Algorithm for searching for the sequence of falling out of a number. Is it possible to implement this?

Question

Programming

Given a task.
1. There is a range of numbers from 1 to 100.
2. At a certain (unknown) time, one of the numbers falls out.
3. Again an (unknown) amount of time passes and one of the numbers comes up.
4. etc...
Numbers and times are NOT random. There is a certain sequence.
Question: Is it possible to write an algorithm that, based on the time and the number that has fallen, would try to find this sequence. And "guess" what number, and after what period of time will fall next. For example, it would show that this number can fall out with a probability of 40% and the more data (dropped numbers), the more accurate the forecast ... Until a 100% probability is determined.
I'm not asking you to write such an algorithm, I'm interested in whether it is theoretically possible to write such a thing?
Thank you.

Answer 1

yes, it is possible, if the numbers are not random, then there is an algorithm by which they fall out, and if there is already something, then it can be repeated with a data set for an example.
PS: there is only one nuance, the algorithm can be based on actions that you may not know, for example, the actions of other users

Answer 2

Use extrapolation. Get a table with x values ​​| f(x) = y, where x is the time, y is the number, f is the desired function. You can try different options: linear function, exponential, exponential, etc. Which one is better to lie down, that one and explore. It's just far from a fact that there lies something so simple as to be picked up through extrapolation.

Answer 3

Create a perceptron type neural network, train until the results are satisfactory

Answer 4

Because you don't know the insides of the algorithm, it's a black box for you. And so you need to describe its behavior based on the sequence of previous values. Markov chains are ideal for you.
In general, read the theory of probability and mat. statistics.
Alternatively, have discrete time. Let's say take into account the probability of a number falling out at the moment, depending on the number falling out before.
To collect statistics, you need a large enough sample.

Answer 5

With such problems, you first need to look at the periods of the function.
If the period or multiplicity is not found, then the values ​​are random.
The collection of information should help answer the question: "Is the function a multiple?" and determine this multiplicity for different input parameters if it is detected.
That is, let's reformulate the question: "what next pair of parameters will produce the same number?"
Then, you need to find the relationship between the maximum number of parameters that produced the same number.