Linear Transposition
Brad said:
Hey dowjones,
posting your link here is a no no as it leads to another forum, can you delete it pls ?
SORRY!
But I don't have the permission to delete my own post.
Anyway, here's the info:-
Track and Wheel your Lottery Numbers with L-Trans
General Information:
Whether you are playing PICK 3, PICK 4, PICK 5 or PICK 6 lotteries it helps you to track your predictions or the results. The Linear Transposition (short L-Trans, or l-trans) is a concept that allows you to divide the numbers within a set into groups of 2 and N numbers. Each group has an assigned index number. These groups can be used to track drawings, evaluate pattern, wheel groups with each other or evaluate predictions.
Base and Starting Point Definition:
The two variables within the Linear Transposition function are the Base (Number of groups) and the Starting Point (or Base Constant, the first Number of the Field). The Starting Point of 0 is standard for PICK 3 and PICK 4 lotteries, for PICK 5 and PICK 6 lotteries the Starting Point is usually 1.
Perfect Groups:
The grouping is based on the field of numbers (or population) of the lottery game. Perfect groups are groups are have an equal amount of numbers. Not every lottery has perfect groups. Lotteries that have a prime number as a the population, cannot have prefect groups. An example would be the 5/37 Cash 5 of the Texas Lottery.
Case Example
For example the perfect group for 6/49 lotteries is a base of 7 with a starting point of 1, or in short L-Trans(7,1) with the following contents:
Index #1 #2 #3 #4 #5 #6 #7
Group 1 1 8 15 22 29 36 43
Group 2 2 9 16 23 30 37 44
Group 3 3 10 17 24 31 38 45
Group 4 4 11 18 25 32 39 46
Group 5 5 12 19 26 33 40 47
Group 6 6 13 20 27 34 41 48
Group 7 7 14 21 28 35 42 49
Group Index and Contents
The Chart on the left show the linear transposition for each number of each group in the example. 8 (Group Index 1) transposes by 1 to 9 (Group Index 2) up to 14 (Group Index 7). 24 (Group Index 3) transposes by 3 linearly to 27 (Group Index 6).
In the chart you can see that every column belongs to a Group (e. g. 45, 38, 31, 24, 17, 10 an 3 are part of Group 3).
Tracking with L-Trans Index
Using the Group Indexes (one complete set of group index is also known as the L-Trans index) you can easily simplify Lottery drawings, results or predictions.
Set Example:
2,16, 32, 33, 42, 49
has the following l-trans index: 224577
The tracking through l-trans index compresses the numbers to only six digits (if less than 10 groups) and can show transposition trends very easily.
Number 2 16 32 33 42 49
Group Index 2 2 4 5 7 7
Imperfect Groups
As mentioned earlier not every lottery can have the same amount of numbers in each group. The number is based on the population. Here an example of a typical lottery with Imperfect groups.
Texas Cash 5 5/37 can for example be grouped by using L-Trans (9,1):
Index #1 #2 #3 #4 #5
Group 1 1 10 19 28 37
Group 2 2 11 20 29
Group 3 3 12 21 30
Group 4 4 13 22 31
Group 5 5 14 23 32
Group 6 6 15 24 33
Group 7 7 16 25 34
Group 8 8 17 26 35
Group 9 9 18 27 36
The groups 2 to 9 contain 4 numbers, the group 1 contains 5 numbers. Even though the groups are imperfect, they can still be used for tracking and wheeling purposes.