If someone attacks a swarm with a single-target spell while it’s in a character’s space, is that character also affected by the spell?

My players have walked into a Spider Lair and fought their first group of Spiderlings, or effectively a Swarm of Spiders from the MM. I didn’t realize until after the encounter that they have a reach of 0 for their attack and that they can move through and stay on a space taken up by another creature (which occurred to me is the only way it can actually make its attack.) The party’s going to fight more next session.

What happens when a swarm is in a character’s space attacking them, and someone casts a single-target spell against that swarm such as Hellish Rebuke or Fire Bolt?
Since the swarm is invading that character’s space (we assume because they are swarming around them or over them), is the character also potentially affected by the spell?

In Ghost Ops do NPCs get free attacks only on total Bullet Time failure or also on partial failure?

I have the original version of Ghost Ops (which uses Fudge dice), not the Savage Worlds version or the OSR version. This question is about that original version, but if you think the rules in one of the other versions can throw some light on this, please chip in.

On page 132 of the core rulebook there is an example of a failed Bullet Time action. The PC was attempting to shoot 3 NPCs in the head, and needed an 8 but only got a 6.

The book then has some more rules:

The Handler can decide that the Operator succeeded in some of the attempt. Maybe they barged the door and managed to get 2 of the attempted headshots off but missed the third. Failing a Bullet Time event places the Operator as prone for 1 round, allowing any Tangos free attacks. Deciding to attempt Bullet Time is risky but can be ultimately rewarding.

So, if the GM has said the failed roll can be partial success (hit 2 of the NPCs) and partial failure (miss the 3rd NPC), which of these applies?

  1. It still counts as a normal fail – the PC is prone and subject to a free attack by all three NPCs (assuming the two he shot aren’t dead or disabled).
  2. It still counts as a ‘reduced’ fail – the PC is prone but only the third NPC, who was not hit, gets a free attack.
  3. It counts as a success – the PC is not prone and the NPC/s don’t get free attacks.
  4. The GM decides on a case by case basis.

I’m hoping there is clarification for this question in one of the expansions, or in an updated version of the pdf (I only have a print copy). I’ve failed to find any errata on the internet.

Complexity of finding a Eulerian path such that the image under a bijection is also a Eulerian path

Problem input: undirected graphs $ G$ , $ H$ and a bijection $ f: E(G) \to E(H)$
Question: Is there a Eulerian path $ p: \{1,\dots,|E(G)|\} \to E(G)$ in $ G$ such that $ f \circ p$ is a Eulerian path in $ H$ ?

Is this problem in $ P$ , $ NP$ -complete or maybe equivalent to some other well-known problem that isn’t known to be either yet?

The problem turned up as a special case of a more general problem first in the Bachelors thesis of another student last year and now in mine as well (I was improving some of the results of the other thesis). All other cases of the problem are now known to be either NP-hard or solvable in polynomial time, but neither one of us managed to make any progress on that case. On the other hand it feels like a much more "natural" problem than the other cases, so I think we may have missed a simple proof.

If undirected graphs are replaced by directed graphs in the problem statement there is a simple polynomial time algorithm (find a Eulerian path in the graph with vertex set $ V(G)\times V(H)$ and edge set $ $ \{((v_1, w_1), (v_2, w_2)) | (v_1, v_2)=e \in E(G), f(e) = (w_1, w_2)\}$ $ ignoring isolated vertices). The analogous graph for the undirected case contains 2 edges for each edge in $ G$ , so just finding a Eulerian path is no longer enough.

Does reducing a character’s max HP with a spell also reduce the “negative HP” threshold needed to cause instant death?

Here’s my situation: In a fight with a group of vampire thralls, the party’s wizard got caught in a corner and was being savaged by vampire bites, his max HP dropping from 24 to 11. They fended off the vampires, but the wizard was at 3hp (He refused to be healed by the cleric due to his character’s hatred of religion and gods). He activated a trap collapsing the temple, and ended up getting hit by a falling chunk of stone ceiling, taking 15 damage (the rock rolled better than any of the vampires).

Now, the wizard is reduced to 0 hp, with 12 damage left over. The cleric’s player says that exceeds the wizard’s current max hp of 11, causing insta-death. The wizard’s player argues that the death threshold for negative HP isn’t affected by max-hp-reducing spells, claiming that would make those kinds of spells more powerful than intended.

I have stories planned in either case, but I’d rather be certain that I’m following the rules.

Is the threshold for instant death based on current max hp or normal max hp?

Union of every language within group of decidable languages is also decidable?

So I was trying to solve following exercise:

Let $ (L_{i})_{i \in \mathbb{N}}$ be a family of decidable languages – this means that every $ L_{i}$ is decidable. Then $ \cup_{i \in \mathbb{N}}L_{i} $ is also decidable. Right or wrong?

The solution states, that this statement is wrong because we can set $ L_{i}:=\{f(i)\}$ with $ f : \mathbb{N} \rightarrow H_{0}$ and will therefore receive $ \cup_{i \in \mathbb{N}}L_{i} = H_{0}$ . At the same time $ L_{i}$ languages are still decidable, for every $ i \in \mathbb{N}$ because they are finite.

However I still struggle to understand how exactly a language can be decidable with $ f : \mathbb{N} \rightarrow H_{0}$ , because I thought that $ H_{0}$ was not decidable.

Thanks in advance!!

How do I DM for this group when we can’t handle a large group properly, but also can’t count on any smaller group all attending?

I just concluded an online game with my players. (We played 5E, but I want to move to Dungeon World.) I started with four players, and that has since grown to around ten people wanting to play, which is a problem as even with only six players I’ve started getting comments about there being too little time spread around to too many people.

I’ve tried a few approaches to help mitigate this, but every time I try playing with a smaller group, I run into the same problem: someone in the smaller party can’t make it.

This means running for the active party is that much harder because so much more of the party is gone, and the inactive players start wanting to play because they actually showed up on time ready to play. But there are enough of them that if I find a narrative reason someone else can come along, they all try to take it, and grumble about having to stay in town (or wherever) for no reason if they don’t get it.

How do I DM for this group when we can’t handle a large group properly, but also can’t count on any smaller group all attending?

As I descend vertically when affected by Feather Fall, can I also move horizontally?

The feather fall spell (PHB, p. 239) says:

Choose up to five falling creatures within range. A falling creature’s rate of descent slows to 60 feet per round until the spell ends. If the creature lands before the spell ends, it takes no falling damage and can land on its feel, and the spell ends for that creature.

Am I able to move horizontally as I descend (to "glide", basically), or can I only fall vertically in a straight line, directly down to the point below me when the spell was cast? Or is this simply something that isn’t specified and is something that the DM is expected to resolve?

This came up in a game I ran a couple of weeks ago. Luckily, this was asked preemptively as they were planning how to storm an orc camp, and the plan was changed before I was pressed for an answer, so I was able to dodge making a ruling entirely. However, if it were to come up again, it is simply up to me (the DM), or is there anything that suggests one or the other ruling?