# 3-digit and 4-digit Game Tools

Without being too mathematical, but practical, we shall present here the tools necessary to generate the various arrangements and groupings of a 3-digit and 4-digit 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 sub-groups 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 sub-groups of 2 members, then n will be 2. The resulting sub-groups 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 3-digit and 4-digit Games

Permutations are useful to generate all the possible arrangements of a 3- or 4-digit 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 3-digit or 4-digit 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 4-digit numbers from numbers that have more than the game's digits. For example, you may wish to play all even numbes in a 3-digit game. Since the even numbers are 02468 (five members), you will have to group them into sub-groups of 3 members, like 024, 046, 268, etc. These numbers can be generated using the tools provided below.

#### Permutation and Combination Generators

3-Digit Pemutation generator
Enter a 3-digit number

Permutations

Total =
4-Digit Pemutation generator
Enter a 4-digit number

Permutations

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In the following combinations generators, you may elect to generate all or some of the possible combinations such as numbers with non-repeating digits, numbers with one-repeating 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.

3-Digit Combinations Generator
Enter a number
upto 10 digits long

Mark which ones
to generate
Non-repeats
Doubles
Triples
Combinations

Total =
4-Digit Combinations Generator
Enter a number
upto 10 digits long

Mark which ones
to generate
Non-repeats
One-Double
Dual-Doubles
One-Tripled
Combinations

Total =

The following are non-categorized generators where you do not have to specify non-repeating, 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 3-digit combinations of 1234 where only 1 and 3 are to be repeated. To accomplish this, enter 112334 to see that all non-repeating, 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.

3-Digit General Combinations
Enter a number
upto 30 digits long
with or without
repeated digits

Combinations

Total =
4-Digit General Combinations
Enter a number
upto 40 digits long
with or without
repeated digits

Combinations

Total =

Please note: To obtain the intended results, repeated digits should be entered contiguously (like, 12223). If they are not entered in this way a partially-permuted combinations will be generated which will cause some combinations to be duplicated in a different arrangement (try 21232 and compare it to 12223).