How to hack PRNG with numbers: 21 ;10; 49; 32...?

Question

Burglary protection

Given numbers are
21;10; 49; 32; 5; 20;13; 39; 24;13; 46; 51
- number of each unknown
- unlimited available

Answer 1

You are given a sequence, start collecting information on it, build a distribution (maybe it is not uniform), calculate the probabilities above and below the number, try to prove the hypothesis that one number depends on the previous one (to choose from your task) and so on.
Probability theory provides a lot of tools for this.

Answer 2

What do you mean by "hack"? if "hack = find period", then you need the PRNG itself and preferably a description of its algorithm.
The simplest thing is to just start and wait - sooner or later (rather later on a good PRNG) it will repeat.
If you know the generation algorithm, you can try to solve it analytically, but again, it depends on the algorithm, if it is one-sided, then just wait for the repetition.

Answer 3

You need to know the algorithm.
The longest is overkill.
The most effective, at least to know the original value.
Each next number depends on the previous one, each next number is tied to a section of time, each next number is envy from the previous one using the Caesar cipher.