But if you're at work and your boss says "I have a puzzle I need you to solve: Given these constraints, find an answer" You need to be able to say "Here is my solution" or "No solution is possible, and here is why."
Or take something simpler: a 500 piece "Puzzle" only there's a manufacturing defect in all copies: one piece is miss shaped. The puzzle can't be completed; there is no "solution". It's still a puzzle.
So no, you don't get to "unfair!" your way out of the MU Puzzle through narrow semantic definitions, especially given the, well, grammatical nature of language, because then you have gone and missed the entire point.
You and the parent comment claim it's not a puzzle, it's a riddle, with the implication that's somehow unfair or deceptive in how the problem was framed.
That is a semantic hair splitting that dodges the problem & its answer. In real life problems you don't get to define away responsibility for problems put in front of you. And if thoroughly stating my case is "overractive", then I'm guilty, but I find it's generally better to over-support my argument than state claims without justification.
All of which is besides the point: "Puzzle" and "Riddle" are pretty much interchangeable. They appear as synonyms for each other in thesauri; "riddle" is given as one of multiple definitions for "puzzle" in wiktionary. Many sources treat "riddle" as a kind of "puzzle". The degree to which riddle might be more appropriate in a given context relies on a few factors, for example riddles often tend towards more verbal basis, spoken or written. A puzzle is the broader category and can include things like physical object such as a 500-piece jigsaw puzzle. But any difference is still only that of broader category and specific type. Either term is valid here.
So stating "It's not a puzzle, it's a riddle" is indeed splitting hairs, or simply not knowing the nuances of the actual definitions of those words. The OP of that comment appeared to be doing so with the implication that the whole problem was somehow unfair as a result. I cry foul on that assertion for the reasons stated.