Subset lexicographic Number Relashionship

[Kenya649]

In a pick 6 game (6/49) take the following combinations and their lexicographic numbers

2,11,24,30,27,48 lexicographic number 2730451

2,11,29,30,27,48 lexicographic number 2738256

Both combinations have 2,11,30,27,48 as a subset.

Using only lexicographic numbers, how would you know 2,11,30,27,48 is a subset of 2730451 and 2738256?

Thank you.

 

[Frank]

To get the correct Lex value you need to list numbers in ascending sorted order. When you do this, you will find that:-

2,11,24,27,30,48 =2,729,939

2,11,27,29,30,48 =2,735,674

None of this detracts from the validity of your question, which is something I have been wondering about too. The answer may lie in the factorisation process I described in another thread, (for 5/56 lotteries) but I have not researched into its possibilities enough to be able to answer your question yet.

 

[Frank]

I forgot to mention that 2,11,30,27,48 would be a subset of 44 lines of 6 , all of whom may be repesented as Lex numbers. So any query as to the parentage of 2,11,30,27,48 would need to return 44 Lexocological 6/49 values.

 

[Kenya649]

To get the correct Lex value you need to list numbers in ascending sorted order. When you do this, you will find that:-

2,11,24,27,30,48 =2,729,939

2,11,27,29,30,48 =2,735,674

None of this detracts from the validity of your question, which is something I have been wondering about too. The answer may lie in the factorisation process I described in another thread, (for 5/56 lotteries) but I have not researched into its possibilities enough to be able to answer your question yet.

Hi Frank,

I forgot to sort those numbers, otherwise thanks for the correction.

 

[CMF]

In a pick 6 game (6/49) take the following combinations and their lexicographic numbers

2,11,24,30,27,48 lexicographic number 2730451

2,11,29,30,27,48 lexicographic number 2738256

Both combinations have 2,11,30,27,48 as a subset.

Using only lexicographic numbers, how would you know 2,11,30,27,48 is a subset of 2730451 and 2738256?

Thank you.

Begs the question how on earth you can have a lexicographic enumeration of combinations of six integers with an integer on the right greater than one on the left?

Here is the lexicographic index 2730451 with the corresponding combination which is nothing like what you give: -
ID Comb
2730451 02 11 24 29 38 44
2730452 02 11 24 29 38 45
2730453 02 11 24 29 38 46
2730454 02 11 24 29 38 47
2730455 02 11 24 29 38 48
2730456 02 11 24 29 38 49
2730457 02 11 24 29 39 40
2730458 02 11 24 29 39 41
2730459 02 11 24 29 39 42
2730460 02 11 24 29 39 43
2730461 02 11 24 29 39 44
2730462 02 11 24 29 39 45
2730463 02 11 24 29 39 46

Colin Fairbrother

 

[CMF]

Correction meant to say integer on the right less than integer on the left - only 5 minutes for corrections!

There is a such a thing as a combinadic which allows finding the combination by the lex index and vice versa. Do a search on this site or Google

Colin Fairbrother

 

[Frank]

I have designed a spreadsheet which also converts both ways. This Google docs version is not protected, so only type in the yellow cells. Better still download it before someone else overwrites the formulas.

https://spreadsheets.google.com/ccc?key=0AlKaBInOf3v4dEM4Z3RGcDBiUmpYOFpZMW1NYkdEZ1E&hl=en&authkey=CLGrqPYM

 

[CMF]

The lexicographic number for a given combination is simply a mapping. I have the 6/49 Lotto game numbers enumerated in a table with the index as the primary key. The main reason I have this is to approach some task from a different angle by using SQL and see whether the answer is the same as what I get by code. The table does enable me to find the combination for a given index in less than a second but this can be done just as easily in code.

To be talking about a 1 to 1 index for CombSixes as being a set in which CombFives are a subset comes across as nonsense to me. You can enumerate the CombFives lexicographically and have a 1 to 1 index. If you want a 1 to many relationship between the CombSix index and each CombFive it can't be done. From a relational database point of view you have a many to many relationship and need to introduce an intermediate table.

But what is the use of all this and what is the objective?

I note that Kenya649 is asking exactly the same questions at LotteryPost.

To be honest they come across to me as the ramblings of someone that does not have a clue about the subject in general.

Colin Fairbrother

 

[Kenya649]

But what is the use of all this and what is the objective?

I note that Kenya649 is asking exactly the same questions at LotteryPost.

To be honest they come across to me as the ramblings of someone that does not have a clue about the subject in general.

Colin Fairbrother

Colin,

Objective of all this is to compare combinations without necessarily looping each of the six numbers for a pick 6 game.

Different forums have different people and I do not see anything wrong posting the same question here or there.

I know what I want and I do not just ask questions for the sake of it. Maybe my communication is poor and I do not drive the point home.

Thanks

 

[hopefull]

has any one ever printed out all the 13 million + companations in a lexicographic order to find out where on the list all the already drawn combinations had fell?if not,why not? and why not do it?

 

[time*treat]

has any one ever printed out all the 13 million + companations in a lexicographic order to find out where on the list all the already drawn combinations had fell?if not,why not? and why not do it?

Unlikely ... because it would take tens of thousands of pages to print them all.

 

[CMF]

Enumerating Combinations for Lotto Games

has any one ever printed out all the 13 million + companations in a lexicographic order to find out where on the list all the already drawn combinations had fell?if not,why not? and why not do it?

I assume you mean storing all the combinations in a file or table where they can be viewed on screen or selectively printed out. I give a step by step method in a page in my Lotto Google group which will be there to January 2011.
http://groups.google.com/group/lottogroup/web/enumerating-lotto-combinations-or-permutations-if-you-have-excel

The same article is available on my LottoPoster site under Lotto Number Analysis Using Excel, Access and Visual Basic.

The efficient way to store is using a table with an index as mentioned previously in this thread: -
"I have the 6/49 Lotto game numbers enumerated in a table with the index as the primary key. The main reason I have this is to approach some task from a different angle by using SQL and see whether the answer is the same as what I get by code. The table does enable me to find the combination for a given index in less than a second but this can be done just as easily in code."

With indexes and fields as sampled below less than 1GB disk space is taken up.
ID Sel1 Sel2 Sel3 Sel4 Sel5 Sel6 Comb Comb6
1 1 2 3 4 5 6 01 02 03 04 05 06 010203040506
2 1 2 3 4 5 7 01 02 03 04 05 07 010203040507
3 1 2 3 4 5 8 01 02 03 04 05 08 010203040508
4 1 2 3 4 5 9 01 02 03 04 05 09 010203040509
5 1 2 3 4 5 10 01 02 03 04 05 10 010203040510
6 1 2 3 4 5 11 01 02 03 04 05 11 010203040511
7 1 2 3 4 5 12 01 02 03 04 05 12 010203040512
8 1 2 3 4 5 13 01 02 03 04 05 13 010203040513
9 1 2 3 4 5 14 01 02 03 04 05 14 010203040514
10 1 2 3 4 5 15 01 02 03 04 05 15 010203040515
11 1 2 3 4 5 16 01 02 03 04 05 16 010203040516
12 1 2 3 4 5 17 01 02 03 04 05 17 010203040517
13 1 2 3 4 5 18 01 02 03 04 05 18 010203040518
14 1 2 3 4 5 19 01 02 03 04 05 19 010203040519
15 1 2 3 4 5 20 01 02 03 04 05 20 010203040520
16 1 2 3 4 5 21 01 02 03 04 05 21 010203040521
17 1 2 3 4 5 22 01 02 03 04 05 22 010203040522
18 1 2 3 4 5 23 01 02 03 04 05 23 010203040523
19 1 2 3 4 5 24 01 02 03 04 05 24 010203040524
20 1 2 3 4 5 25 01 02 03 04 05 25 010203040525
21 1 2 3 4 5 26 01 02 03 04 05 26 010203040526
22 1 2 3 4 5 27 01 02 03 04 05 27 010203040527
23 1 2 3 4 5 28 01 02 03 04 05 28 010203040528
24 1 2 3 4 5 29 01 02 03 04 05 29 010203040529
25 1 2 3 4 5 30 01 02 03 04 05 30 010203040530
26 1 2 3 4 5 31 01 02 03 04 05 31 010203040531
27 1 2 3 4 5 32 01 02 03 04 05 32 010203040532
28 1 2 3 4 5 33 01 02 03 04 05 33 010203040533

Colin Fairbrother

 

[hopefull]

yes so what it will take tons of paper and tons of ink. it is the one and only way to see where the bulk of the game is.

 

[Frank]

I disagree its the only way to see where the bulk of the game is. You would not be able to see the bigger picture within your tons of paper and visualise where everything fell.
You could for example imagine the Lottery combinations (lex values) laid out in stacked rows to form a 2 dimensional array which can be plotted. In a 6/49 lottery the 13983816 combinations could fit in a grid 3740 of rows by 3740 columns. One can convert the lexographic values to X and Y coordinates X =INT(lex value/3740) Y=MOD(Lex value/3740) in Excel then plot an X Y scatter graph. Note that similar X values (dots along the horizontal) represent closely clustered Lexographic values and possibly similar ball values, but the Y values do not. These plotted points would also respond to filtering in Excel. By inference the empty spaces and the co ordinates of them are the missing undrawn combinations. You could work back to specific but approximate missing Lexographical values from the co-ordinates if you spotted areas of interest.

This idea could be extended to a 3 dimensional 241 X 241 X 241 plot of results but a 3D plotting package would be required.
I would regard this an an interesting but approximate way of visualising a lottery in a single view.

 

[CMF]

An index speeds up finding a record - that's all!

yes so what it will take tons of paper and tons of ink. it is the one and only way to see where the bulk of the game is.

An index for a lexicographic enumeration enables fast finding of any combination. A different index would be needed if the combinations were enumerated by Last Number or Pool as you can see from the sample below: -

ID Sel1 Sel2 Sel3 Sel4 Sel5 Sel6 Comb Comb6
1 1 2 3 4 5 6 01 02 03 04 05 06 010203040506
15181 1 2 4 5 6 7 01 02 04 05 06 07 010204050607
991 1 2 3 5 6 7 01 02 03 05 06 07 010203050607
45 1 2 3 4 6 7 01 02 03 04 06 07 010203040607
2 1 2 3 4 5 7 01 02 03 04 05 07 010203040507
178366 1 3 4 5 6 7 01 03 04 05 06 07 010304050607
1712305 2 3 4 5 6 7 02 03 04 05 06 07 020304050607
1034 1 2 3 5 7 8 01 02 03 05 07 08 010203050708
46 1 2 3 4 6 8 01 02 03 04 06 08 010203040608
88 1 2 3 4 7 8 01 02 03 04 07 08 010203040708
992 1 2 3 5 6 8 01 02 03 05 06 08 010203050608
15182 1 2 4 5 6 8 01 02 04 05 06 08 010204050608
16127 1 2 4 6 7 8 01 02 04 06 07 08 010204060708
1937 1 2 3 6 7 8 01 02 03 06 07 08 010203060708
15224 1 2 4 5 7 8 01 02 04 05 07 08 010204050708
3 1 2 3 4 5 8 01 02 03 04 05 08 010203040508
29371 1 2 5 6 7 8 01 02 05 06 07 08 010205060708
1726495 2 3 5 6 7 8 02 03 05 06 07 08 020305060708
3246244 3 4 5 6 7 8 03 04 05 06 07 08 030405060708
341551 1 4 5 6 7 8 01 04 05 06 07 08 010405060708
192556 1 3 5 6 7 8 01 03 05 06 07 08 010305060708
178367 1 3 4 5 6 8 01 03 04 05 06 08 010304050608
179312 1 3 4 6 7 8 01 03 04 06 07 08 010304060708
178409 1 3 4 5 7 8 01 03 04 05 07 08 010304050708
1712306 2 3 4 5 6 8 02 03 04 05 06 08 020304050608
1713251 2 3 4 6 7 8 02 03 04 06 07 08 020304060708
1712348 2 3 4 5 7 8 02 03 04 05 07 08 020304050708
1875490 2 4 5 6 7 8 02 04 05 06 07 08 020405060708

Generally, there is no compelling need to enumerate and store all the 13,983,816 combinations for a Pick 6, Pool 49 Lotto game as they can be temporally stored in an array and worked with faster in memory.

Colin Fairbrother