For example, my entire party is versed in Arcana and they attempted to recall lore on a spell.   Party member A made the skill check while being helped by B and failed with advantage. B tried while being helped by A and failed with advantage. C tried while being helped by D and failed with advantage. D tried while being helped by C and failed with advantage. E tried while being helped by A and succeeded because of advantage.   By working together in this way can a party of X size perform 2X skill checks on the same task?
Picking a lock typically requires a DC 15 Dexterity check (Basic rules, p. 49). Likewise for manacles (p. 50), which can alternately be escaped with a DC 20 Dexterity check or broken with a DC 20 Strength check. But what happens if you fail?  The general rules for ability checks state (p. 58):     If the total equals or exceeds the DC, the ability check is a success—the creature overcomes the challenge at hand. Otherwise, it’s a failure, which means the character or monster makes no progress toward the objective or makes progress combined with a setback determined by the DM.   As a DM, how can I handle this in practice? In our last session, the players wanted to get inside a locked building to rescue people trapped inside. Picking the lock seemed like an easy enough task for the rogue, but unluckily he failed the check, and I wasn’t prepared for the consequences. There wasn’t much time pressure and no obvious reason why he couldn’t try again, so I allowed another attempt, but it just didn’t feel right.  I’m sure that similar situations will come up again, so I’d like some advice on how to deal with checks so that they don’t just turn into a tedious exercise of rolling until you succeed. I presume that  was left out of the game for good reason, but I’m not sure what to do instead. I suspect that this was a good occasion to use “progress with a setback” but that’s a fairly new thing for D&amp;D and I’m not sure how to go about it. I’m unsure when I should use setbacks versus lack of progress, and in the latter case I’m unsure when I should allow players to try again versus requiring a different approach.  For example, suppose that a manacled player tries to pick the lock and fails the DC 15 Dexterity check. Now, the player could try to pick it again, or he could try one of the other escape methods, or he could wait for somebody else to rescue him, or he could simply succeed with some setback like a minor injury. How do I choose how to proceed? Or do I let the players choose?
Trying to find a book about kids with 'sunguns' revolting against alien overlords I'm trying to identify a book (or possibly a series, as I seem to recall reading a sequel which still left the story unfinished).  I read the book or books in the early 90's and had picked them up from a jumble sale at school, so they were probably published in the 80's or possibly 70's. I guess you would class them as YA fiction, though that wasn't really such a thing back then...  As I recall the story began with a slave transport craft crash landing on an alien world, with only a handful of teenage and pre-teen humans surviving. They scraped together what they could, including a couple of functional 'sunguns' (basically, laser rifles) and began a low level guerilla rebellion against the alien race that were using humanity as slave labour on the planet.  I've googled 'sungun' repeatedly, thinking that this should be the best way of finding the story but the references that come up are all for other stories or conspiracy technologies.  Anyone got any vague recollections of a book or series like this? Official ESTA application website and are the others scams? A quick search for ESTA application returned many results. According to , the official site to apply for an ESTA is .  Are the others scams, legitimate third party resellers or "added value" services?    (defunct - domain is for sale circa 2020)     Can anyone confirm either way?  Updated 2020: The above have better "not affiliated with the U.S. Government" warnings now, but beware there are newer more sneaky sites starting all the time:        And fortunately more official guidance about this issue: Whenever I open my files, my hidden files show up. I can hide them but when I open up my files again, they're showing again. How do I make the hidden files invisible permanently? Is causality a formalised concept in physics? Unbiased estimator for geometric distribution parameter p How do I prevent mouse movement from waking up a suspended computer? Definitions of "linearity" across branches of mathematics or levels of math education Linearity is a ubiquitous concept in mathematics; however, each branch of mathematics appears to have its own definition of what a linear map (function, functional, functor, transformation, form, operator, or whatsoever) is. These different definitions can lead to confusion, especially when people apply conflicting definitions of linearity to the same mathematical object (just  to figure out what I mean).  One of my favorite examples with potential for conflict is the natural logarithm $\ln : \mathbb{R}_{&gt;0} \to \mathbb{R}$, which the majority of people, as I could learn during hot disputations not only  but also with colleagues in my field, regard as clearly non-linear, even though it fully complies with the definition of a linear map from the vector space $\mathbb{R}_{&gt;0}$ to the vector space $\mathbb{R}$ (cf. Definition 4 below). A similar conflict arises analogously for the exponential function $\exp :\mathbb{R} \to \mathbb{R}_{&gt;0}$.  I do not want to initiate yet another discussion here, about what the right and what the wrong definition of linearity is! Rather, ...  ... I would like to compile a list of existing definitions, to get a better overview of the different uses of the term "linearity" across the different branches of mathematics and levels of education.    Let be begin with the following four, which are certainly far from constituting a complete list. What about bilinear or multilinear forms, linear morphisms and linear functors in category theory, linear metrics, or other concepts of linearity? I am looking forward to see your answers.  At school I was taught that     Definition 1:   A function $f$ is linear if it is of the form $f(x) = ax + b$.   Later I learned that $f(x) = ax + b$ is affine, rather than linear, because     Definition 2:   A function $f$ is linear if it is of the form $f(x) = ax$.   From real analysis and systems theory, I know the following     Definition 3:   A map $f$ is linear if         $f(x + y) = f(x) + f(y)$   $f(a \cdot x) = a \cdot f(x)$.      This definition also applies to the expected value in statistics, as        $\mathrm{E}(X + Y) = \mathrm{E}(X) + \mathrm{E}(Y)$   $\mathrm{E}(a \cdot X) = a \cdot \mathrm{E}(X)$.      In a linear algebra course, I learned for the first time that we must not forget to take into account that the vector-space operations of the domain and the codomain of a map $f$ may be dissimilar. In fact, if $(V, \oplus, \odot)$ and $(W, \boxplus, \boxdot)$ are two $\mathbb{K}$-vector spaces, then     Definition 4:   A map $f : V \to W$ is linear if         $f(x \oplus y) = f(x) \boxplus f(y)$   $f(a \odot x) = a \boxdot f(x)$.         Notice that I deliberately used distinct symbols for the operations in both vector spaces, to emphasize how this definition differs from Definition 3.   Correct me if I am wrong, but this definition should also apply to maps between two modules.    Updates: How to calculate $\int_0^{\pi/2} \sin^a x \cos^b x \,\mathrm{d} x$ What is the default password of the sudo? I visit some forums, it tells that the default password is password, but it doesn't work, how can I determine the password? Why with two classes, LDA gives only one dimension? I am working with dimensionality reduction algorithms. Linear Discriminant Analysis (LDA) is a supervised algorithm that takes into account the class label (which is not the case of PCA for example). I am using Python to do a comparative study between some algorithms.  Why with two classes (k = 2), regardless of the data dimensionality, LDA gives one dimension, i.e. the new subspace is composed of only one dimension? For example if I try to project my dataset (of 100 attributes and 2 classes) to 10-dimensional space by using LDA(n_components=10) I only obtain 1 dimension?  For k&gt;2 I can obtain the number of discriminant vectors that I specified as n_components. How can I get n_components dimensions for k=2? Which Ubuntu repositories are totally safe and free from malware? How to understand dot product is the angle's cosine? How can one see that a dot product gives the angle's cosine between two vectors. (assuming they are normalized)  Thinking about how to prove this in the most intuitive way resulted in proving a trigonometric identity: $\cos(a+b)=\cos(a)\cos(b)-\sin(a)\sin(b)$.  But even after proving this successfully, the connection between and cosine and dot product does not immediately stick out and instead I rely on remembering that this is valid while taking comfort in the fact that I've seen the proof in the past.  My questions are:   How do you see this connection? How do you extend the notion of dot product vs. angle to higher dimensions - 4 and higher? PostgreSQL CPU 100% after configure Wal log shipping hot standby I have configured Hight Avaliabily WAL Log Shipping Hot Standby (SSL) with one node. But after I configure, both hosts (primary and secondary) take 100% CPU usage. The most strange is because I have only one database called &quot;TESTE&quot; with one table called &quot;EXAMPLE&quot; to check if replication was OK. The replication worked perfectly but I don't understand why my CPU takes 100% usage because I don't have any application connect on my cluster. I ran HTOP command and get this results: Image 1 - Primary Server HTOP Info  Image 2 - Secondary Server HTOP info  S.O. version: No LSB modules are available. Distributor ID: Debian Description:    Debian GNU/Linux 10 (buster) Release:        10 Codename:       buster  PostgreSQL version: postgres (PostgreSQL) 12.3 (Debian 12.3-1.pgdg100+1)  Primary server postgres.conf file: max_connections = 100 SSL = on shared_buffers = 2GB work_mem = 10485kb maintenance_work_mem = 512MB dynamic_shared_memory_type = posix effective_io_concurrency = 200 max_worker_processes = 4 max_parallel_maintenance_workers = 2 max_parallel_workers_per_gather = 2 max_parallel_workers = 4 wal_level = replica wal_buffers = 16MB max_wal_size = 200MB min_wal_size = 80MB checkpoint_completion_target = 0.7 archive_mode = on max_wal_senders = 3 wal_keep_segments = 8 hot_standby = on hot_standby_feedback = on random_page_cost = 1.1 effective_cache_size = 6GB default_statistics_target = 100  pg_stat_activity info:  pg_stat_archiver info:  pg_stat_replication info:  If I stop postgres service in both servers the CPU still has 100% usage. Anyone can help me? $\text{Let }y=\sqrt{5+\sqrt{5-\sqrt{5+\sqrt{5-...}}}} $, what is the nearest value of $y^2 - y$? I found this question somewhere and have been unable to solve it. It is a modification of a very common algebra question.          $\text{Let }y=\sqrt{5+\sqrt{5-\sqrt{5+\sqrt{5-...}}}} $,  what is the     nearest value of $y^2 - y$?          $\textbf {(1) } 1 \qquad \textbf {(2) } \sqrt5 \qquad \textbf {(3) } 4 \qquad \textbf {(4) } 2\sqrt5$      I worked the problem and got $$y^2 - y = 5+ \sqrt{5-\sqrt{5+\sqrt{5-...}}} -\sqrt{5+\sqrt{5-\sqrt{5+\sqrt{5-...}}}} \\ = 5+ \sqrt{5-y} - y = 5-y + \sqrt{5-y}$$ What do I do next? What's with the very slightly larger mass of the neutron compared to the proton? Generalised rule for verb usage in simple present tense using participle I am having trouble finding out why the white space between my paragraphs is variable. Sorry, I am not allowed to post images but sometimes there is no white space (like it should be), just an indent to denote that a new paragraph has started. While sometimes the paragraphs start with an indent AND there is (sometimes substantial and thus variable) white space between the last sentence of the previous paragraph and the first sentence of the new paragraph.  In my tex file, there is no difference between what I do in the first and second examples of my text: just two hard returns to denote the start of a new paragraph. I was wondering whether it could be due to placement of figures and footnotes but I have no idea how to change it. I don't mind a little variable white space between paragraphs but the above example is too extreme for my taste. Thanks for your advice! Query Activity for ORDER BY xxx DESC LIMIT I want to open a file for reading, the C++ way. I need to be able to do it for:   text files, which would involve some sort of read line function. binary files, which would provide a way to read raw data into a char* buffer. Suppose someone from "Harry's world" married a Muggle, and they want to escort their child. Can the Muggle parent get through to the Hogwarts platform?