Formula Mind-boggler

[The Thing]

Woooo. This question is very mind boggling. Try it:

 

If you use a certain formula (you do something to) on 13, you end up with 7.

Under the same formula (doing the same thing), 2352 becomes 16, 246 becomes 14, 700 turns into 16, and 1030 becomes 14.

What would 9304 become? And WHY?

 

A hint for those that are struggling (don't look if you can do it yourself):

[hide]Think outside of base-10 system[/hide]

[Callipygous]

i believe the term you are looking for is "function." as in "for the function f(n), f(13)=7 and f(2352)=16"

 

still working on the actual problem. : P

[The Thing]

Erm, it's not much of a function. I haven't figured out any f(x)=formula, as you have to [hide]Think outside of base 10 system[/hide]. Anyways, consider them functions if you want. Trying to make the point here that you have to virtually disect the numbers, not just multiply things to them.

[razorfane]

can you give more examples?

[The Thing]

Okay. More numbers.

222 becomes 14.

800 becomes 13.

999 becomes 18.

111 becomes 13.

Try it now.

HINT: [hide]Think outside of base 10! Think things like octal, hexadecimal, or binary?[/hide]

[Algebracus]

A function is not necessarily a formula, it is just a correspondance between elements of one set and elements of another set, with the only restriction that every element in the first set can only be attached to one element in the other set. We are surely taking about a function here (even if the answer is something like "the n th random natural number in he interval from 1 to 20 that The Thing works out using a specific calculator, beginning at some specific moment).

[The Thing]

Consider it a function if you think it will help you. Now, anyone has any ideas?

[Martin]

... Now, anyone has any ideas?

 

sure i have ideas, but none of them work. here is an idea that works for two cases but not any of the others

 

f(111) = 13

and f(13) = 7

 

now if that was all there is, then the recipe could be "sum up the digits and make that the base of the number system, and interpret the number in that base"

 

because summing 111 would give 1+1+1 = 3, so now make that the base

and interpret 111 in base 3 system as 9+3+1 = 13

 

and because summing 13 would give 1+3 = 4 so now make that the base

and interpret 13 in base 4 system as 4+3 = 7

 

you asked if anyone has an idea, there's an idea, but it doesnt work for the other cases

[The Thing]

You are kinda, 10% on the right track, Martin.

Anyways, when I said think outside of base 10, I meant think other widely-used bases. Now, what bases are widely used?

Try it now. Also, [hide]It DOES have something to do with the digits, but not adding them together.[/hide]