Are all units of measurement the same in all nations?
Did Athens or any other Nations have miles?
Did Athens or anyone else have miles back then?
stoopid double post…reported
Incidentally, the original problem in the PDF states these are cities in “Mensaland”. I think people are overthinking the problem.
Think of it like Paris, Texas. These aren’t world capitals but cities which happen to share names with world capitals.
The fact the city names are all in caps is also suggestive. Each letter represents a number, and there’s some algorithm to combine the values to get the desired result.
I have just noticed a very leading property:
If we add the number of letters of each country to the mileage we get
219 + 6 = 225 = 15²
136 + 8 = 144 = 12²
43 + 6 = 49 = 7²
74 + 7 = 81=9²
Coincidence? I think not!
Thinking on I notice that :
15 is the number of straight line segments in ATHENS
12 in BUDAPEST
7 in LISBON
9 in VILNIUS
Which of course makes HELSINKI
17² - 8 = 281
What do I win?
I’m so pleased with myself, I haven’t won a thread in AGES!
Just noticed the time for submission on the original quiz, which I have to assume is the source for the question that I was asked. There is a deadline for answers to be submitted tomorrow, so in the interest of fairness to all competitors (especially as this thread will no doubt be showing on Google now) if you do find a satisfactory answer to the puzzle, perhaps waiting until tomorrow to post it would be sensible. Thanks. (I’m not entering the quiz, but don’t want to ruin the competition for others should an answer be found).
Ah - never mind them. Only moments too late!
Good work though. 
I think we have a winner.
If you’re right, you should be pleased. That was amazing.
I’ll be more pleased if my other “solution” is right!
The author of this puzzle missed a trick: instead of “How far logically is it to HELSINKI?” they could have asked “Logically, where are you?”
OSLO
(because 2² - 4 = 0)
I was thinking a possible solution might be that you’re not in Europe at all. A lot of small towns in the United States are named after European cities. There are, for example, towns named Athens, Budapest, and Lisbon in Ohio - but apparently no Vilnius or Helsinki.
And besides The Great Unwashed’s answer is a lot better.
You could tautologically reply “Standing in front of a signpost.”
How many cities did you try before you got Oslo?
Honestly none.
I was getting on with my life when the question struck me “Are there any capitals ‘0 miles’ away?”
Two things were apparent: capitals with a square number of letters are the only possible candidates (making 4 or 9 letters the most likely possiblilities) and candidates should contain relatively many curvy letters.
And then I thought “Oslo”, did the short calculation to check, and YAY! it worked.
But if you want proof of my fallability, I did have to check on Wikipédia that Oslo was in fact a capital.
Then I Googled for 4- and 9-letter capitals to see if there were other candidates and quickly satisfied myself that Oslo is the only contender.
And then I thought “Sweet!”
No, the solution may have been distances on a spiral or a square in a square shape, but yes well if you translate Mensaland as Rainmanland…??
Trouble is, “Norway” has 6 letters.
And I now see it’s done on the city lenth, not the country. I got confuses as The Great Unwashed said “country” and I never went back to check the maths.