How can I determine what the algorithm is?

Question

If I have several pairs of numbers, say 10 digits each, how can I determine the algorithm used to obtain the second set of 10 numbers? Example:
1234543210--8695249713;

9521238528--7221083126.

This example is not the correct numbers but just for an example.

I may have about 10 pairs. Any idea how to figure it out so I can determine the 10 digits that would correspond to 10 digits that I would choose?

Thanks.

Zippy

Answer 1

It seems like what you are asking is how to determine a mapping f:S->S, where S = {0000000000, 0000000001, ..., 9999999999}.

In general this is not possible, as there are 10000000000! possible mappings. If however, you knew a certain property of your mapping, you might be able to obtain a precise mapping from 10 (or fewer) pairs. Some examples, might be if it mapped individual digits to other digits, or if it swapped the order of certain digits, or if it multiplied the numbers by something and then took the remainder when the result is divided by 10000000000...

If you would like to post more specifics about the mapping, or some of the pairs, I could try to tell you something more specific about how you might try to find the mapping.

Answer 2

Where do the numbers come from ?
If you don t know, can you give the actual pairs that you have and the ones you are looking for ?
Otherwise, we have to assume that the numbers can come from any algorithm like the names of pages of a phone book;
If it is a purely mathematical algorithm what you are looking for , you could try to construct polynomials of maximum degree: the numbers of pairs that you have -1 .
Example:
4--20
3--7
2pairs so degree 1:
a*4+c=20;
a*3+c=7;
Resolving it gives :
a=13;
b=-32;

So to find the left pair (called y) of number x:
13 * x - 32 = y

Answer 3

Your problem as stated is unsolvable as there are an infinite number of functions which will transform one number to another.
If you can assume the pairs of numbers are the result of a single common function then the only solution I can suggest is the "brute force" method ie start with subtraction, see if it applies to all pairs, if that fails, try division, logarithms etc... or any algorithm that context might suggest.

Answer 4

IF then 2nd set 10 numbers are just re-arrangements of the first set, you have a chance. However, that does not look to be the case.
The 2nd set of numbers is an ENCRYPTION of the 1st set. You are basically asking us for an algorithm that determines the encryption key.

Good luck- you'll need it.