I'll grant it's clean, but that's sort of a problem from the other direction: actual play IS messy, and it's the messiness that makes the question difficult (and interesting). It also gives us a perfect example of a flaw even in non-degenerate SP: the problem when no one at the table comes up with a solution, and thus play grinds to a halt. This is particularly apt in an equally-clean example: "Persuade the king to help you." If that's based purely on player skill, it may quite literally be the case that no one at the table is bold and charismatic enough to convince the king, even though convincing the king is fantastically important. Such cases are not uncommon; they may not happen constantly, but if you have a group of very shy people (e.g., mine) they'll crop up a lot more often than is acceptable.
But this is an assumption error, in my opinion.
See, if there is a bottleneck that can only be solved in one way, that isn't an issue with SP, that's a different type of problem. And that's not just an SP issue. It would be the same if it was a mechanical resolution system and you fail a roll (in a system with binary fails).
The reason I offer the SP hypo is because it allows someone to easily see that SP specifically allows for
player knowledge, and not just
character ability, which goes into the whole "metagaming" issue.
That said, in a true SP scenario, if you had the sphinx provide a riddle, then:
1. You could provide an answer based on player knowledge; or
2. You could go do other things, since it was an open world and the sphinx wasn't the end-all, be-all, and return after you've given it some thought; or
3. You could do
anything else you could dream of to get by the Sphinx.
The (3) is important. Maybe you just watched an Episode of Star Trek and thought that out-logicing the Sphinx would work; or maybe you want to Holy Grail the Sphinx (African or European?). Perhaps you have a magic item you acquired that might be helpful, or maybe you use your gold at the local town to go and research the answer.
You aren't limited in any way, other than the ideas you come up with. You can endeavor to get by the Sphinx, or not. It's your choice.
(Same for your King- if the only way to continue is to persuade the King, that shows a lack of imagination on the part of whomever designed that scenario, and a lack of respect for the players.)
Yeah, that's...basically my position as well. Which is why it's hard for me to view it much as "skill," because it feels far too much like "know the right code-words to induce the DM to rule favorably rather than unfavorably."
I am generally not a cynical person; I just find that the cases people gush about look, from the outside, rather a lot like "manipulating" rather than "strategizing."
See, I'm going to mention this again. I recognize that "SP" is specific jargon used to describe a certain modality of play, and does not overlap with "skilled" in all senses, and does not mean that other methods of engaging with the RPG lack skill.
....BUT (and to paraphrase the Good Knight, Sir Mix-A-Lot, this is a YUUUUUGE But) when people are using terms like "code words" and "manipulating" (which are not being used in any technical or jargon-y way) to describe a modality of play, it begins to seem like ... well, like you are being needlessly denigrating without understanding, which I am sure is not your intent.
SP is not "manipulating" in the same way that having defined abilities is not "mindless button pushing," or story now is not "campfire wish fulfillment" or role playing is not "silly thespians who couldn't cut it in local theater."
See? It's easy to mock things you don't engage in, but at a certain point a lack of understanding of how other people do (or did) things begins to become a needless denigration of the way other people play. There are advantages (and drawbacks) of the various ways of engaging with TTRPGs, and what works for you and your table will not necessarily work for all tables, but it is helpful to try and understand different modalities of play on their own terms, especially given that these are usually continuums.
IMO, etc.