Generate combinations of Massachusetts Lottery The Numbers Game numbers with option of fixing digits, pairs, triads. Also, filter by sum, high-low, even-odd, consecutivity.

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Massachusetts Lottery The Numbers Game Combinations Generator

This is a re-designed utility to generate all the combinations of a selected set of Massachusetts Lottery The Numbers Game numbers, with the option of fixing some digits as well as pairs and triads. It also allows you to extract several The Numbers Game patterns such as even-odds and high-low, in addition to filtering out by sums or consecutivity. If this is the first time you are using this tool, we strongly recommend that you read the Instructions on how to use the Massachusetts Lottery The Numbers Game Combinations Generator further down on this page.



Instructions for the Massachusetts Lottery The Numbers Game Combinations Generator

This tool generates Massachusetts The Numbers Game combinations of boxes (4-digit numbers without regard to their arrangement). Basically, two steps are involved: 1, make your selections on the "Selection Panel" and, 2, click on the "List Results" button. The generated numbers will be listed under the "Results Panel", which also contains the total numbers generated, the odds (and probability) of winning with the generated The Numbers Game set, frequency of the digits of the generated numbers, and the summary of selection criteria.

There are eight selection criteria most with All and None buttons that will facilitate some selections. For example, if you want to list all numbers with a sum of 18, you have to unselect all the other sums one by one. Alternatively, a faster way would be to click on None and then click on 18. Note that you cannot leave all options of a criterion unselected.

The "Summary of Selection Criteria" displayed at the end of the "Results Pannel" will show in red whatever modifications you have made on the default values.

Every selection you make is appended to your previous selection. So, the results listed will always incorporate all previous choices. To start all over again, or to return to the initial default selections, click on the Reset All button at the bottom.

Initially, all the 715 possible The Numbers Game combinations will be listed, with all checkboxes checked. Then, you can use one or more of the following criteria to filter out your desired set of Massachusetts The Numbers Game list.

  1. Digit Selection

    By default, combinations of all the Digits 0123456789 are considered. If you want not to include some The Numbers Game digits, you can do so by deleting them. To generate all combinations of the digits 135689, for example, just enter them and click on the "List Results" button. If you want futher filtering such as non-repeating digits, go to the selection labeled 3. Repeating or not and unselect Doubles, Dual-Doubles, Triples, and Quadruples. Alternatively, you may click on None and then mark Non-Repeating. If you still want to impose more conditions, such as The Numbers Game sums, go ahead do it; note that at some point you may end up with no numbers generated if you specify a set of incompatible conditions.

  2. Key (fixed) Digit/Pair/Triad Selection

    Sometimes, you may wish to generate numbers that must contain a digit, a pair, or a triad. For example, if you feel that 8 is due in the Massachusetts The Numbers Game, then enter 8 in the box to generate The Numbers Game numbers that must contain 8. The same goes for a pair and a tiad; just enter 234 to geneate all The Numbers Game numbers that contain 234. There is still more hosepower to this tool - you may impose "either or" condition by separating your entries by commas. If you enter "2,8", for instance, only numbers that contain either 2 or 8 will be listed. In fact, you may enter more than two digits, pairs, and triads such as "2,8,07,234" to list the numbers that contain at least one of 2, 8, 07, or 234.

  3. Repeating or not

    Here, you may choose to list only The Numbers Game non-repeating numbers, doubles, dual-doubles, triples, quadruples, or any combinations thereof.

  4. Even-Odd

    If you want 1, 2, 3, or all 4 digits of The Numbers Game to be even or odd, then use this selection criterion.

  5. Low-High

    If you want 1, 2, 3, or all 4 digits of The Numbers Game to be low (0,1,2,3,4) or high(5,6,7,8,9), then use this selection criterion.

  6. Sums

    Sums are simply the sum of the four The Numbers Game digits. Some sums are more likely to be drawn than others simply because they cover more numbers. If you want to filter out numbers with certain sums, then use this option.

  7. Root Sums

    The Root Sum is the sum of the sum. For example, the number 3489 has a sum of 24, thus its Root Sum is 6 (i.e, 2+4). Root Sums have the interesting characteristic of distributing all the The Numbers Game numbers into nearly equal groups, that is, except Root Sums of 0, all the rest have nearly equal Root Sum (79 and 80). So, unlike Sums, Root Sum have about equal chances of being drawn. This will allow the player to choose members of a hot or cold The Numbers Game Root Sum.

  8. Consecutivity

    The numbers with obvious consecutive digits are 0123, 1234, 2345, 3456, 4567, 5678, and 6789. If we analyze the frequency of digits in this set, we will see that 0 and 9 appear only once, 1 and 8 appear twice, 2 and 7 appear 3 times, while the rest appear four times. In order to have an equal frequency of all the digits, we have to view the arrangement of the digits as circular, as shown in the figure, rather than linear as 0-1-2-3-4-5-6-7-8-9. As can be seen on the figure, 7890, 8901, and 9012 are also consecutive. So, our list of numbers with consecutive digits has to include 0789, 0189 and 0129.

    What we refer to here as consecutivity is "within how many digits a number is spread". The numbers listed above are consecutive within 4 digits therefore have a consecutivity of 4. Only quadruples have a consecutivity of 1, only dual-doubles and triples can have a consecutivity of 2, and only doubles, dual-doubles and triples can have a consecutivity of 3. In many case, the consecutivity of a number is the difference between the highest and the lowest digts plus 1. However, since we are using the circular arrangement of the digits, the actual consecutivity is the shortest distance that includes all the four digits along the circular path.

    To illustrate, consider 0234 and 0678. Both of these numbers are consecutive within 5 digits. It is obvious for 0234 since (4-0)+1 = 5, but not for 0678. Here is how you determine the consecutivity of 0678 (or any other number in general). Start from one of the digits and go clockwise until you have encountered all other digits on your way. If you start from 0 and go to 8 you'll cover 9 digits; if you start from 6 and go to 0 you'll cover 5 digits; if you start from 7 and go to 6 you'll cover 10 digits; if you start from 8 and go to 7 you'll cover 10 digits. So, 0678 is consecutive within 5 since the second one is the shotest path.

    Note that the digits are equally distributed within a given consecutivity. For instance, for a consecutivity of 3, all the digits of the generaed numbers appear 24 times.


Finally, if you still want to use the old tool, click here -> Old Massachusetts The Numbers Game Combinations Generator

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