I would continue arguing that "unsolvable" is not a valid solution to this puzzle. If the description asks you to "find the solution" and the solution does not exist, then it is a riddle, not a puzzle.
You're simply playing semantics and defining "puzzle" as "something that has a solution".
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.
I think his point: "If it asks you for a solution that doesn't exist, It's a Riddle" is a perfectly valid point and your comment was a bit "overreactive", in my opinion.
What makes it a valid point? I see nothing in the definition of either word that would definitively preclude "puzzle" as an appropriate label. Riddle is fine too, but no mutually exclusive.
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.
Different contexts. In the real world it's understood that anything is possible (you can also clarify if unclear). But in a book like this, you put trust in the author to use precise language, and especially given the nature of this particular book. Maybe it was done purposefully for effect, but that's still jarring.
No. In the real would "anything" is not possible, and that it is an odd statement to make. It's not at all uncommon for me to see or be a part of a problem solving process that at some point includes a statement like "given the constraints we're under, there is no current solution." Now the next stage might be something like "We can eliminate one constraint by doing X, which will cost Y dollars" etc. So in the MU problem one might say "Given the string transformation rules, MI cannot become MU. However, if we added rule X, then such a transformation would become possible."
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.