Which one of the following two sentences is more correct/appropriate than the other? Why?
- That's a both interesting and challenging problem.
- That's both an interesting and challenging problem.
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Of your original two sentences, neither is very smooth-sounding, but only the second one is grammatical; you can't really use "both" and a pair of adjectives to make a countable noun phrase like that.
The cleanest way to rephrase this using the rhetorical effect of "both" is to put the adjectives at the end, in a restrictive clause, and link them with "that is":
That's a problem that is both interesting and challenging.
This simplifies the structure so that the reader or hearer does not have to keep track of so many things at once, and subtly builds up emphasis as it goes so the rhetorical impact of the adjectives is increased.
If you don't really need the emphasis, you can simplify this further:
That's an interesting and challenging problem.
The best way to write this sentence is to make it simple and direct by eliminating the somewhat awkward-sounding phrase using "both" (in any version): "That's an interesting and challenging problem."
This says the exact same thing and is much more to the point. I spent many years on a newspaper copy desk and would strongly recommend grammar and composition guidelines found in Strunk & White's "The Elements of Style." One of their Elementary Principles of Composition is "Omit needless words."
1.That's a both interesting and challenging problem. 2. That's both an interesting and challenging problem. Here, both is used as a correlative conjunction , so no determinant should precede it. The first sentence is ungrammatical. The second one is ok. It is used for clarification. There are other correlative conjunctions that shouldn't be preceded by a determinant. Eg: either... or
Still doesn't sound quite right though.
I would recommend putting an indefinite article before both noun phrases:
The role of both...and in NP (Noun Phrase) structure is of a Correlative coordinator.
... both interesting and challenging problem.
Generally it's ungrammatical to place a pre-head dependent like the, a or other determiner, adjectives etc before both when it's used as a correlative coordinator.
That's why the followings are ungrammatical -
a both interesting and challenging problem. [drop a and it would be fine]
beautiful both Kim and Mery [UNGRAMMATICAL] => both beautiful Kim and Mery [CORRECT]