Rorrian Number Classification System! (As of 6/7/14)
Well, here it is, my full classification system for numbers as of today.
This is the system that I use in the Count To a Million thread and sometimes in my head in real life too.
<Geekiness>
There are three parts to the system: Grades, Types, and Tiers.
Grades:
Grades are the simplest of the three categories, being a measure of how many palindromes can be found inside the number.
Any Palindrome inside the number counts to the grade as long as it's at least two digits.
(For instance, in the number 14151 there can be found Two Palindromes, 141 and 151. And in the number 13131 there can be found Four Palindromes, 131, 313, 131, and 13131)
Types:
Types are a bit more complicated, though as the name suggests, types have to do with the Type of Palindromes that be found in the number.
Type 1 are Common Palindromes, simply being when a number can be written backwards and be the same number.
(For example, the number 12321 can be spelled backwards and still read as 12321)
Type 2 are Rotational Palindromes, which if you rotate the number by 180 degrees, it reads the same.
Block numbers are the easiest to use to find Type 2 Palindromes and are what count for finding them.
The numbers that are usable in Type 2 Palindromes are 0, 1, 2, 5, 6, 8, and 9. However, 6 and 9 have to be used with each other, as 6 rotated is 9 and vice-versa
(Examples of Type 2 Palindromes include 659, 69, and 56895)
Type 3 are Mixed Palindromes, including both Type 1 and Type 2 Palindromes in the number.
Type 3 Palindromes are a type of Palindrome that can only be found in the Partial Tier (More on tiers later)
(Examples of Type 3 Palindromes include 6090, 699, and 75857)
Type 4 are "Double" Palindromes, all of the Palindromes that can be found in this type are both Type 1 and Type 2 at the same time.
Type 4 Palindromes can only use the letters 0, 1, 2, 5, and 8, as all others can not be found in a Type 1 and 2 at the same time.
(Examples of Type 4 Palindromes include 505, 828, and 18281)
Type 5 are Mirror (or Rorrim) Palindromes, in Type 5 Palindromes if you split the number down the middle, the right half looks like a flipped version of the left half.
Type 5 Palindromes can use the letters 0, 1, 2, 5, and 8
(Examples of Type 5 Palindromes include 502, 818, and 12051)
Type 6 are [unnamed at the moment] Palindromes, which are Palindromes that include Type 1 and Type 5 Palindromes
(Examples of Type 6 Palindromes include 522, 252, and 52025)
Type 7 are [Again Unnamed] Palindromes, which include Type 2 and Type 5 Palindromes
Type 7 Palindromes can use the letters 0, 1, 2, 5, 6, 8, and 9
Type 8 are Perfect Palindromes, which all the Palindromes that can be found inside the number are both Type 1 and Type 5
Due to the nature of Type 5 and Type 1 Palindromes, this Type is also made up of all Type 2 Palindromes
Type 8 Palindromes can use the numbers 0, 1, and 8
Tiers:
Palindrome Tiers represent the purity of the number (How much of the number is composed of Palindromes)
Tier 0 Palindromes are honestly not Palindromes at all, they are composed of no Palindromes and as such Tier 0 doesn't really exist.
Tier 1 Palindromes are also called Partial Palindromes, part of the number is composed of Palindromes, but not all of it.
(Examples of Tier 1 Palindromes include 84836, 554, and 8440)
Tier 2 Palindromes are named Significant or Non-Trailing Palindromes, Tier 2 Palindromes are composed of numbers that are full (Tier 3) Palindromes if Trailing Zeroes are not included.
Tier 2 Palindromes are often a lower grade than if they were counted as Tier 1 Palindromes, but being a higher tier they are still "Stronger" Palindromes than Tier 1
(Examples of Tier 2 Palindromes include 85800, 220, and 241420)
</Geekiness>
And there you go, my full classification system for numbers. If you read all the way through it, you're most likely a nerd, geek, or totally bored, and if you're either of the first two, I Salute You!
Also, if you have any ideas for improvements to the system, feel free to tell me in the comments!
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