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 tha 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

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.