"How do you solve a problem like Maria?" [closed]
You're right: "How do you solve a problem like Maria?" is syntactically ambiguous.
The phrase "like Maria" can modify either a preceding noun phrase ("a problem") or a preceding verb phrase ("solve a problem").
Both of these usages are recognized as valid by traditional prescriptive grammars (Fowler 1926 describes "He talks like an expert" as an "unexceptionable" usage of like, where "like is equivalent to a prepositional adverb"—p. 325 in republished 2009 edition). Prescriptive grammars have traditionally condemned a third use of like, the use "as a conjunction" where it is followed by a clause (e.g. "like Maria does") rather than by a noun phrase. However, as the comments point out, that construction would allow you to express "How do you solve problems the way that Maria solves problems" without ambiguity.
Many modern linguists analyze like as a preposition when it takes a bare noun phrase like "Maria" as its complement (although like is not always a preposition, and even when it is, it doesn't always behave exactly the same way as other prepositions). The same kind of ambiguity is seen with many prepositional phrases, as illustrated by the joke "One morning, I shot an elephant in my pajamas. How he got in my pajamas, I don't know," which relies on this ambiguity. You can see further examples and discussion in the answers to Does “I am eating vegan cheese in my underpants” really imply that the vegan cheese is inside my underpants? (the "shot an elephant in my pajamas" joke is mentioned in JoeTaxpayer's answer there).
While the sentence in isolation can be interpreted that way, if you actually listen to the whole song, as well as the dialogue surrounding it, you would understand that Mother Superior considers Maria to be a problem, not a problem solver. So it wouldn't make sense for her to ask how Maria would solve problems.
Given the overall context, it's clear that the question means "How do you solve the problem of an impertinent nun, such as Maria."
The nuns are using a simile. They are likening Maria to a problem that needs to be solved.
You could say:
How do you solve a problem like Global Warming?
Implicitly, "Global Warming" is a problem, and the question is then "how would we solve a problem like that one?"
The rest of the song goes on to list a series of intractable problems, such as how to pin down a moonbeam. This implies that "Maria" is like an intractable problem that has no solution.