Have you learned a new language? It's basically an exercise in memorizing vocabulary and phrases and pattern recognition. Linguistics is the study of those patterns across different languages. Therefore, I don't think there is anything wrong with problems focused on pattern recognition. I also think you are overstating the amount languages break their own rules. The only reason that your list makes sense is because there is such a clear pattern for the vast majority of plural nouns.
> Linguistics is the study of those patterns across different languages.
Linguistics is the study of languages in a scientific manner. Pattern recognition can be one approach, and it's great when it works to provide insight but it is (or should be) a means to an end and one must also be aware of its limitations.
> The only reason that your list makes sense is because there is such a clear pattern for the vast majority of plural nouns.
This perhaps could be a somewhat valid point if we were only talking about English. However, examples from languages with more complicated conjugation or declension could readily provide much better illustration why any naively-reconstructed rules reproduced from just a couple of hand-picked examples should not be assumed to hold.
So, as I said, while I find those puzzles interesting, I just don't think there's much linguistic insight to it. It's just an exercise in deductive logic. Nothing wrong with it of course, and I concede that might have been the point all along, just call me surprised.
Similarly: "Bob is twice as old as Alice and was 4 when the first man landed on the moon. How old is Alice?" is not a problem in astronomy. It's just a fancy way of stating: "b == 2a && b - ($CURRENT_YEAR - YEAR_OF_FIRST_MOON_LANDING) == 4, solve for a."
"Linguistics is the study of those patterns across different languages." vs.
"Linguistics is the study of languages in a scientific manner." I take the first answer to be a bit different: I don't think the emphasis is on "patterns", rather it's saying that linguistics is about looking for ways that all languages are similar (like the claim that they can all be described by a context free grammar, or that apart from full word reduplication, the morphology of all languages is finite state). The alternative--your answer--is valid, although linguists of the first sort (I'm thinking of many generative linguists) look down their noses at it.
"examples from languages with more complicated conjugation or declension could readily provide much better illustration why any naively-reconstructed rules reproduced from just a couple of hand-picked examples should not be assumed to hold": Agreed that you'll need at least one example of each conjugation or declension class. But since there aren't usually more than a few such productive classes, that's not too many examples. There are of course those languages that clearly violate this--there's an African language that seems to have bizarrely many pluralization classes, like hundreds IIRC.
FWIW, languages with agglutinating morphology (long sequences of prefixes and/or suffixes) tend to be more regular than fusional languages (languages where each word takes at most one prefix or suffix, at least from what I've seen.
