At Travel.SE it was pointed out that in Georgia (the country), a visitor would have use of learning Georgian, Russian, and Armenian. That's three very different languages, with three quite different scripts, for such a small country! That prompts me the question:
In what country do we find the highest linguistic density? I don't know if this concept exists, but I mean the geographic derivative of the linguistic distance: e.g. a country where very different languages are natively spoken in a small area. Of course, this tends to infinity close to the language border, so let's stick to countries for now.