Taking inspiration from "What is the word™" series, here the numbers conforms to a special rule, I call it a RAP number™. Use the following examples below to find the rule.

enter image description here

Note : This is my first crack at this type of puzzle, so suggestions and edits are welcome.

I don't think the CSV is needed here, but for those who need it, here it is

RAP number™,  NOT RAP number™  
12,     19
27,     78
43,     37
110,    193
122,    364
611,    561
5132,   5096
4703,   7961
25117,  25169
810221, 71423

Note : You can differentiate any number into these categories. This "Rule" can be applied to each and every number existed.
I am thinking about the way to give hint without spoiling the answer.

NOTE I am so sorry, I misprinted last number it is supposed to be 810221

  • $\begingroup$ Unless, there is some tricky need to use an image representation of these numbers, it is way better to have a plain text representation. It is easier to copy-paste, and to have found by search algorithms. Having an excel sheet in an image file is only needed in some exceptional cases: puzzling.stackexchange.com/questions/42124/what-is-a-shy-word. In any case, in most cases it just adds an unnecessary and simply avoidable layer of extra noise to your puzzle, and annoys all those people who sadly rely on the use of word-processing software as a visual aid. $\endgroup$ – Matsmath Sep 20 '16 at 5:25
  • $\begingroup$ @Matsmath Whoa, thanks for notifying! Added it.(This is what I get, for opening multiple tabs and forgetting in which I am typing my question -_-)(BTW, is that the reason for downvote?) $\endgroup$ – smriti Sep 20 '16 at 5:42
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    $\begingroup$ It was about time that the word puzzles got extended to numbers ;c) But in the spirit of these puzzles: Is the same implicit assumption valid? i.e.: The "property" of the numbers is a property of each number, not of the collection of numbers; (Hence order of the list is not imporant and "other" numbers are not important. One could remove any number (and maybe add a suitable one) without loosing the property.) $\endgroup$ – BmyGuest Sep 21 '16 at 9:52
  • $\begingroup$ @BmyGuest yes, in this case it is true...eg take RAP number 5132, if 1 is replaced by 2 it will still be RAP number $\endgroup$ – smriti Sep 21 '16 at 10:19
  • $\begingroup$ @smriti Actually, I meant that the puzzle is still "valid" if I swap the order of listed numbers, i.e. 12,122,43,110... instead of 12,43,110,122,.... Or that it is still valid, if the RAP number 5132 is not listed. Or that it is still valid, if another (?) RAP number is inserted anywhere. In short: Each RAP number on its own has the property. It is not a property of the list. $\endgroup$ – BmyGuest Sep 21 '16 at 11:44

Does RAP stand for

Reverse, Add, Palindrome?

Some examples:

RAP numbers: 12+21 = 33, 611+116 = 727, 25117 + 71152 = 96269
NONRAP numbers: 19+91 = 110, 193+391 = 584, 5096+6905 = 12001

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  • $\begingroup$ That's very good, but unfortunately, it doesn't work for the RAP number 81022 + 22018 = 103040. (It's the only one that doesn't fit, though.) $\endgroup$ – M Oehm Oct 6 '16 at 19:37
  • $\begingroup$ @MOehm Oh wow, you're right, I'm not sure how I missed that... my bad. $\endgroup$ – Sconibulus Oct 6 '16 at 20:02
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    $\begingroup$ @smriti: Maybe, but I think it's more likely that it is just hard for others to see the rule. Authors often misjudge the difficulty of their puzzles. $\endgroup$ – M Oehm Oct 7 '16 at 7:20

Possibly a RAP number may be one where the numbers are

Read Alphabetically Progressing and are non-decreasing in order from left-to-right

The description below needs to call the 0 digit the ten(s) digit - if acceptable?

12 = One Two
43 = Four Three
110 = One One Tens
122 = One Two Two
5132 = Five One Three Two
4703 = Four Seven Tens Three
81022 = Eight One Tens Two Two

And all the non-RAP words' digits are not in alphabetical order.

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  • $\begingroup$ Whoa, That is one mind blowing answer!!(I wish I can give more than 1 upvote) But unfortunately it is not correct, even I did not notice this..... 27 is also RAP number and 78 is not RAP number, I will add some more examples $\endgroup$ – smriti Sep 21 '16 at 9:12
  • $\begingroup$ @smriti you may want to consider offering a small bounty for this answer. There is an option of "one of the answers is exemplary, and worthy of an additional bounty", where it is clear that your intentions are to award one of the existing answerers (and not prospective ones). $\endgroup$ – Matsmath Sep 21 '16 at 10:36
  • $\begingroup$ @smriti Ahh.. I thought 78 is a RAP number. $\endgroup$ – EKons Sep 21 '16 at 10:39
  • $\begingroup$ @Matsmath I don't no how to do that, thanks for suggestion, I will look it up, and add(still, I have to wait for 17 hours) $\endgroup$ – smriti Sep 21 '16 at 10:43
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    $\begingroup$ What if you called 0 ought? $\endgroup$ – Engineer Toast Oct 3 '16 at 20:02

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