I was thinking about the "does something interesting necessarily have to be a solution to something" question, too. I reached my default conclusion for this sort of philosophical question, namely that the terms are too poorly defined to yield any answer that is accurate/definite/unambiguous (here I am using lots of words that mean basically the same thing in the hope that any subtleties that one word might have missed will be covered by the others). But under a few assumptions regarding the nature of the question, I can say, "yes." By assumptions, mainly I just mean giving a very broad interpretation to the "something" that we are finding solutions to. So: to be interesting, something must surprise us, and to do that it must violate a norm or challenge an assumption, and this can be interpreted as an answer (and now I will take the liberty of equating "answer to question" to "solution to something") to the omnipresent questions that themselves define norms and assumptions--e.g. questions like "is this the only way for things to work" or "could what currently seem to be the extremes in fact be surpassed"--basically, questions about the completeness of our current knowledge of things. So, in that way, anything interesting is also a solution to a problem: the problem of whether or not our knowledge is complete/the problem of whether or not our knowledge of the completeness of our knowledge is correct (the second one probably makes a safer statement).