I was watching the Sound of Music and the song "How do you solve a problem like Maria" was playing and then they say "How do you keep a wave upon the sand" and "How do you catch a moonbeam in your hand"
I am just wondering if there exists a term from the realm of logic to describe the connection between the latter two "How do you"'s and the first.
If the relationship you're looking for is that the impossibility of A is illustrated by mentioning an impossible thing B (and C), then the rhetorical device is known as an adynaton. (A phrase frequently used as example is "when pigs fly"; there are other idioms of impossiblity like "until hell freezes over".)
"I will sooner have a beard grow in the palm of my hand than he shall get one of his cheek." — Shakespeare, Henry IV, Part 2
In the "How do you solve a problem like Maria" case, the relationship is not explicitly made with a connective like "when" or "only if", but the rhetorical device is still an adynaton. The structure — all sentences begin with "How do you [verb]" — that implicitly makes the connection clear is simply parallelism.
These statements constitute a rhetorical device expressing the impossibility of a task. In a sense they are non sequiturs, but in actuality they are repetitive statements of absurdity, which taken together underscore the impossibility of the original query.
By "unconnected", I guess you mean that they're not joined into a single statement, such as:
To solve a problem like Maria is like catching a wave upon the sand.
Or:
To solve a problem like Maria is to catch a wave upon the sand.
Because the lyrics are in verse, there is some room for interpretation, but I'd say it's just an ordinary metaphor. It's a comparison between Maria and various supposedly impossible things to describe the impossibility that she represents, and that's basically the textbook definition of a metaphor: describing one thing in terms of another.
