Against which AC do you check on the strikes of the Tiger Claw discipline?

As the title says. If, let’s say, I catch my opponent flat-footed and use Claw at the Moon, do I check against flat-footed AC or complete AC?

Claw at the Moon:

As part of this maneuver, you attempt a Jump check to leap into the air and make a melee attack that targets your foe’s upper body, face, and neck. The Jump check’s DC is equal to your target’s AC. If this check succeeds your attack deals +2d6 damage. if this attack threatens a critical hit, you gain a +4 bonus on your roll to confirm it. If your check fails, you can still attack but deal no extra damage or gain a bonus to confirm a critical hit. The maneuver is still considered expended.

Check for common element in two arrays using FFT

My task ask me to check whether there is a common element in two arrays $ (x_1,x_2,…,x_n)$ , $ (y_1,y_2,…,y_n)$ with $ x_i,y_i\in\mathbb{N}$ using the Fast Fourier Transform(FFT). (I’m aware that there is a simple $ O(n\log(n))$ algorithm to solve this problem using sorting and binary search.) The tasks hints that we should consider the following product to solve the problem: $ $ \prod_{i+j=n} (x_i-y_j) $ $ The product is obviously zero if there is a common element, but I am still not sure how I could compute it faster via FFT.
… I know how to use FFT to multiply polynoms efficiently, but somehow I seem to overlook something.

How am I supposed to check Defender’s capability when it trusts me blindly after I mark a test malware file as “allowed”?

With enormous amounts of fighting with Windows/Microsoft Defender, I finally managed to download the "test virus" file from onto my desktop.

However, Defender (on the command line) still just says:

Scanning C:\Users\John Doe\Desktop\ found no threats. 

No threats? You just had me work for 30 minutes straight to make you not remove the file before it ever even landed on my desktop, and now you consider it to not contain any threats? Is this just because I have "allowed" it?

My entire point of downloading this file was to check if Windows/Microsoft Defender returns a "1" code instead of "0" when it detects a virus (and what it says as text output), but now I can’t even test that because it thinks that the file is not "harmful" just because I allowed it to exist temporarily on my system for the purpose of testing this?

Bottom line: I can’t see any way to test Defender’s output/return code for an actual malware-detected file because it doesn’t even allow me to have the file on my desktop without "allowing" it, which apparently makes it believe me blindly as an authority.

Troika! How to check for normal skill or action?

For example a player wants to kick a door open or transport glasses over a slippery wet floor. The player has no fitting advanced skill for those.

The base SKILL is 1d3+3 which can be very low. Rolling that under 2d6 is very hard. Everyday tasks become impossible. I could let them spend extra LUCK to boost their roll but that feels unnatural. Players tend to save their LUCK when they need it.

Alternatively I could let them roll 2d6 + SKILL versus or under a given difficulty but the Troika! does not have any rulings for this.

How to check for an normal task that sometimes fail?

Ramsey Theory Check

So, I want to create a program that would check if a graph contains a complete sub-graph (more in the Party Problem) and my point is to prove that the computer fails to do so quickly as the number of graph’s vertices increase. So far, I have come up with only this code, but it doesn’t work for some reason. Any suggestions?

   RamseyNumber[k_, l_] := Module[{i = 3, r = 0},   While[    i <= Length[list] && r == 0,    If[((#[[1]] >= k || #[[2]] >= l) & /@       (And @@ list[[i]])), r = i, i++]    ]; r   ]  RamseyNumber[n_] := RamseyNumber[n, n]  Timing[  in = Table[     Length /@ MaximumIndependentSet /@ Graphs[n], {n, 8}     ];  ] 

Algorithm to check gibbs phase rule

I am looking for an algorithm to solve the following problem. I am unsure whether to post this in computational science or here, but since this is an algorithm I thought I would try here first.

I have a set of species made from a number of components.
Let’s number each component $ 0, 1, 2 … n$ .
So now each species can be described as a set of these components.

I am given a set of species, and I need to check whether any subset of these species fulfills the following condition: that the number of species in this subset is greater than or equal to the number of unique components in this subset.

For example: the set of species {[0, 1, 2], [0, 2], [1, 2]} fulfills the criterion, as the set has 3 species and 3 unique components. The set of species {[0, 1, 2], [0, 2], [1, 2], [3,4]} also fulfills the criterion, as a subset of the set fulfills the criterion. The system {[0, 1, 2], [0, 2]} does not fulfill the criterion, as there are 2 species and 3 unique components.
In case it is relevant: there can be many species (40-50) and components (10-20) but the number of components per species remains relatively small (2-5)

Can this be done with polynomial time complexity? It seems kind of similar to the set cover problem, so I don’t have much hope.

How can I check if a new group is OK with a plotline from an ethical standpoint without spoiling the plot?

TL;DR: I am unsure if the plotline I planned is "too dark" for a new group, and would like to discuss the level of grit with them without spoiling the plotline. How can I do this?

I am planning a campaign where an evil dryad witch has kidnapped a bunch of children and is planning to turn them into trees which she can sell to the local sawmill. My idea is for there to be a grove where the kids are kept prisoner, where the heroes (have the option to) fight her and save the children.

The next idea is that she can mind control the children, using them as meat shields.

I feel like this could be a pretty epic moment if they manage to keep the children safe/heal them from the mind control and slay the witch. However, I’m worried that this triumphant moment will turn sour if they mindlessly hack and slash at the mind controlled children instead of saving them all, and realise only afterward what they have done.

The problem with all this is that I am planning this adventure for a new group – I have neither played nor DM:d with them previously (although I know some of them personally). The experience level ranges from near-beginner to intermediate. Since I am a bit concerned that the plot I planned could be considered "too dark", I would like to bring up the topic of what we consider in-bounds (as a group) in advance of the session. How can I start this discussion without spoiling the plot specifically?

How can I resolve a repeatable skill check when there’s no time constraint or clear drawback from repeating it? [duplicate]

Willem Renzema’s answer to "Can you Investigate the same room twice?" and abalonemacaroni’s answer to "I failed to open a lock. Now what?" seem to lean towards the idea that if an ability check can be repeated indefinitely given enough time, a drawback should occur on each failed attempt to offset that.

But how can I resolve a repeatable skill check when there’s no time constraint or clear drawback from repeating it?

For example, making a History check in a library, lockpicking a safe that you’ve already stolen and brought back to your hostel, or making an Investigation check on an emptied dungeon, etc.

Basically, it feels like they are going to succeed in both cases, and the roll looks useless.

Multi check are too easy?

When asking for a skill check that all the players can attempt, it is quite easy to have at least one player to succeed.

Indeed, a 15 DC investigation (that is a 30% chance with a +0) is quite easy for a group of 5 PC (83% chance to succeed). Even a 20 DC would not be that difficult if there is enough people with a +3/+4.

How to manage group check to avoid the check to be too easy ?

To notice that I am not talking about a group check (in that case it looks that half+ of the player need to succeed), but rather a check that everyone can attempt one at a time (opening a safe, decipher a scroll, looking at an ancient item to know its history…)