# A number of representations

What number, when used to represent all numbers, can be used to represent something else?

To get credit you need the number and the reason behind it.

EDIT: Puzzle Rewording

Its been a while since putting up this puzzle. Given its problems, but also the elegance of the answer I was trying to go for, I figured I would try rewording it entirely. Here goes:

Which natural number, when symbolically used to represent numbers, can be used to represent something else, and why?

• The question describes itself.
• A number being used in this way is pretty ________.
• The number of letters in the "blank" above, is the number you're after.
• The "blank" with the number describes the question.
• I'm hoping this isn't the case, is it rot13(vasvavgl)?
Commented May 20, 2019 at 21:20
• @Adam Nope. I'm not even sure what the meaning of what you wrote is? Though, I am curious about it. Commented May 21, 2019 at 21:20
• @user330504 The text that Adam wrote is encoded by rot13. If you decode it, it will become clear what he is saying. Commented May 21, 2019 at 21:22
• It would be helpful if people who downvote could leave a comment telling me how I might improve future puzzles! Thanks. Commented May 21, 2019 at 21:22
• I think people are downvoting because the puzzle is too broad and has several answers, a few of which I’ve listed below. Commented May 21, 2019 at 21:59

I think the number is

e

Reason:

It is the mathematical constant e, where e is an irrational and transcendental number and it can represent all numbers(2.71828182845904523536028747135266249775724709369995...)  It is the base of the natural logarithm(Representing something else).

Is the number

PI π

Because

It is said to contain every number in its digits and it also reminds everyone of pie!

This has many answers, depending what is meant by 'the set of all numbers' including:

R = real numbers, N = Natural numbers, Z = integers, C = complex numbers. All of those letters have several other meanings as well.

• Thanks for the feedback. I've tried to be more open / explicit regards to the maths required to solve the puzzle, but would appreciate feedback if I've over/under-stepped the mark. Commented May 21, 2019 at 22:46
• @user3303504 I think that the natural next step is to expand the puzzle itself. A well crafted puzzle doesn't need extra explanation or additional context (your edits) for a solver to logically arrive at the answer, everything is apparent from the get-go. Similar puzzles to this commonly face the same problem and that is the lack of 'information' (loosely using this term). Some careful word choice and bloating of the puzzle can be really effective in adding vague scraps of 'information' which in turn reduces the risk of unintentional well-fitting answers
Commented May 21, 2019 at 23:31
• @Adam Thanks for the feedback. I've had a few chats over this and updated the puzzle with a (hopefully) improved rewording. Would you say I'm headed in the right direction? (I've also been told to look into Q&A's for cryptic crosswords to get more of a feel for these types of puzzles). Commented May 22, 2019 at 21:40

In case curious eyes cross this puzzle again in the future, the answer is:

4. The idea was that a number being used to represent many other numbers was kind of meta. If the number used is 4, then you get meta-4, which sounds like metaphor. The question can also be considered a metaphor for a metaphor... which is kind of meta...

Thank you for all the constructive feedback! I will endeavour to make a better puzzle next time.

• Now that you have shared the answer, I get why it was difficult to make into a puzzle. It is a great idea for a puzzle, with the answer I can now give proper feedback. The words 'used' and 'represent' are the problem (from "used to represent all numbers"). With the answer in mind, it makes perfect sense however the puzzle didn't exactly convey that there was more to the number than just itself so solvers probably won't be able to naturally solve this in its current state (good use of wordplay tag though). It is interesting, cannot wait to see more from you!