Limit amount of posts made within a custom taxonomy

Is there a way to limit the number of posts that can be created within a custom taxonomy?

I have a custom post type called Preferred Agents and a custom taxonomy called Agent Location. I want to be able to limit the amount of Preferred Agents in an Agent Location to only 3. Is this possible?

Any help is appreciated! Thanks.

How many blood points can a ghoul use within a turn?

I have recently started running a ghoul campaign however no matter how hard I look I can’t find how many blood points a ghoul can use a turn. I know that vampires are limited by their generation with lower generation vampires being able to use more blood points in a turn.

As such my question is how many vitae points can a ghoul use within a round?

Note: I am using the anniversary edition core book and fatal addiction addition book.

Is there any lore within the Forgotten Realms about the history of metal-working?

On Earth, (very abbreviated) tools began as stone, wood, and bone until eventually bronze could be cast using stone molds. From there people learned to work with iron and then much later, steel.

Is there any lore within the Forgotten Realms about this sort of technological advancement, (or lack of?)

For the Charger feat, is it possible to move at least 10 feet in a straight line while staying within an enemy’s reach?

The Charger feat lets you make a bonus-action attack with +5 to the damage roll if you take the Dash action and “If you move at least 10 feet in a straight line immediately before taking this bonus action”.

When playing on a grid, am I correct that you would very often be able to move around the enemy to get this benefit, often without provoking an opportunity attack?
(On a 5-foot grid, excluding obstacles, there are a minimum of 8 squares within an enemy’s reach; from one diagonally adjacent square to the next are 3 squares.)

What’s the maximum amount of lines from Sunbeam possible within a single round?

I noticed that sunbeam allows you to to create multiple lines within a single turn. What’s the maximum possible amount of sunbeam lines able to be created by a single caster within one turn?

For reference, the spell has a casting time of 1 action and states:

A beam of brilliant light flashes out from your hand in a 5-foot-wide, 60-foot-long line. Each creature in the line must make a Constitution saving throw. On a failed save, a creature takes 6d8 radiant damage and is blinded until your next turn. On a successful save, it takes half as much damage and isn’t blinded by this spell. Undead and oozes have disadvantage on this saving throw.

You can create a new line of radiance as your action on any turn until the spell ends.

Rules

  • Level 20 Character, any combination of multi-classing allowed
  • Only official material published by WOTC in book form is allowed. No Unearthed Arcana
  • Setup is allowed, including any magical items present in the Dungeon Master’s Guide or any other source-book. Items only present in campaign books are not allowed.
  • You may have 4 allies at level 20
  • Simulacrum is allowed

Is there a way within the rules and options to selectively remove or lose a specific class feature?

A player selects a class or prestige class.

Then they realize that a specific class feature (Ex) doesn’t fit the character concept.

Ignoring it is insufficient, the player wishes to eliminate it.

Are there any existing rules, powers, spells, items, or other options in 3.x that would accomplish this? The retraining rules and rebuilding rules in PHB II don’t have an option for this.

disable (read only) a field if within a custom post type name

I have two bidirectional fields ‘album_band’ in two different custom post types ‘album’ and ‘band’.

this field allow multiple selection and is mandatory in ‘album’

I’ve been trying to disable or set it as ‘read only’ this field in one custom type ‘band’ (backend side) to avoid empty value in ‘album’ but without success

many thanks for your help

Upper bound on the average number of overlaps for an interval within a set of intervals

Let $ \mathcal{I}$ be a set of intervals with cardinality $ L$ , where each interval $ I_i \in \mathcal{I}$ is of the form $ [a_i, b_i]$ and $ a_i, b_i$ are pairwise distinct non-negative integers bounded by a constant $ C$ i.e. $ 0 \leq a_i < b_i \leq C$ . We say a pair of intervals $ I_i, I_j \in \mathcal{I}$ overlap if the length of overlap is $ > 0$ .

Define a function $ F(i)$ which computes the number of intervals in $ \mathcal{I} \backslash I_i$ that interval $ I_i$ overlaps with. \begin{equation} F(i) = \sum_{j=1, j \neq i}^{L} Overlap(I_i, I_j) \end{equation} where the function $ Overlap(I_i, I_j)$ is an indicator function which returns 1 if $ I_i, I_j$ overlap, else it returns 0.

The average number of overlaps for the intervals in $ \mathcal{I}$ , denoted by $ Avg(\mathcal{I})$ is given by $ Avg(\mathcal{I}) = \dfrac{\sum_{i=1}^{L}F(i)}{L}$ .

The question is, suppose we are allowed to choose the intervals in the set $ \mathcal{I}$ with the following additional conditions:

  1. For any $ t \in [0, C]$ , we have at most $ M$ (and $ M < L$ ) intervals in $ \mathcal{I}$ such that $ t$ is contained within those $ M$ intervals. Stated differently, at most $ M$ intervals overlap at any point in time.
  2. Any interval in $ \mathcal{I}$ overlaps with at most $ K$ other intervals, and $ M < K < L$ .

then, what is an upper bound on $ Avg(\mathcal{I})$ for any choice of the intervals in $ \mathcal{I}$ satisfying 1, 2?

In case you are wondering, this problem is of interest to me in order to be able to study the run-time of a scheduling algorithm.

I am unable to come up with a non-trivial upper bound for $ Avg(\mathcal{I})$ and would be interested to know if the problem I stated has been studied. I am also open to ideas on how one may be able to obtain a tight upper bound for $ Avg(\mathcal{I})$ .