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I have a bunch of input numbers and output numbers that were run through an algorithm that I don't know. What is the approach for discovering the algorithm that generated the outputs? I assume this is possible by comparing the input to the output, so here are some random examples:

376492 = 648442463866
142731 = 643864412342
548437 = 838302054282
728439 = 834664368782
935765 = 050587050384

I'm aware that the algorithm is something very simple, like taking each number in the input and doing simple math like multiplication by single digits or such, then taking a digit from the sum and putting it all together with the result of a different operation or something like that.

I see so far that each digit of input results in two digits of output, as the function requires a 6 digit number and always returns a 12 digit number.

Also tried a few of these these inputs because they show patterns, maybe it'll make it easier to deduce the algorithm:

565656 = 030303030303 (interestingly, input of 656565 gave the same output as above.)

000000 = 000000000000
010101 = 000000000000
333333 = 696969696969
888888 = 666666666666
999999 = 686868686868
222222 = 646464646464
111111 = 414141414141
121212 = 828282828282

So, bottom line, my question is: Mathematically, How do i go about to deduce the algorithm -?-

[Please keep in mind that I am a noob, and don't understand advanced mathematical expressions! Thank you.]

rogerpark
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1 Answers1

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Here is an example (not unique) $$f(x)=\cases{648442463866, x=376492\\643864412342, x=142731\\838302054282 , x=548437\\834664368782, x=728439\\050587050384, x=935765\\0, {\rm otherwise}}$$

Andrei
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