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.