So, this is my second D&amp;D campaign as a dungeon master and I wanted to try it with more than 3 people. I told 5 other people that they could join in and we will start in a month.   However, I’ve read that over 5 people will create complications. Should I try it with 8 people, if so then how?   If not, I’ll just do 5. I know this is more of a personal problem question, but in the name of D&amp;D I need some help please.
I am currently running a Dungeons and Dragons 4 campaign for a group of 9 players.  Whittling the group down to a more manageable size is not really an option since they are all family.  When we do combat it takes forever even if I have one player help me and allow them to go 2 at a time.  When we do story based adventure there are 2-3 players that do most of the talking and the others twiddle their thumbs.  I've tried encounters with many foes, encounters with only a few tough foes, dialog only encounters, social puzzle encounters, everything I can think of.  What else can I try to get this group more engaged?
Proof Check: Every Cauchy Sequence is Bounded Sorry if I keep asking for proof checks. I'll try to keep it to a minimum after this. I know this has a well-known proof. I understand that proof as well but I thought I'd do a proof that made sense to me and seemed, in some ways, simpler. Trouble is I'm not sure if it's totally correct. It's quite short though. I was just hoping someone could look it over and see if it is a valid proof. Thank you!  Lemma: Every Cauchy sequence is bounded.  Proof: Let $(a_{n})$ be Cauchy. We choose $ 0&lt;\epsilon_{0}$. So $ \forall \; n&gt;m\geq N_{0}$ we have that $\vert a_{n}-a_{m} \vert &lt; \epsilon_{0}$. Therefore $(a_{n})$ is bounded for all $ m \geq N_{0} $ by $ \epsilon_{0} $. Since $ \mathbb{N}_{N_{0}}$ is finite, it is bounded. So, for all $ m&lt;N_{0} $, $ (a_{n})$ is bounded. Therefore $(a_{n})$ is bounded.  I realize I haven't said what the bounds are but I think that's sort of irrelevant. So long as we know it's bounded. Any help is much appreciated! Essentially, I wonder that if X is a plural noun, should we use a plural or singular verb in a sentence such as "X are a subject that [verb] ..."? I believe that we should always use the singular verb form there (for example, "Eatable flowers are a subject that comes up ..."). However, I was surprised to find this sentence on the  page:     Eatable flowers are a subject that come up in almost all cooking classes eventually and I am a big fan of them.   as well as this on Google Books:     Tools are a subject that come up at our house from time to time.   I think they are typos, but I would like a double check to be sure. Firmware vs. Software What's the meaning of a dot before a command in shell? While following android eclipse debug tutorial, I encounter following commands.  cd /path/to/android/root  . build/envsetup.sh  lunch 1     make        emulator   My problem is what the dot before build/envsetup.sh means? Rotating a gyroscope's output values into an earth-relative reference frame For whatever reason, I seem to have gotten myself twisted into quite a confusion on how to process data from my 3 axis gyro and 3 axis accelerometer to get gyro rotation values related to the earth's reference frame. i.e. Given my accelerometer measures gravity (we assume it's stable) along the sensors (x,y,z) reference frame, how do I adjust the values of my gyro, measured along the sensors same (x,y,z) reference frame such that I am actually measuring the rotating about the Earth's frame x (North), y (West), and z (downwards) direction?  I just can't seem to wrap my head around the use of the rotation matrix. Do I simply employ a 3d rotation matrix, and multiply the vector, \$[gyro_x, gyro_y, gyro_z]^T\$, by a rotation matrix, R? I then assume the rotation angles, are somehow derived from the filtered accelerometer outputs, but I'm having trouble deciding on what those should be.  I have yet to find a concise reference on how to move the rotation and acceleration values from the sensor reference frame into the earth global reference frame. Perhaps someone can help? Thanks Why didn't the IF want Peter Wiggin? Why didn't the IF want Peter Wiggin?  Ender's Game implies that they didn't want him for being too violent/aggressive (I believe the quote from Graff was something like "doesn't know half the time if he wants to be a human or a jackal").  But this seems to be contradicted by two facts:   They already have specimens like that in school. Bonzo Madrid, for one, is the same except dumber.  Or Bernard, of who Alai said "I'm not Bernard, I never tortured cats for fun.". If you recall, the main signal that Peter was dangerous was his torturing small animals. Less importantly, Peter turned out way non-jackaly. We can write that off on faulty analysis during early years.   I'd prefer answers based on book sources or Card's statements if any are available. Please don't quote Graf's original statement from beginning of Ender's game as an answer - that's what I'm questioning.   IMPORTANT: Any answers that cite Peter as being a possible impediment to Ender should take into account the fact that Peter was rejected before Ender was even authorized to be born.    P.S. Just to clarify - I didn't ask why IF didn't think Peter Wigging was as genius of a commander as Ender. I am asking why he wasn't taken to the School like all the other talented bullies were. They took plenty of other kids who weren't Ender, so why wasn't Peter among them? What is the ideal way to handle data pins D+ and D- on a USB power adapter to be compatible with fast charging on devices? When one should use spacing line \quad or \, Let $p,q$ be primes, $p≠q$, then I have to show that $\mathbb{Q}(\sqrt{p},\sqrt[3]{q})= \mathbb{Q}(\sqrt{p}\cdot \sqrt[3]{q})$  So far I've tried a lot of things with minimal polynomials and bases, but I'm far from any argument that I find sufficient.  This is an example from my algebra course, first chapter about field extension. So far we know about basic definitions, minimal polynomials and their properties, algebraic elements and algebraic fields.  Could someone maybe give me a hint about how to proceed? Thanks a lot!!! Getting / setting file owner in C# 'both in terms of' or 'in terms of both'? Query for list of attribute instead of tuples in SQLAlchemy Alarm is working even when the phone is powered off I just discovered that if I set the alarm clock and then power off the phone (by holding the power button and then selecting "Power Off") the alarm will still go off when the time comes.  Is this expected behavior? It makes me feel like "power off" doesn't actually power off the phone.  I have a Huawei Y530-U051 running android 4.3. A very quick question:   Is it correct to say "In case I won't be able to watch that"?  If it's acceptable to say that, what type of sentence is it?  UPDATE:  As a clarification, I want to say "Can you give me that in case I won't be able to have it later". Probably, it's more a supposition than a conditional. This is probably a silly question, but how can I run ANOVA using only the mean, standard deviation, and the sample size?  i.e.  Group  mean    sd    n  1:    200      5    5    2:    100     22    5  3:    150     14    5   I am using Statsoft Statistica software.  I know how to run it using the spreadsheet with all the data, but I have never done this using only the information listed above.  Any information would be greatly appreciated. A ring of a planet has an inner radius of approximately 52,000 km (measured from the center of the planet) and a radial width of 19 km. Use differentials to estimate the area of the ring. (Round your answer to the nearest thousand.)   I hate asking questions where I have nothing to contribute but I have absolutely no Idea on how to approach this question. A step by step solution to this problem which I could apply to similar problems would be greatly appreciated, thanks in advance. Using sets of arguments from a list I unintentionally and stupidly wiped my Clash of Clans game data. I went to Application Manager on my Android and clicked 'Clear data'. (I used this for fixes before and it never started a new game.)   Now, my level 60 or so base has been wiped as if was to start a new game. Have I doomed myself to starting again or is there a way in which I can retrieve my old game save? Maybe by contacting Supercell? I have a snapshot of my base. How do I get a tourist visa (or a tourist card) for Cuba?  I live in the Netherlands, but I'm not a Dutch citizen, I have an Italian passport. Given a DateTime object, how do I get an ISO 8601 date in string format? Given:  DateTime.UtcNow   How do I get a string which represents the same value in an -compliant format?  Note that ISO 8601 defines a number of similar formats. The specific format I am looking for is:  yyyy-MM-ddTHH:mm:ssZ