Determining “level” of an NPC ally for purpose of budgeting encounter XP

Hypothetical party:

1st level human wizard (PC)
3x guard NPC
1x acolyte NPC

This is the player’s first time, and it’s a solo campaign. The first mini-adventure involves recovering the cargo of a supply caravan that didn’t make it to her magic academy due to bandit hijacking (as a sort of graduate-test). The guards and healer are on contract from the school to assist her. The acolyte is essentially just to hang back and tend to wounds and probably won’t engage in combat unless someone goes down or the PC is seriously wounded.

So, with that “party” makeup, how do I determine the XP budget for a “medium” or “hard” encounter since there’s no clear CR->level mapping in 5e for those NPCs (who will certainly factor into any combat as meatshields and melee damage)? I was thinking about reverse-engineering them as crumby lvl2 fighters (given the 2 HD worth of HP they have), but they certainly aren’t on par with a lvl2 fighter, given the lack of action surge, second wind, etc., so the encounters would end up being too hard compared to PCs or DMPCs.

Could they be lvl1-equivalents, essentially trading any abilities a PC would have for extra HP? How would this work at later levels with higher CR NPCs (veteran, priest, mage, etc.)? I’d rather not have to build a bunch of DMPCs as hirelings, because I want the NPCs to be a bit vanilla compared to the versatility of my player. I’m already introducing 1-2 DMPCs to the game for her to take control over as she gets a feel for the flow of the game (for now, she’ll handle them out of combat, and I’ll effectively show her how to utilize them until she’s ready).

Just to be clear, I’m comfortable with the monster-generation rules for crafting NPCs as enemies to determine their CR, but I’m confused on how to use them in the adventuring party when budgeting encounter difficulty XP.

Does hurling a thrown weapon change the weapon’s category for determining proficiency?

On Weapon Categories says, “A melee weapon with the heavy thrown or the light thrown property counts as a ranged weapon when thrown” (Player’s Handbook 215). (Similar text is absent from the Rules Compendium, but I’m not familiar enough with 4e to know if this absence is an issue.)

With this in mind, if a character who has proficiency with military melee weapons but lacks proficiency with military ranged weapons throws a handaxe—a military weapon—, does the character still receive his proficiency bonus on the attack roll?

That is, when a military melee weapon is thrown does the military melee weapon remain a melee military weapon therefore the character above gains his proficiency bonus with it? Or does the thrown military melee weapon now count as a military ranged weapon therefore the character above does not gain his proficiency bonus with it? Or is this even more—or less!—complex than I’m imagining?

Note: My level 3 battlemind who has Strength 10, Dexterity 12, proficiency with simple and military ranged weapons, and proficiency only with simple ranged weapons will still normally make his ranged basic attacks with daggers—preferring accuracy to damage—, but I want to assess my future options just in case. Also, I know I’m late to the party, and I apologize if this is a topic that’s already been discussed to death elsewhere.

What determining the DC to notice an invisible enemy during combat, what counts as “in combat” or “not moving”?

What modifiers should be applied when when determining the Perception DC to locate an invisible creature during common combat situation?

As per the Core Rulebook, the base DC is 20, and to pinpoint the exact square is another +20. There are various additional modifiers on this DC, but three that are of particular relevance to me are:

  • -20 if the creature is in combat or speaking
  • +20 if the creature is not moving
  • -10 if the creature is moving at full speed

I’m curious exactly what constitutes as “in combat” or “not moving”, as I can’t seem to get a consistent answer from the rules or various discussion threads on invisibility.

Let me illustrate with a few scenarios, where we assume that a PC has cast Greater Invisibility on themselves, and a few rounds later, has attacked NPC 1. Later that round, NPC 2 (who was not attacked by the PC), wants to locate the invisible PC.

  • Scenario 1: The PC begins their turn adjacent to NPC 1 and spends a full round action to attack NPC 1 before ending their turn with no other actions performed (thus did not take a move action and remained in their square). NPC 2 now tries to locate the PC.

  • Scenario 2: As above, but this time the PC takes a 5-foot-step away from NPC 1 in an unknown direction after attacking. NPC 2 now tries to locate the PC.

  • Scenario 3: As above, but this time the PC only uses a standard action to attack NPC 1, before taking a move action to move at their full speed away from NPC 1 in an unknown direction. NPC 2 now tries to locate the PC.

And finally, for a slightly different scenario from above

  • Scenario 4: The PC is no longer performing melee attacks, and is not standing adjacent to any enemies. Instead, they begin their turn by taking a potion and drinking it. NPC 2 now tries to locate the PC.

Which modifies would you apply in each scenario? My interpretation of the DC to pinpoint the exact square would be

  • Scenario 1: In Combat, Not Moving => DC = 40 – 20 + 20 = 40
  • Scenario 2: In Combat => DC = 40 – 20 = 20
  • Scenario 3: In Combat, Moving at full speed => DC = 40 – 20 – 10 = 10
  • Scenario 4: In Combat, Not Moving => DC = 40 – 20 + 20 = 40

However I’m unsure of the modifiers in italics are applied correctly.

Does Not Moving here specifically refer to taking a move action, or is it anything other than standing completely still? Is swinging a weapon equivalent to drinking a potion when it comes to this?

Does In Combat specifically refer to having rolled initiative as part of an encounter? Or does it mean actively participating with aggressive actions?

Any help clarifying RAW or RAI would be appreciated!

(Note: I’m aware that in these combat situations, NPC 1 can easily locate the PC as they were the target of an attack. I’m also aware that invisibility only removes vision of the invisible creature, and that the PC could be located by other means – including environmental factors or being told by an ally to target a particular square. I’m specifically interested in the scenario where there’s no additional stimulus, and another NPC is rolling perception to pinpoint the PC’s location)

Determining Volume of an Irregularly Shaped Triangular Prism

I need help using Mathematica to determine the volume of an irregularly shaped triangular prism. I have very little experience with Mathematica but thought this task could easily be performed using the program.

The shape generated should look like:


Prism[{{3.767, 4.523, 1}, {0, 0, 0}, {7.948, -2.451, 0}, {3.699,

8.156, 1}, {1.146, 10.24, 0}, {4.837, 10.24, 0}}]]

I’ve tried using the Volume[] function but with no luck. Any help would be greatly appreciated!

Determining which block a word will be mapped to

Is it possible to know which block in a cache a word will be mapped to if you do not know how many bits each word has? I have this problem that seems incomplete to me.

The question asks something similar to this:

A cache has 1024 blocks, and each block has 64 words. If a word address is 6400, to which block will it be mapped?

My thinking is: if there are 32-bits per word, then the word will be mapped to the 4th block because the 4th block contains the addresses 6144-8192. However, if there are 64-bits per word, then it would be mapped to the 2nd block because the 2nd block contains the addresses 4096-8192.

Is there a way to answer this question with a specific answer without knowing how many bits each word holds?

In determining whether any segments intersect, why there must be some sweep where segments $a$ and $b$ are consecutive?

In CLRS, Section 33.1, we are given the any-segment-intersect algorithm. It’s a cool algorithm for sure but going through the correctness proof, I don’t know how to prove the following:

“Given that we have two segments (call them $ a$ and $ b$ ) that intersect at some point $ p$ , then there must be some sweep line $ x$ for which intersecting segments $ a$ and $ b$ are consecutive in the total preorder.” why they must consecutive at some sweep line?

I do see why visually using the figure on page 33.4 (page 1023) but I don’t know a proof for this statement. How can I prove this?

If anyone had read that section, please enlighten me. Thank you

Determining recursive enumerability of given languages

I came across following problem:

  1. $ L=\{M$ is a turing machine $ M$ accepts two strings of different length $ \}$
  2. $ L=\{M$ is a turing machine $ M$ accepts atleast two strings of different length $ \}$

Which one Recursively Enumerable (RecEn)? Which one Recursive (Rec)?

I feel both are not recursively enumerable and hence not recursive. We may list strings in some order and run Turing machine on them. But we may never come across two strings of same length accepted by same TM. So we cannot answer both questions “accepts two strings of different length” and “acceptes at least two strings of different length”. Am I correct? Also is my approach correct?

Is this a valid equation for determining certificate lifetimes in a PKI infrastructure?

I have an intuitive sense of how certificate lifetimes should work in a PKI infrastructure, but I don’t consider myself an expert in this field so I would like someone to validate or critique my assumptions:

The “leaves” on a PKI hierarchy are the certificates issued by a CA. The maximum lifetime of one such certificate is equivalent to:

renewal interval          + renewal period           = certificate lifetime (renew yearly, i.e. 1 yr) + (1-month renewal period) = 13 month lifetime 

An intermediate/issuing CA’s cert’s lifetime follows the same pattern, plus the maximum lifetime of a cert it can issue:

renewal interval + renewal period + child lifetime = certificate lifetime 2 years          + 1 month        + 13 months      = 3 year, 2 month lifetime 

The last step “recurses” up the PKI hierarchy through any more intermediate CA tiers until you get to the root cert.

This means, necessarily, a CA’s cert must always have a lifetime longer than the certs it issues.

Context: Apple’s Announcement about 13-month maximum cert lifetimes starting September 1st 2020 must therefore only apply to leaf certs, and not to certs issued to intermediate or root CAs.