A basic structure of numbering system can split any number to 2 basic sections:
- Prefix, which is a set of digits or letters identifying the “series” the subject number belongs to
- Running or functional part, which contains the numeric unique value
In many cases, there can be some additional parts of the numbers like suffix, parity flag, or error correction codes. But we will assume the simple form of 2-part numbers as described above.
A prefix can be a set of digits or letters or a mix of digits and letter. There are two important notes related to the presence of prefix,
- It adds to the length of the number
- It can be a part of the number classification.
As an example, a prefix in mobile dial numbers like 012 will add 3 more digits to the length of the running number as well it can help classify dial numbers like 012-34xxxxx as an easy number because it simplifies the way you can recall it (01234 is a straight ascending set of digits).
We will fix a notation for prefix digits as P1, P2, P3
Running numbers also include 2 important factors
- The count of digits which indicate maximum possibilities of digit combination (referred to as series length), and this can be easily estimated by the formula
Series length = 10 to the power n
- It indicates the level of complexity to classify the numbers, the longer running code, the more complex classification is
We will fix a notation for running digits as d1, d2, d3, … , dn
Formation of a simple number pattern
Now, let’s start the fun, the following example shows how a classified pattern will look like.
A simple “4 twins number” may look like:
- P: AABBCCDD
- P is the full prefix
- A, B, C, D: unique digits
- D1 = D2 = A
- D3 = D4 = B
- D5 = D6 = C
- D7 = D8 = D
When applying this “rule” to a series of 8 digit numbers, we can extract a lot of numbers in the 4-twins category like:
- P: 33 99 22 00, P: 44 99 22 33
Note that a problem will arise for some numbers in this pattern like the number (P: 22 33 44 55) as it will fall between two categories, 4-twins and 4-ascending-twins.
In the next article, I will focus on patterns and the hierarchy of classification so we can understand how to solve such problem.