3digit and 4digit Game Tools
Without being too mathematical, but practical, we shall present here the tools necessary to generate the various arrangements
and groupings of a 3digit and 4digit number games. We shall use two mathematical tools called permutations
and combinations.
Permutation and Combination Theory
The permutation of a number, a string, or any other set of objects with N members is the possible arrangements of
its N members. For example, there are two possible permutations of the string 'XY' and they are {'XY', 'YX'}; there are 6
possible permutations of the string 'XYZ', namely, {'XYZ', 'XZY','ZXY','YXZ','YZX','ZYX'}
The combination of a number, a string, or any other set of objects with N members is the possible grouping of the
N members into subgroups of n members. For example, the string 'XYZ' has 3 members (that is N=3). If we want
to to group the three members into subgroups of 2 members, then n will be 2. The resulting subgroups will be {'XY', 'XZ', 'YZ'}.
So, permutation is arranging, and combination is grouping. The positions of the members do not matter in combinations.
Application to 3digit and 4digit Games
Permutations are useful to generate all the possible arrangements of a 3 or 4digit number. For instance, if you want to play
all the possible starights of the number 8174, then you have to generate all the 24 possible arrangements. They are used only if
the 3digit or 4digit lottery game you are playing does not offer combo or box plays. If it does, then you do not need a permutation generator.
On the other hand, combinations are very useful in order to list all the possible 3 and 4digit numbers from numbers that
have more than the game's digits. For example, you may wish to play all even numbes in a 3digit game. Since the even numbers are
02468 (five members), you will have to group them into subgroups of 3 members, like 024, 046, 268, etc. These numbers can be generated
using the tools provided below.
Permutation and Combination Generators
In the following combinations generators, you may elect to generate all or some of the possible combinations such as
numbers with nonrepeating digits, numbers with onerepeating digit, etc. Only unique digits are allowed, that is, if you
enter 11223499, it will remove the repeated digits and consider only 12349. Another generator is supplied further below
where you can enter repeated digits.
The following are noncategorized generators where you do not have to specify nonrepeating, doubles, etc. Instead, you
can repeat digits so that any digit can be generated using the number of times you entered it. This is especially useful
if you wish to generate combinations with only selected digits to be doubled or tripled. For instance, you may wish to
generate 3digit combinations of 1234 where only 1 and 3 are to be repeated. To accomplish this, enter 112334 to see that
all nonrepeating, plus doubles which contain only doubles of 1 and 3 are listed. If you want triples of a digit to be
included, then enter it 3 times.
Please note: To obtain the intended results, repeated digits should be entered contiguously (like, 12223). If they are
not entered in this way a partiallypermuted combinations will be generated which will cause some combinations to be
duplicated in a different arrangement (try 21232 and compare it to 12223).
