Hi all,

I have the following set of numbers and my problem is to select/identity the correct minimum combinations that will ensure if any of the selected lines come out, I still have a five number match.

I will appreciate any algorithm that can do the job

8,10,21,32,39,49
9,10,27,32,39,41
5,14,25,31,36,49
5,14,27,31,32,49
5,16,23,32,34,49
5,16,24,36,39,49
7,8,27,34,39,49
7,10,21,30,34,49
7,10,21,34,39,47
7,10,23,32,39,47
7,10,23,32,39,49
7,13,14,30,41,46
7,14,16,35,41,46
5,14,21,36,37,41
8,9,20,30,34,49
5,14,21,34,39,49
8,10,23,31,32,46
8,10,24,31,37,42
8,10,24,32,35,41
8,13,20,30,31,46
8,13,24,31,32,46
8,13,24,34,37,46
8,13,26,32,34,41
8,13,28,34,35,46
8,14,28,31,32,49
9,10,13,26,39,46
9,10,14,27,30,41
4,10,23,32,36,47
7,16,23,32,34,49
5,9,20,32,35,49
7,10,23,32,34,49
4,10,25,32,36,41
4,10,27,36,37,47
4,13,20,31,36,42
4,13,20,32,35,46
4,13,24,35,37,42
4,13,26,30,31,47
4,13,26,30,36,47
4,13,28,32,35,41
4,16,24,35,37,46
5,7,27,31,34,46
5,8,24,35,39,49
5,14,23,31,36,42
5,8,28,34,39,49
9,13,24,34,37,42
5,9,25,35,36,42
5,10,13,24,31,49
5,10,23,30,32,47
5,10,23,31,34,42
5,10,23,32,34,49
5,10,24,31,32,49
5,13,24,34,37,46
5,13,24,34,37,49
5,13,26,36,39,46
5,13,28,30,31,42
5,13,28,34,35,49
5,14,21,34,39,47
5,8,28,32,39,49
5,10,23,30,34,49
9,10,23,32,34,47
4,5,20,32,35,49
4,7,20,32,37,41
4,9,23,32,35,41
4,10,20,36,37,41
4,10,21,32,39,47
4,10,23,31,32,47
4,10,23,32,34,49
5,8,24,35,37,42
5,8,27,32,34,47
5,9,23,35,36,46
5,9,24,34,37,42
3,16,25,36,37,42
5,10,23,30,32,49
3,13,26,32,34,47
5,10,23,31,32,47
5,10,23,32,39,49
5,10,24,30,31,49
5,10,27,31,34,47
5,13,24,31,37,42
5,14,27,31,32,46
5,14,28,31,32,49
5,16,23,31,32,47
5,16,25,36,39,41
7,8,23,32,34,41
7,8,28,34,39,49
7,10,21,34,39,49
5,10,21,30,34,49
1,16,26,32,35,49
9,13,25,35,36,46
9,13,26,35,36,41
9,13,26,35,36,49
9,13,26,36,37,49
9,13,27,30,32,41
9,14,23,32,36,47
9,14,27,30,31,41
1,4,23,30,32,49
1,4,26,32,39,49
1,10,24,31,32,47
1,10,25,30,32,49
1,10,27,30,34,49
3,16,27,34,37,49
1,14,20,37,39,49
4,10,23,31,32,46
1,16,27,34,39,49
3,4,21,32,35,49
3,4,24,31,36,49
3,4,27,32,35,46
3,5,26,36,39,46
3,8,25,32,34,49
3,8,25,34,35,49
3,8,27,34,37,49
3,10,24,34,37,49
3,10,26,31,32,47
3,10,27,30,39,49
3,10,28,31,32,49
1,13,24,32,39,49
5,13,24,30,31,46
1,10,21,30,34,49
3,9,25,32,36,49
3,10,26,31,32,49
3,10,26,31,39,49
4,7,23,31,32,46
4,8,24,35,37,42
4,10,27,36,37,41
4,13,21,35,36,46
4,13,24,36,37,41
4,13,26,31,32,47
4,13,28,32,35,46
4,16,24,35,37,42
3,8,25,32,34,47
5,10,21,30,32,49
3,8,24,34,37,49
5,13,24,31,37,46
5,14,21,34,37,49
7,10,23,30,34,49
7,10,27,32,39,41
7,10,27,34,39,49
8,10,28,31,35,41
8,16,28,34,39,49
1,3,24,32,39,49
1,4,21,30,34,49
1,4,21,32,39,47
1,4,26,31,32,47
4,10,23,32,39,47
5,8,25,34,39,49
1,10,26,32,39,49
7,10,27,34,39,41
7,16,27,32,34,49
7,16,27,34,39,49
8,9,26,32,36,49
8,10,23,31,37,42
8,13,24,32,35,41
8,13,28,30,31,46
8,14,21,37,39,49
9,10,23,32,37,41
9,10,25,30,34,41
9,10,27,30,37,49
9,13,26,32,35,49
3,8,26,32,39,49
1,10,23,34,35,49
1,10,23,30,34,49
1,10,26,34,37,47
1,13,26,30,39,49
3,4,24,37,39,46
3,5,24,31,34,46
3,5,24,31,34,47
3,5,24,31,34,49
3,5,24,34,37,46
3,5,24,34,37,49
3,5,26,32,39,49
3,5,27,34,37,46
3,8,24,31,34,49
3,8,24,34,35,49
1,3,26,32,39,49
3,16,20,31,37,47
1,10,13,32,47,49
3,9,28,32,35,49
3,10,16,39,41,49
3,10,23,31,34,47
3,10,24,31,32,47
3,10,27,31,36,47
3,13,14,26,35,42
3,13,14,32,46,49
3,13,14,32,47,49
3,13,16,31,42,49
3,13,16,32,47,49
3,13,16,34,42,49
3,8,28,34,35,49
3,14,28,31,32,49
3,8,25,34,35,46
3,16,24,30,31,49
3,16,27,32,36,49
3,16,27,36,39,46
4,5,27,30,34,42
4,7,23,32,36,41
4,8,27,35,37,47
4,8,28,35,37,42
4,8,28,35,37,46
4,8,28,35,37,47
4,10,21,31,32,47
4,10,23,30,31,47
4,10,23,30,32,47
3,14,24,32,35,47
3,4,27,32,36,49
1,10,23,31,34,47
1,13,14,30,46,49
1,13,14,32,47,49
1,13,16,36,47,49
1,13,24,30,39,49
1,13,26,32,39,49
1,16,21,32,39,49
1,16,23,32,34,49
1,16,23,32,35,49
1,16,26,35,39,49
1,16,27,32,34,49
1,16,27,32,39,49
3,8,28,37,39,49
3,4,27,32,35,49
7,10,23,32,39,41
3,4,27,34,36,49
3,5,16,25,36,41
3,5,20,32,35,46
3,5,24,34,39,46
3,5,26,32,35,49
3,5,28,32,39,49
3,7,21,32,34,49
3,7,24,34,36,49
3,8,20,32,39,49
3,8,21,32,34,49
3,8,25,31,32,41
3,8,25,32,34,41
3,4,25,32,36,41

I have gone through the list and found out in stead of playing lines
4,10,23,32,36,47
5,10,23,31,32,47
4,10,23,31,32,46
4,10,23,32,39,47
4,10,21,31,32,47
4,10,23,30,31,47
4,10,23,30,32,47
you can play 4,10,23,31,32,47 and still hit 5/6 if any of the above lines hits the jackpot. Using the same argument I have the following algorithm
1. for each line, produce its corresponding 5 number combinations and have an extra column that keeps track same 5 combinations e.g. if you consider line 4,10,23,31,32,47 as the first its corresponding 5 number combinations are
4,10,23,31,32,1
4,10,23,31,47,1
4,10,23,32,47,1
4,10,31,32,47,1
4,23,31,32,47,1
10,23,31,32,47,1
if you assume the second line is 5,10,23,31,32,47, then after exploding it to 5 combination, you will have the following
10,23,31,32,47,2
5,23,31,32,47,1
5,10,31,32,47,1
5,10,23,32,47,1
5,10,23,31,47,1
5,10,23,31,32,1
4,23,31,32,47,1
4,10,31,32,47,1
4,10,23,32,47,1
4,10,23,31,47,1
4,10,23,31,32,1

if you assume the third line is 4,10,23,31,32,46 the result will be
10,23,31,32,47,2
4,10,23,31,32,2
5,23,31,32,47,1
5,10,31,32,47,1
5,10,23,32,47,1
5,10,23,31,47,1
5,10,23,31,32,1
4,23,31,32,47,1
4,10,31,32,47,1
4,10,23,32,47,1
4,10,23,31,47,1
10,23,31,32,46,1
4,23,31,32,46,1
4,10,31,32,46,1
4,10,23,32,46,1
4,10,23,31,46,1

you continue the same way to the last line.
2. pick the line that will have produced highest 5 hit e.g for the case of
4,10,23,31,32,47
4,10,23,32,36,47
5,10,23,31,32,47
4,10,23,31,32,46
4,10,23,32,39,47
4,10,21,31,32,47
4,10,23,30,31,47
4,10,23,30,32,47

after explosion you have
4,10,23,32,47,4
10,23,31,32,47,2
4,10,23,31,32,2
4,10,23,31,47,2
4,10,23,30,47,2
4,10,31,32,47,2
5,23,31,32,47,1
5,10,31,32,47,1
5,10,23,32,47,1
5,10,23,31,47,1
5,10,23,31,32,1
10,23,32,39,47,1
4,23,32,39,47,1
4,10,32,39,47,1
4,10,23,39,47,1
4,10,23,32,39,1
10,23,32,36,47,1
4,23,32,36,47,1
4,10,32,36,47,1
4,10,23,36,47,1
4,10,23,32,36,1
4,23,31,32,47,1
10,23,31,32,46,1
4,23,31,32,46,1
4,10,31,32,46,1
4,10,23,32,46,1
4,10,23,31,46,1
10,23,30,32,47,1
4,23,30,32,47,1
4,10,30,32,47,1
4,10,23,30,32,1
10,23,30,31,47,1
4,23,30,31,47,1
4,10,30,31,47,1
4,10,23,30,31,1
10,21,31,32,47,1
4,21,31,32,47,1
4,10,21,32,47,1
4,10,21,31,47,1
4,10,21,31,32,1

in this case line 4,10,23,32,47,4 and it is part of 4,10,23,31,32,47
3. repeat the same procedure from 1-3 till you exhaust all the lines.

For the case of the above 232 lines my program is able to remove 103 lines and retains the following 129 lines.
4,10,23,31,32,47
5,10,23,32,34,49
1,3,26,32,39,49
3,5,24,34,37,49
1,10,21,30,34,49
3,8,25,32,34,49
7,10,27,34,39,49
1,16,27,32,34,49
5,8,28,34,39,49
4,8,24,35,37,42
3,14,28,31,32,49
3,4,27,32,35,49
5,13,24,31,37,46
7,10,23,32,39,41
3,13,14,32,47,49
9,13,26,35,36,49
3,10,26,31,32,47
3,8,24,34,35,49
5,10,24,31,32,49
4,13,28,32,35,46
3,5,24,31,34,46
1,16,26,32,35,49
4,10,27,36,37,41
4,13,26,31,32,47
5,14,21,34,39,49
1,13,24,30,39,49
4,8,28,35,37,47
1,10,23,31,34,47
3,16,27,34,37,49
3,4,25,32,36,41
9,10,14,27,30,41
5,9,20,32,35,49
8,13,28,30,31,46
8,13,24,32,35,41
4,10,21,32,39,47
8,10,23,31,37,42
3,5,26,36,39,46
3,13,16,31,42,49
5,14,27,31,32,46
3,5,16,25,36,41
9,13,24,34,37,42
3,5,28,32,39,49
8,10,21,32,39,49
5,10,27,31,34,47
4,7,23,32,36,41
3,16,27,32,36,49
9,10,23,32,34,47
3,10,27,30,39,49
1,10,25,30,32,49
3,4,24,31,36,49
7,16,23,32,34,49
8,13,28,34,35,46
9,13,25,35,36,46
3,5,26,32,35,49
3,9,25,32,36,49
5,10,23,30,32,47
1,10,13,32,47,49
8,10,23,31,32,46
5,14,23,31,36,42
9,10,23,32,37,41
3,8,28,37,39,49
8,13,26,32,34,41
3,7,24,34,36,49
7,13,14,30,41,46
7,10,23,30,34,49
3,5,27,34,37,46
3,10,16,39,41,49
5,16,24,36,39,49
9,10,27,32,39,41
5,9,23,35,36,46
8,13,24,34,37,46
8,14,21,37,39,49
4,16,24,35,37,46
3,8,20,32,39,49
3,7,21,32,34,49
4,9,23,32,35,41
5,16,23,31,32,47
3,14,24,32,35,47
4,13,24,36,37,41
3,10,27,31,36,47
1,4,23,30,32,49
4,5,27,30,34,42
3,13,26,32,34,47
5,13,28,34,35,49
7,10,21,34,39,47
3,5,20,32,35,46
1,13,16,36,47,49
8,10,28,31,35,41
7,8,23,32,34,41
3,4,24,37,39,46
1,10,26,34,37,47
9,10,27,30,37,49
9,10,25,30,34,41
3,9,28,32,35,49
1,10,24,31,32,47
1,13,14,30,46,49
4,13,26,30,36,47
3,8,25,34,35,46
3,8,25,31,32,41
3,4,27,34,36,49
1,16,21,32,39,49
4,7,23,31,32,46
3,10,26,31,39,49
1,10,23,34,35,49
5,10,21,30,32,49
8,9,26,32,36,49
8,13,24,31,32,46
5,8,27,32,34,47
4,7,20,32,37,41
3,16,25,36,37,42
1,14,20,37,39,49
9,14,23,32,36,47
4,13,21,35,36,46
9,10,13,26,39,46
3,13,14,26,35,42
8,9,20,30,34,49
7,14,16,35,41,46
5,14,25,31,36,49
3,16,24,30,31,49
9,13,27,30,32,41
3,16,20,31,37,47
5,14,21,36,37,41
3,16,27,36,39,46
4,13,20,31,36,42
5,7,27,31,34,46
5,8,24,35,39,49
5,9,25,35,36,42
5,10,23,31,34,42
5,13,28,30,31,42

Can your algorithm do better? if so please explain how it works

Thanks

Hi Kenya649,

if you are interested in actually playing a covering with these properties, then my program Wheel Generator has been designed for this particular task among other possible optimizations. In your example, a quick run made it in 121 blocks.
If you are interested in optimization theory, then I just can't help This is an NP-hard case problem anyway, so heuristics, dedicated optimization and tricks have to be used to produce something of quality.

cheers
lottoarchitect

Hi Lottoarchitect,

Thanks for responding to my thread.

How do I get your Wheel Generator program?

regards and

Just google "Wheel Generator". The current version is 1.8. However, the above optimization is advanced and is not supported in the free version. Your example requires the concept of a mother covering as explained in the help file.

cheers
lottoarchitect