Julio - I meant for \\(X\\) and \\(Y\\) to be countries, \\(x \in X\\) to be a city in the country \\(X\\), and \\(y \in Y\\) to be a city in the country \\(Y\\).

So, just one word in my description was wrong, and I'll fix it now. Thanks for catching it!

And yes, you're right about Puzzle 174, too.