What benefit (if any) do horses or carriages offer when travelling long distances?

The rules for Travel Pace in the PHB and Basic Rules are good and straightforward, with players able to travel on foot for 8 hours per day without over-exerting themselves, choosing a pace of Slow (2 miles/hour, 18 miles/day; can move stealthily), Normal (3 m/h, 24 m/d) or Fast (4 m/h, 30 m/d, take a penalty to pass Perception).

In this same section, there are two paragraphs about mounts and vehicles; they specify that mounts can gallop at twice the normal fast pace for an hour, and with frequently freshened mounts – typically only available in highly populated areas – a rider can travel fast over long distances. However when it comes to vehicles, only water going vessels or flying mounts get you travelling faster; for commonly available forms of transport:

Characters in wagons, carriages, or other land vehicles choose a pace as normal.

Is this right? Rules as written it seems there is no benefit to travelling by wagon or carriage, and certainly it takes the same amount of time as walking. In my current game of Dragon of Icespire Peak, the players have spent quite a bit of time demanding horses or a carriage in order to travel the 65 miles from Phandalin to Butterskull Ranch, believing it would get them there faster (as the quest there seems urgent). But looking up the travelling rules it really seems there’s no speed benefit to them paying for a ride or hiring horses, except that they might shave an hour off their travel time each day in the latter case. That makes sense for a wagon which is designed only for hauling stuff, not speed, but what about a carriage or a riding horses?

I’d like to know if there are any additional benefits (beyond the purely narrative) that I am missing for travel by carriage, or any ways that mounts or vehicles can decrease their travelling time (beyond the double fast pace for one hour).

I’m also interested in any house rules you may have used to give players a speed boost through riding over walking.

Need help with an interesting variant of the travelling salesman problem

I’m working on an assignment in my CS class and the gist of the problem is as follows.

A salesman has a map of some apartments (over 300 blocks). I am given the (x,y) coordinates of each block as well as the “money” he will earn by visiting each block. I need to find the shortest route for the salesman to take such that he will earn x amount of money. He does not have to visit all the blocks. At the end of the day he will have to return to the origin (0,0).

I used a greedy algorithm by finding the shortest possible path he can take at each step. E.g from the origin I find the block with the lowest euclidean distance from the origin. Lets say this block is (2,2). I then find the block with the lowest euclidean distance from (2,2) until I have x amount of money. Using this greedy algorithm I then performed a 2-opt local search to improve my solution further.

The problem lies here though: when I perform a 3-opt local search using the implementation from wikipedia (https://en.wikipedia.org/wiki/3-opt), I get a much worse result than either the greedy or the 2-opt. Is there something wrong with the wiki code and if not, what did I do wrong? Thanks.

Solving a modified Travelling Salesman Problem(TSP)

I am trying to solve a modified version of the TSP. In my version, multiple visits to a city are allowed, as long as the path is the shortest, and also, only subset of the cities are compulsory to visit, as in, you can go through other cities to visit all the subset cities if path is shorter, but if not, the other cities can be ignored. For simplicity, starting city is fixed. I know approx. solutions for the traditional TSP, but, I have trouble solving this one. A naive approach can be to find all possible combinations of the subset cities and check which has the shortest total path length, but that solution will have a n^2 complexity for trying each combination, plus the complexity for finding shortest path for each two cities. So, what should I use to solve this problem?

How can I avoid getting exposed while travelling to Russia?

I am a Japanese student learning the Russian language and will soon travel to Russia to have a kind of internship or training.

I have a security concern and a background to it. The background is that I actively participated in Internet discussions on the Russian social network vk.com under a fake name and made many provocative posts there, so a number of people explicitly wrote there that they would do their best and utmost to find my real identity and make it public. My posts are definitely of no concern to police and were not even deleted by the admins, but quite a large number of people got really agitated as my posts were about politics, religions, cultures, and similar sensitive stuff and written in a provocative manner. I cannot afford getting my real name publicly associated with those posts, but I did not see how people could find my real name, so I even made some posts saying they would not be able to find my name.

Some time ago one Russian sent me a message telling me he had discovered my real Japanese IP addresses, and he told me some of them. Although I had not used any proxy servers to make my posts, I got shocked, because vk.com is not supposed to share my IP addresses with anyone. The guy then wrote he had been able to find my IP addresses because he works in a Russian company that has access to a lot of data related to the use of the Internet in Russia. He added that he had somehow tried to find my real name based on my Japanese IP addresses, but had not succeeded. Indeed, my Japanese IP addresses do not give any leads, and no Japanese provider will tell my name to Russians.

Now I am travelling to Russia and intend to use there the same laptop I used to make my posts; I will be given an Internet connection in Russia and, in view of what the guy told me, will obviously need to avoid any possibility of leaving any traces in Russia that could link my Russian IP address with my past posts. The reason is that knowing my Russian IP, people might find my real name by contacting my Russian hosts. Ideally, I would like to continue using the same account in the social network to make posts while staying in Russia.

My question is this: What should I do to meet these needs?

I am asking because I know little about such security matters and, in particular, what kind of information is collected from my laptop by Internet providers and servers such as vk.com, so I am afraid to even connect my laptop to the Internet in Russia. I humbly hope that security experts of this SE could kindly instruct me how I can safely use my laptop in Russia without any risk of getting exposed in relation to my past posts made from Japan from the same laptop, given that at least one Russian who wants to find my real identity may have access to any data related to the use of the Internet in Russia.

Are there any lower-level means of travelling between planes of existence?

In Dungeons & Dragons 5th Edition, plane shift is a high-level spell that allows a party to journey between planes of existence. Are there any means available for lower level characters to journey between planes?

Plane shift is really convenient, with a casting time of 1 action and no expended material components – but as a 7th level spell, it is available only at 13th level, minimum. This means that only high-level parties can travel to the Feywild or the Elemental Planes.

Are there any spells (or similar abilities), that would allow lower-level parties to travel to other planes? Official material or third-party material is fine, as are setting-specific conceits/items.

Number of Solutions for Brute Force Algorithm of Travelling Salesperson Problem

We are learning about the travelling salesperson problem in my high school class and we are discussing how computers could solve for the problem, even though the problem is intractable, using a brute force algorithm.
I was wondering if the brute force algorithm calculates ALL possibilities for a number, n, or only UNIQUE possibilities.

For example:
If there were 4 locations, labelled A, B, C & D. Starting from A, would you include both A,B,C,D and A,D,C,B even though they are essentially the same?

Thank you for the help 🙂

Dual USA and UK travelling to USA for funeral – expired USA passport

I’m travelling to the USA on Monday for a sudden and unplanned funeral. I have just realised that my USA Passport is expired- only just (June 15 2019). I do have my UK Passport which is in date and valid but I am unsure of what might happen if I travel into USA on UK. I ca obviously arrange to fill an ESTA and I also have a valid USA Driving license. What do you recommend? Should I just chance it and travel in as a UK citizen?