Randall Munroe Q&A
You have a ball pit (and we are all jealous). These colorful spheres are made of plastic, which - while fantastic throw people into - seems to be pretty good at collecting all sorts of dirt and such by way of static electricity.
How do you keep your balls clean?
Also, several people have told both of you that you're crazy because you're only doing this for a day and that really, money's not that big of an issue if you go for two or three days. You're kind of stubborn. There's an air of spontaneity about the whole one day thing. Compactness, tightness. But you want to do it properly. Your 35 lei route only gives you about 4 hours of walking on the beach before you hop on back on the train. You could go via Constanța and take a minibus from there. But then you hit the money issue.
You seriously start reconsidering the whole thing. You're going to leave a few more weeks to pass so you 2 can talk it out, find alternative destinations etc. etc. You start looking at potential other places. Piatra Neamț. Timișoara. Arad. A bit far. Târgu Jiu. Târgoviște. Brașov. Been there. Done that. Cluj is especially nice, as it's somewhere none of you has been to and the train ride's cheaper than the Neptun-via-Constanța thing. But you'd maybe want to make it two days anyways. And that's another small logistics nightmare, because you don't really now how cheap the accomodation can get or how many options you have (it's a bit of a tourist city, but also a bit of an industrial one and a city with a big University). Plus the sea is what she wanted and you'd feel a bit awkward about changing the destination, although she doesn't appear very bothered. And you're not sure how many days your parents are comfortable with, financially.
What do you do?
You are allowed use this site for information on trains and you're allowed to learn Romanian. To learn more about Romanian tourism, you can start on Wikipedia and there's plenty of info about the country on the net.
For bonus points: generalize the problem (n people, a list of destinations, you get a function that describes each person's preference towards a certain city and a graph or road information). What is the problem's complexity class? Propose an algorithm. Compare the problem to traveling salesman.
Good luck, Mr. Munroe. Good luck.