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10 Digits, in How many 5 Pairs groups of them are there?

Topic closed. 20 replies. Last post 8 years ago by jr-va.

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LANTERN's avatar - kilroy 28_173_reasonably_small.jpg
Tx
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May 4, 2004
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Posted: November 3, 2008, 1:17 pm - IP Logged

With 10 digits from 0 to 9

How many groups of 5 pairs each are there?

In which each group of 5 pairs has all the 10 digits from 0 to 9 among the 5 pairs in that group.

-------------

There are 100 possible pairs of the digits 0 to 9, But of them, Which 5 combination of pairs have all the 10 digits in them and How many such groups are there?

Some pairs can repeat from one group of 5 pairs to another group of 5 pairs, so long as not all the pairs repeat from one group to another group.

And can a list of all such groups be made? or Are there way too many?

    johnph77's avatar - avatar
    CA
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    December 10, 2003
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    Posted: November 3, 2008, 3:12 pm - IP Logged

    With 10 digits from 0 to 9

    How many groups of 5 pairs each are there?

    In which each group of 5 pairs has all the 10 digits from 0 to 9 among the 5 pairs in that group.

    -------------

    There are 100 possible pairs of the digits 0 to 9, But of them, Which 5 combination of pairs have all the 10 digits in them and How many such groups are there?

    Some pairs can repeat from one group of 5 pairs to another group of 5 pairs, so long as not all the pairs repeat from one group to another group.

    And can a list of all such groups be made? or Are there way too many?

    Off the top of my head, so may not be completely accurate.....

    There would be 10,000,000,000 different possibilities, ranging from 00 00 00 00 00 to 99 99 99 99 99.

    Of these, there would be 3,628,800 combinations listed where each number is unique, ranging from 01 23 45 67 89 to 98 76 54 32 10.

    Allowing for this, for instance, the second grouping would be 01 23 45 67 98.

    No reason why they couldn't be listed.

    Is this what you were asking?

    gl

    j

    Blessed Saint Leibowitz, keep 'em dreamin' down there..... 

    Next week's convention for Psychics and Prognosticators has been cancelled due to unforeseen circumstances.

     =^.^=

      LANTERN's avatar - kilroy 28_173_reasonably_small.jpg
      Tx
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      Posted: November 3, 2008, 4:44 pm - IP Logged

      Off the top of my head, so may not be completely accurate.....

      There would be 10,000,000,000 different possibilities, ranging from 00 00 00 00 00 to 99 99 99 99 99.

      Of these, there would be 3,628,800 combinations listed where each number is unique, ranging from 01 23 45 67 89 to 98 76 54 32 10.

      Allowing for this, for instance, the second grouping would be 01 23 45 67 98.

      No reason why they couldn't be listed.

      Is this what you were asking?

      gl

      j

      JohnPH

      I was talking about combinations where each number (Digit from 0 to 9) is unique such as on your 2 examples:

      01 23 45 67 89 = 10 32 54 76 98

      98 76 54 32 10 = 89 67 45 23 01

      And also like:

      02 13 46 57 98 = 20 31 64 75 89

      97 86 53 42 01 = 79 68 35 24 10

      That should make them even fewer combinations.

      Each pair is: Pair 1, Pair 2, Pair 3, Pair 4 and Pair 5. or SubGroup 1, 2, 3, 4 and 5.

      They would be used for digits' stats, so the order 01 or 10 on any pair does not matter, only that there are 2 digts out of the 10 on any subgroup or pair.

      --------------

      For example:

      Group # 1 (Just an example). First possible group out of many.

      SubGroups:

      01       02        03        04        05  Always from SubGroup 1 to SubGroup 5

      01       23        45        67        89

      XX                   X                              Oldest Draw. Sample true stat data from a state.

                  X                      X           X

                             X           XX

      X                                  X           X

      X          X                                   X

      X                                  XX

                  X                                    XX

      X          X                      X                  Newest Draw.

      How to use it? That is yet to be seen, depends on the patterns themselves.

      Mon, Nov 03, 2008    7-0-2 Newest Draw
      Sat, Nov 01, 2008    9-9-3
      Fri, Oct 31, 2008    1-6-7
      Thu, Oct 30, 2008    3-0-8
      Wed, Oct 29, 2008    8-1-7
      Tue, Oct 28, 2008    6-7-5
      Mon, Oct 27, 2008    7-3-9
      Sat, Oct 25, 2008    1-0-5 Oldest Draw.

      ----------

      Now, this might or might not be exactly like that it is just an example.

      These would be stats for possible filtration, I might want from 30 to 300 such groups, that should be more than enough, of which I might (rotate) use from 1 to 30 such stats-filter-groups (Maybe).

      This might be basic stage 1,2 or stage 2 filtration (I am not sure yet), a beginning, so far.

      Thanks a lot, very much, too hard for me to figure out by hand, but I could do a few of such groups by hand by myself.

      As always, I can make mistakes on the posts.

        LANTERN's avatar - kilroy 28_173_reasonably_small.jpg
        Tx
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        Posted: November 3, 2008, 8:03 pm - IP Logged

        John

        I just found a no software way that I can use for getting enough such groups of numbers, it is not fast like software, but about a minute to 5 minutes per matrix is not too bad, I really need only about 2 to 10 of them, I wanted more, but they are not really needed for that particular filtration stage, those will be the small matrices, there will also be bigger matrices, for second stage filtration and last for third stage filtration, but I won't need any help for the later 2 kinds, that is for the making of the groups matrices, the stats themselves I still would have to do them by hand, the hardest part of all as always is for the right use of such filter groups, but I have practice at interpreting some kinds of stats, I should in good time do good enough, as I did with the regular filters.

        Thanks a lot!

          LANTERN's avatar - kilroy 28_173_reasonably_small.jpg
          Tx
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          Posted: November 3, 2008, 9:51 pm - IP Logged

          I just perfected the chart from which the 5 pairs (SubGroups) per each group of 2 X 5 filter matrices will be picked from, the first chart that I made was half wrong.

          Looking at that chart made me remember that those groups can also be used (I think) as a sort of VTracks if a person wanted to, as some prior early and basic VTracks work showed.

          I had dropped my VTracks work as I didn't want to get into any other kind of filterering ways, than what I was already using.

          Now, it is either this kind of matrices groups  filtering or VTracks filtering, but this kind of matrices groups filtering seems to be more powerful and flexible than even my Multi-VTracks could maybe be.

          The work will go more or less slowly, but it is a beginning, I will try to make 5 to 10 such groups and then pick 2 of them for some testing, then will move on to the next boxed filter stage, which might be 1 or more 9 X 5 and or 11 X 5  Numbers Grids (Matrices),  then the final filter stage would have  much bigger grids, maybe 22 X 10 and or 12 X 10 Numbers Grids, so there might be filtration at 3 levels.

          But there might not be need for so much, I don't know, only the testing will tell, as the more filtration done the higher that filters failures can be, same as always with any filters system.

          ----------

          Group # 1 (Just an example). First possible group out of many.

          SubGroups:

          01       02        03        04        05  Always from SubGroup 1 to SubGroup 5

          01       23        45        67        89

          XX                   X                              Oldest Draw. Sample true stat data from a state.

                      X                      X           X

                                 X           XX

          X                                  X           X

          X          X                                   X

          X                                  XX

                      X                                    XX

          X          X                      X                  Newest Draw.

          Above is the simple form of that grid, a sort of compound grid of the same group is shown below:

               AB

          1    01

          2    23

          3    45

          4    67

          5    89

          The draws and their stats are not shown for the later.

          That could maybe give more detailed stats.

            johnph77's avatar - avatar
            CA
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            Posted: November 5, 2008, 4:09 am - IP Logged

            JohnPH

            I was talking about combinations where each number (Digit from 0 to 9) is unique such as on your 2 examples:

            01 23 45 67 89 = 10 32 54 76 98

            98 76 54 32 10 = 89 67 45 23 01

            And also like:

            02 13 46 57 98 = 20 31 64 75 89

            97 86 53 42 01 = 79 68 35 24 10

            That should make them even fewer combinations.

            Each pair is: Pair 1, Pair 2, Pair 3, Pair 4 and Pair 5. or SubGroup 1, 2, 3, 4 and 5.

            They would be used for digits' stats, so the order 01 or 10 on any pair does not matter, only that there are 2 digts out of the 10 on any subgroup or pair.

            ***************

            Hopefully your explanation has helped my understanding of the question.

            Assuming 01 23 is the same as 10 32 but not the same as 23 01 then:

            In the first pair there would be 45 possibilities, from 01 through 89.

            01 02 03 04 05 06 07 08 09 12 13 14 15 16 17 18 19 23 24 25 26 27 28 29 34 35 36 37 38 39 45 46 47 48 49 56 57 58 59 67 68 69 78 79 89

            For the sake of simplification, let us assume 01 is selected.

            In the second pair there would be 28 possibilities.

            23 24 25 26 27 28 29 34 35 36 37 38 39 45 46 47 48 49 56 57 58 59 67 68 69 78 79 89

            Again, for the sake of simplification, let us assume 23 is selected.

            In the third pair there would be 15 possibilities.

            45 46 47 48 49 56 57 58 59 67 68 69 78 79 89

            45 is selected.

            In the fourth pair there would be six possibilities.

            67 68 69 78 79 89

            67 is selected, leaving only one pair - 89.

            Total number of possibilities? 45x28x15x6x1 = 113,400.

            ok?

            Blessed Saint Leibowitz, keep 'em dreamin' down there..... 

            Next week's convention for Psychics and Prognosticators has been cancelled due to unforeseen circumstances.

             =^.^=

              LANTERN's avatar - kilroy 28_173_reasonably_small.jpg
              Tx
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              Posted: November 5, 2008, 6:02 am - IP Logged

              JohnPH

              I was talking about combinations where each number (Digit from 0 to 9) is unique such as on your 2 examples:

              01 23 45 67 89 = 10 32 54 76 98

              98 76 54 32 10 = 89 67 45 23 01

              And also like:

              02 13 46 57 98 = 20 31 64 75 89

              97 86 53 42 01 = 79 68 35 24 10

              That should make them even fewer combinations.

              Each pair is: Pair 1, Pair 2, Pair 3, Pair 4 and Pair 5. or SubGroup 1, 2, 3, 4 and 5.

              They would be used for digits' stats, so the order 01 or 10 on any pair does not matter, only that there are 2 digts out of the 10 on any subgroup or pair.

              ***************

              Hopefully your explanation has helped my understanding of the question.

              Assuming 01 23 is the same as 10 32 but not the same as 23 01 then:

              In the first pair there would be 45 possibilities, from 01 through 89.

              01 02 03 04 05 06 07 08 09 12 13 14 15 16 17 18 19 23 24 25 26 27 28 29 34 35 36 37 38 39 45 46 47 48 49 56 57 58 59 67 68 69 78 79 89

              For the sake of simplification, let us assume 01 is selected.

              In the second pair there would be 28 possibilities.

              23 24 25 26 27 28 29 34 35 36 37 38 39 45 46 47 48 49 56 57 58 59 67 68 69 78 79 89

              Again, for the sake of simplification, let us assume 23 is selected.

              In the third pair there would be 15 possibilities.

              45 46 47 48 49 56 57 58 59 67 68 69 78 79 89

              45 is selected.

              In the fourth pair there would be six possibilities.

              67 68 69 78 79 89

              67 is selected, leaving only one pair - 89.

              Total number of possibilities? 45x28x15x6x1 = 113,400.

              ok?

              John

              Thank you very much, but there might be still fewer combinations as any-one pair-subgroup can be in any position, the pairs-subgroups are as if they were jacpot games' lotto numbers they are BOXED or Any Order.

              So: 01 23 is the same as 10 32 and it is also the same as 23 01 and 32 10, each 2 digits combination is 1 Unit and can be on any position out of the 5 possible subgroups positions, same as on a lotto jackpot game, they are boxed, so:

              01 23 45 67 89 is exactly the same as 98 45 32 67 01

              Thanks a lot John!.

              I no longer need to know how many combinations there are, but if it can be done, it would be interesting to know.

              ----------

              Are you interested in cracking jackpot games? Knowledge of numbers and patterns combinations and such things could be of help, maybe together with some kind or kinds of numbers and patterns groups filtering, would be best to start with some kind of pick 4 (Tx2SteP) or pick 5 main numbers of a jackpot game, just a thought!

              Probably not, you seem to be a very busy person.

                johnph77's avatar - avatar
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                Posted: November 5, 2008, 6:18 am - IP Logged

                Then the above product would have to be divided by 120, since there are that many different ways of arranging any specific five-pair grouping. This leaves you with 945 different groupings meeting your criteria. And you are correct - I'm swamped with work right now - I probably have enough of that to keep me occupied through the end of next year. But thanks for the thought.

                gl

                j

                Blessed Saint Leibowitz, keep 'em dreamin' down there..... 

                Next week's convention for Psychics and Prognosticators has been cancelled due to unforeseen circumstances.

                 =^.^=

                  LANTERN's avatar - kilroy 28_173_reasonably_small.jpg
                  Tx
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                  Posted: November 5, 2008, 5:48 pm - IP Logged

                  John

                  Thank you very much.

                  That is a lot of combinations.

                  That would mean 2 things:

                  That there are that many possible sets of VTracks and:

                  That there are that many 2 X 5 Digits Boxed Filter Groups for a game such as the pick 3, so per each pick 3 draw maybe (I am not sure about this) there would be 945 possible boxed patterns for that particular kind of filter.

                  Thanks a lot again!

                    LANTERN's avatar - kilroy 28_173_reasonably_small.jpg
                    Tx
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                    Posted: November 5, 2008, 10:44 pm - IP Logged

                    Answering DiamondPalace's question on another thread-post, might had answered also one of my questions:

                    Below there might be 35 possible patterns made by the Xs below the SubGroups, either 35 or 125 3Xs patterns, probably 35.

                    Doing a very very long section of past draws would let me know for sure, what do I mean? Look at the text in Red on the right of the patterns.

                    Group # 1 (Just an example). First possible group out of many.

                    SubGroups:

                    01       02        03        04        05  Always from SubGroup 1 to SubGroup 5

                    01       23        45        67        89

                    XX                   X                              Oldest Draw. Sample true stat data from a state.Pattern # 1

                                X                      X           X Pattern # 2

                                           X           XX            Pattern # 3

                    X                                  X           X Pattern # 4

                    X          X                                   X Pattern # 5

                    X                                  XX            Pattern # 6

                                X                                    XX Pattern # 7

                    X          X                      X                  Newest Draw. Pattern # 8


                    Every pattern is the signature made by a pick 3 number, some pick 3 numbers will share the same pattern-signature as they are made by 5 SubGoups of 2 digits each.

                    Interesting, I think!

                      Mark J's avatar - 66296264041c9609293964
                      florida
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                      Posted: November 30, 2008, 1:27 pm - IP Logged

                      With 10 digits from 0 to 9

                      How many groups of 5 pairs each are there?

                      In which each group of 5 pairs has all the 10 digits from 0 to 9 among the 5 pairs in that group.

                      -------------

                      There are 100 possible pairs of the digits 0 to 9, But of them, Which 5 combination of pairs have all the 10 digits in them and How many such groups are there?

                      Some pairs can repeat from one group of 5 pairs to another group of 5 pairs, so long as not all the pairs repeat from one group to another group.

                      And can a list of all such groups be made? or Are there way too many?

                      Hi LANTERN,

                      I created 9 groups of 5 without the doubles and it was hard to do, the pais are in one position only, u may call these box pairs not straight like FT Pairs and BK Pairs in both positions,

                      so if U would like me to post them let me know U can also find me on the florida forum were I'm thinking of posting them if anyone need them.

                        CARBOB's avatar - FL LOTTERY_LOGO.png
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                        Posted: December 1, 2008, 3:01 pm - IP Logged

                        In case someone is interested.

                         

                        01-23-45-67-89
                        01-23-45-68-79
                        01-23-45-69-78
                        01-23-46-57-89
                        01-23-46-58-79
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                          LANTERN's avatar - kilroy 28_173_reasonably_small.jpg
                          Tx
                          United States
                          Member #4570
                          May 4, 2004
                          5180 Posts
                          Offline
                          Posted: December 1, 2008, 4:42 pm - IP Logged

                          In case someone is interested.

                           

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                          As I don't program nor make spreadsheets, I don't have use for all those numbers, I myself can already make the few groups that I would use if any at all, as I have to delay that particular research as it takes too much time and work.

                          Just the same, thanks a lot!

                          I better not talk any more about possible uses for such numbers, cause if I am right, (I might not be) I don't dare.

                          Thanks again!

                          Too bad that I can't no longer trust anybody on the Web to help me with the pick 3 game, might as well, what little I know about the game, I found out about all by myself, I got very little of use from others, other than a few lottery programs, which everybody else also got anyway and they didn't do any work for them.

                          Happy Holidays!

                          As there are more than one possible use for such groups and the work by hand is so hard and takes so long I gave it up for the time being, I might sometime try one of the easier uses for them, one easier to understand even for me and easier to use also.

                            Raven62's avatar - binary
                            New Jersey
                            United States
                            Member #17843
                            June 28, 2005
                            51244 Posts
                            Online
                            Posted: December 2, 2008, 8:55 am - IP Logged

                            Many Thanks Carbob! I appreciate the chart you posted! This will be very useful in the evaluation of Pair Strings.

                            A mind once stretched by a new idea never returns to its original dimensions!

                              CARBOB's avatar - FL LOTTERY_LOGO.png
                              ORLANDO, FLORIDA
                              United States
                              Member #4924
                              June 3, 2004
                              5982 Posts
                              Online
                              Posted: December 2, 2008, 12:28 pm - IP Logged

                               You are welcome, I was hoping we could stir up some discussion on the best way to use them.