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Two list de-cypher

Hi,

I have two lists of numbers, the second list I know is generated from the first, but I don't know how.

Given I have a number of known answers (over 3000) is it possible to decode to find the original algorithm which created the second list (as the first list has 'holes' in it). If it is possible - where and how do I go about doing it?

Thanks

d-glitch

It could also be an attempt at password hacking.
It might help if you could post some examples of your actual data pairs.
In general, you can come up with an algorithm to map your input to your output. In fact, you can come up with an infinite number of such algorithms. That means you probably won't come up with the one that was used originally.

dbiom

ASKER

HI,

certainly not a home work project - nor anything illegal!

000000      8396
000001      5954
000002      3870
000003      2353
000004      8963
000005      0901
000006      0422
000007      9944
000008      2560
000009      6622
000010      5602
000011      1266
000012      8684
000013      4663
000014      8143
000015      4570
000016      3770
000017      2201
000018      6539
000019      5650
000020      5354
000021      1374
000022      1834
000023      2773
000024      8426
000025      4471
000026      0444
000027      9697
000028      4406
000029      3922
000030      2015

Thanks

d-glitch

What are the max and min numbers in your second list?
It looks like a list of four digit numbers with leading zeros allowed.

You said you have 3000 data pairs with some holes. What do the holes look like?
Do you have scattered data, or are there some scattered holes?

There are 10,000 possible 4 digit numbers: 0000 to 9999. And you have 30% of the data.

But there are 10,000! possible ways to shuffle these numbers.
http://gimbo.org.uk/texts/ten_thousand_factorial.txt

One of the techniques that might have been used to generate your list is described here:
https://en.wikipedia.org/wiki/Linear_congruential_generator

Look in particular at the Recurrence Relation formula at the top of the page.

Since your second list has a value of 9944, you might want to try the following values for m:
9949 9967 9973
These are the primes between 9944 and 9999.

You can use your first digit number as X_1, but you would have to guess at the values of a and c.

This technique will let you generate lots and lots of lists like the one you have. But the odds of getting the right one vanishingly small.

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d-glitch

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dbiom

ASKER

Thank you - certainly gives me something to go on - mere curiosity and frustration at my lack of knowledge.