From a Computational Learning Theory perspective, we are faced with an infinite hypothesis space, with an infinite VC dimension. So yes, there's not much strategy that can be employed here.

But, the fact that there is one correct answer is not really an assumption that the puzzle makes, it is information we have been given:

> We've chosen a rule that some sequences of three numbers obey -- and some do not.

This simply means that the solution is realisable. No matter how many ways (in English) we have to describe that solution it is still the same solution.