What country is Durmstrang in? There are certainly a lot of mentions of aspects of the school (especially how cold it is) but the books and movies never actually say what country it is in. For example:
Krum is from Bulgaria and plays for the Bulgarian national Quidditch team but that doesn't necessarily mean that the school is in Bulgaria.
Krum mentions to Hermione that it is "over the mountains" but doesn't specify which mountains.
In the movie, Dumbledore introduces Karkaroff and the Durmstrang students as his "friends from the North" (Bulgaria is far to the South of Scotland).
Ron says in the book that he wished Malfoy went to Durmstrang because it would be easy to push him off of a glacier.
Fur coats are a standard dress item of the Durmstrang students.
So where is Durmstrang? It's said to be "unplottable", like Hogwarts, but at least we know that Hogwarts is in Scotland.