Couldn't the book cost 7.5k and one has 6.5 and the other has 0.5? Along those lines, isn't anything in the range of costing 7->8 (non-inclusive) acceptable (e.g. 0.9k and 6.9k)?

I was wondering the same thing but Kopecks are not currently subdivided.

https://en.wikipedia.org/wiki/Kopek

The second question's solution requires half-kopeks.

These problems aren't current or modernized. There's no way a bottle with a cork in problem #2 costs 10 kopek.

current 10 kopek is worth 0.0013$

They probably come from time when 0.5 kopek was the smallest coin.

#1 problem doesn't have single non-zero solution if the smallest coin has larger or smaller.

That’s a nice approach. (It’s the same one given by bencollier earlier: https://news.ycombinator.com/item?id=27885681). I regard it as requiring a bit of insight, as opposed to my approach, which is more like grinding gears to reach a conclusion.

This is one of my main observations growing up with math: it's the moments of beauty and elegance that are the most exciting, but the grinding gears thing is also a necessity. They complement each other. For instance when you're just learning the basics there's a lot of these "wow what an insight" but over time you figure out that people have distilled it into a mechanical procedure, which also has some attraction to it. Something like quadratic equation turns the search for a pair of numbers that add up some one thing and multiply to another into a simple formula. You then use that mechanism to build ever more elaborate ones.

I came to the same conclusion the same way but it felt wrong due to the phrase "They combined their money to buy one book to share". Perhaps the phrase lost something in translation.