# How to create common number from a set of numbers?

Let's say I have 3 people who each has a random number:

A: 1920970862902
B: 1920970862087
C: 1920970861233

How do I create a single number $X$ from $N$ (in this case, 3) numbers, where if I give $X$ to $A$, $B$ or $C$, they will be able to use $X$ to determine if their own number is inside? Is this even possible?

Extra Info: I'm using this for a programming function, so I would prefer simple formulas.

-
The numbers don't look too random if they share a large prefix... –  lhf May 23 '12 at 2:26
Does 192097086290220871233 count? –  lhf May 23 '12 at 2:28
As lhf suggests, what about just concatenating all the numbers together? Or do you want $X$ to have the same length as the numbers of $A$, $B$, and $C$? –  Austin Mohr May 23 '12 at 2:31
lhf: well they are timestamps, so they aren't that random, the randomness comes from the fact that they can be generated anytime. AustinMohr: well if I have 20 random numbers then it might become an issue. $N$ could range from 1 to ~100 numbers. Preferably $X$ should be the same length, or at least not too long. –  Wei Hao May 23 '12 at 2:33
It's impossible to compress random numbers: if you want to encode a sequence of $N$ arbitrary integers of $d$ digits each, you'll need at least $Nd$ digits to do so. On the other hand, if the numbers are not completely random, some compression may be possible. Look at en.wikipedia.org/wiki/Data_compression –  Robert Israel May 23 '12 at 2:43