Learn English – Should “other than” be followed by the infinitive or the -ing form

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."

I believe #3 will sound best and most natural to a native speaker. I would use two articles if I wanted to draw attention to some distinction between the chapters. For example:

The first chapter is difficult and the second chapter is difficult and long. In this sentence it would sound awkward to leave out the second "the".

It is not incorrect to use just one "the" as in your version #3, nor is it incorrect to use two. You may use the article twice, but to a native speaker it will sound stilted.

On the other hand, sometimes that is the effect you want. For example, if your neighbor is angry because you are playing loud music late at night, he might want to emphasize the distinct number of times he has asked you to turn down your music:

"I asked you politely the first time and the second time to turn down your music. The third time will not be polite."

But in normal everyday conversation you would just say,

"I asked him politely the first and second time, but the third time I punched him in the jaw."