, that means saving (less tickets to pay). For mathematicians (and others), it means challenge, far from having a simple solution. People compete, who will make it smaller. (E.g. in UK)

For more extensive explanation, visit Lotto Tutor / Lottery Wheels.

 

 

Top

Home

 

 

Example wheel, composed of 15 numbers, guarantee 4 of 5:

  1. 1, 2, 3, 6, 8,13
  2. 1, 2, 3,11,14,15
  3. 1, 2, 4, 5, 7,15
  4. 1, 2, 4, 7,10,14
  5. 1, 2, 4, 9,10,13
  6. 1, 2, 5, 8, 9,12
  7. 1, 3, 4, 6, 8,10
  8. 1, 3, 4, 9,11,13
  9. 1, 3, 5,12,13,14
  10. 1, 3, 7, 9,10,12
  11. 1, 4, 6, 9,12,14
  12. 1, 4, 8,11,12,15
  13. 1, 5, 6, 7,10,13
  14. 1, 5, 6,10,11,12
  15. 1, 5, 7, 8,11,14
  16. 1, 5, 9,11,13,15
  17. 1, 6, 7,12,14,15
  18. 1, 8, 9,10,13,15
  19. 2, 3, 4, 5, 9,12
  20. 2, 3, 5, 8,10,11
  21. 2, 3, 6, 7, 8,15
  22. 2, 3, 7, 9,13,14
  1. 2, 4, 5, 6,11,14
  2. 2, 4, 8,13,14,15
  3. 2, 5,10,12,13,15
  4. 2, 6, 7, 8, 9,11
  5. 2, 6, 7,11,12,13
  6. 2, 6, 8,10,12,14
  7. 2, 6, 9,10,11,15
  8. 3, 4, 5, 6, 7,11
  9. 3, 4, 5,10,14,15
  10. 3, 4, 6, 7,14,15
  11. 3, 5, 6, 8, 9,15
  12. 3, 6,11,12,13,15
  13. 3, 7, 8,10,13,15
  14. 3, 8, 9,11,12,14
  15. 4, 5, 7, 8, 9,10
  16. 4, 5, 7, 8,12,13
  17. 4, 6, 9,12,13,15
  18. 4, 7,10,11,12,13
  19. 5, 6, 9,10,13,14
  20. 5, 7, 9,12,14,15
  21. 6, 8,10,11,13,14
  22. 7, 9,10,11,14,15


Top | Home | What are wheels | About Ininuga | Links | Free download | Ordinal numbers | Code tips