Does forbiddance have a distance limitation?

I’m a smuggler, and have just completed digging a mile and a half long tunnel from the shore to the city. I don’t know much about magic, but I do know that I don’t want the recent zombie problem to be able to gain access to my tunnel. I hire a Cleric to keep them out permanently, and they choose to cast forbiddance on the tunnel.

Forbiddance states (PHB p.243):

You create a ward against magical travel that protects up to 40,000 square feet of floor space to a height of 30 feet above the floor.

The tunnel is 10 feet high, 5 feet wide, and 1.5 miles long, or 7920 feet. This makes its total area 39600 feet, so it would be within the size limitations. Is there any restrictions on how far Forbiddance can affect? Assuming the tunnel is completely unlit, the cleric could only see as far as there darkvision; would the lack of vision have any effect?

Does the Telekinetic feat also increase the distance you can move the mage hand?

The Telekinetic feat from Tasha’s Cauldron of Everything says the following:

You learn the mage hand cantrip…. if you already know this spell, it’s range increase by 30 feet when you cast it.

Mage Hand has a range of 30 feet, and says the following:

The hand vanishes if it is ever more than 30 feet away from you or if you cast this spell again.

Does this mean that even though the range for Mage Hand is now 60 feet, if you cast it beyond 30 feet, it still disappears?
Also, Mage Hand says the following:

You can move the hand up to 30 feet each time you use it.

Can you still only move it 30 feet? Or can you move it 60?

At what distance can an Artificer Battle Smith command his Steel Defender?

The Tasha’s Cauldron of Everything brings the most recent version of the Artificer and the Battle Smith subclass, who gains a companion called Steel Defender at level 3. In the description of the Steel Defender ability, there is a part of the text that states:

[…] In combat, the defender shares your initiative coutn, but it takes its turn immediately after yours. It can move and use its reaction on its own, but the only action it takes on its turn is the Dodge action, unless you take a bonus action on your turn to command it to take an action. […]

Altought it states that you have to take an bonus action on your turn to command it to take an action, there is no limitation regarding the distance between the two. Since nothing restricts regarding this condition, by RAW you could command it whenever you are by taking a bonus action. But this sounds off in some cases, like when they are really far apart from each other (miles away for example).

Is there any other official rules that could be used to support a maximum distance between then for the artificer be able to command it?

cumulatively calculate the distance along a line

I am using Postgis to:

  • calculate the cumulative distance in metres along the line
  • store the cumulative distance in "m"

I have a table with points on this line and each row holds lat and lon coordinates. The "m" value is 0 for all rows.

The following code nicely gets me the distance between the first point and the next.

SELECT a.geom FLOOR( ST_Distance(ST_Transform(a.geom, 3857), ST_Transform(b.geom, 3857)) * cosd(42.3521)) AS dist FROM line a LEFT JOIN line b ON a.id = b.id + 1 

however, it does not add up to a total nor does it update the "m" value yet.

I tried a set of permutations of the following, but none of them store a cumulative sum of the previous row’s value for "m" plus the calculation of the distance between this point and the previous.

WITH next AS (     SELECT     ST_Distance(ST_Transform(a.geom, 3857), ST_Transform(b.geom, 3857)) * cosd(42.3521)     AS dist,     a.id AS rowid,     FROM line a     JOIN line b     ON a.id = b.id + 1 ) UPDATE line a SET m = FLOOR(next.m + next.dist) FROM next WHERE a.id = next.rowid RETURNING a.m, next.dist; 

or

update line a     set m = FLOOR(a.m + prev.dist)      from (select             l.*,             ST_Distance(ST_Transform(                 lag(geom) over (order by l.id asc)             , 3857), ST_Transform(geom, 3857)) * cosd(42.3521) as dist             from line l           ) AS prev     where prev.id = a.id - 1     returning prev.m, prev.dist, a.m 

Any ideas?

Total distance per day for different travel paces?

The travel pace description and table on page 181-182 of the Player’s Handbook states that a normal travel day may contain 8 hours, and gives the following table:

 Pace:   /Hour    /Day         Miles in an 8-hour walking day:   Fast   4 miles  30 miles --> 4x8 = 32 miles (-2 miles a day) Normal   3 miles  24 miles --> 3x8 = 24 miles (OK)   Slow   2 miles  18 miles --> 2x8 = 16 miles (+2 miles a day) 

Why is there an difference of 2 miles for fast and slow pace?

Calculating distance on a map

I’m running a campaign in the Sword Coast, and like to provide consistent travel distance and time to my players. As far as I could find, there are no distance charts. And even if there were, they are unlikely to provide all locations (but I might stand corrected!).

A solution could be a piece of software which can open the high resolution Sword Coast map, in which I can draw lines, and which then tells me the length in pixels of the lines, so I could covert that back into miles, and ultimately derive a travel time.

Does anyone know of something to do this in?

Related:

  • Travel Chart for the Forgotten Realms

Largest set of 10-digit numbers where none have Hamming Distance = 1 with any other

I’m working on a system that will require manual data entry of 10-digit numbers (Σ = 0123456789). To help prevent data errors, I want to avoid generating any two strings that have a hamming distance of 1.

For example, if I generate the string 0123456789 then I never want to generate any of these strings: {1123456789, 2123456789, 3123456789, …}

What is the largest set of unique strings in the universe of possible strings that satisfy the constraint where no two strings have a hamming distance of 1? If this set can be identified, is there any reasonable way to enumerate it?

RC-Code if I have a generator matrix for a specific code how do I get the distance to the dual code?

$ \mathcal{R} \mathcal{S}_{6, 3}$ and $ a_{i} \in \mathbb{F}_{11}$

G=\begin{pmatrix}1&1&1 &1&1&1\ 0&1&2 &3&4&5\ 0&1^2&2^2 &3^2&4^2&5^2 \end{pmatrix}

G=\begin{pmatrix} 1&1&1 &1&1&1\0&1&2 &3&4&5\ 0&1&4 &9&5&3 \end{pmatrix}

I now have to determine the distance to the dual code.

Any clue how to accomplish this?

Thanks for any help.