Your example as you have literally explained it entails just deleting all repeats (ambiguous if 121 -> 12 or 121, or for that matter if 121 is possible as an input). Either way a simple for loop could solve it. But you are a self proclaimed smart person who eats for loops for breakfast, so it seems your have over simplified your description of the problem.

Machine learning is essentially the following:

• For sets X and Y, take a collection of some functions F = {f: X -> Y}
• Take a probability distribution D on X x Y. Note this could be of the form (x, g(x)) for fixed unknown function g where only x is random.
• Take a loss function L: F -> R, eg L(f) = ExpectedValue( distance(f(x),y) )
• Sample data from the distribution
• ???
• Have an f in F that is close to minimizing L

So tell us what F, X, Y, D, L are.

So vectors to vectors are extremely abstract and it's hard to understand what those vectors are. ML/DL are functions at the end of the day that are learned from observing a lot of examples of vectors -> vector transformations (inductive learning).

If these transformations are fairly easy to model, you might just be able to solve the function directly. Or you might need simple ML algorithms. If it's very complex, you might need stronger models and/or more data.

For instance image -> vector of probabilities over possible categories requires some powerful models where as a vector of 1 feature (height) -> probability of not hitting the head on the roof requires a basic model.