I’m currently working on a Magic Missile-centered build and want to make sure I’m not missing anything.  As far as I can tell, using Hexblade’s Curse (XGtE 53) and Empower Evocation (PHB 117) are the only ways to increase my Magic Missile damage outside of upcasting.  So assuming I have 20 Int and a proficiency bonus of +6, is 1d4+12 the maximum damage I can do per missile by RAW?
So one of this question's  answers got me curious. What is the maximum damage a 20th level character can do with a 9th level Magic Missile by the rules to a single target.  So my best I've been able to find is Aasimar or Goblin WLK 1/WIZ 19   9th Level slot (1D4+1)(11) [keep in mind you only roll once for damage not 11 times]  per  Empowered Evocation (+5)(11) (assuming 20 INT) Hexblade Curse (+6)(11) (Proficiency Bonus +6)    Radiant Soul/Fury of the Small +20 (Level 20 Aasimar/Goblin)   For a total of (D4+12)(11)+20 for (min-max)avg (163-196)179.5  Am I looking at this correctly? Are there other abilities out there that can increase this?  Feel free to include non legendary magic items. NO TOMES PLEASE  Only use things available on D&amp;D Beyond please.  Acceptable books are :   Basic Rules DMG, MM, PHB Sword Coast Adventure's Guide The Tortle Package Volo's Guide to Monsters Xanathar's Guide to Everything and any officially released Adventure Book
How many solutions are there to $x_1 + x_2 + ... + x_5 = 21$? How many solutions are there to the equation      $x_1 + x_2 + x_3 + x_4 + x_5 = 21$    where $x_1, i = 1,2,3,4,5$ is a nonnegative integer such that $0 ≤ x_1 ≤ 3, 1 ≤ x_2 &lt; 4$, and $x_3 ≥ 15$?  I have correctly completed the previous parts of the question but am having trouble with this particular restriction.  The total number of solutions to the equation is $C(25,21) = 12650$.  I have tried to do each restriction individually:  For $0 ≤ x_1 ≤ 3$, I solved this by subtracting the number of solutions when $x_1 ≥ 4$ from the total number of solutions. This is $C(25,21) - C(21,17) = 5985$.  For $1 ≤ x_2 &lt; 4$, I have $C(24,20) - C(21,17) = 5985$.  For $x_3 ≥ 15$, I have $C(10,6) = 210$.  However, the restriction is when these are all together. I am not sure how to proceed. The answer is $106$. Sometimes when I'm making a sauce or soup that needs to be a bit spicy, I have no troubles spicing how I want to.  But if the dinner party is a bit late, or I made the sauce in advance to really draw out all the flavors of the spices, vegetables and meat, sometimes I end up with a way too spicy/hot dish.  You can always pour a bit water and try to dilute it a bit, but that also takes away all of the good flavor. So is there some trick that I'm missing I can use, when this happens to me (other than being more careful or using the spices later)? Mirror modifier is not working, no mirrored object? There is no or there was no I read a sentence in an exam:     There is no child who did not bring his parents to the picnic.    I think that the sentence does not have tense-agreement. Why is is used instead of was? Please explain it to me. Creating files in C++ Is there an online course in Mathematical Methods for Physics, Covering Matrices and Vector Analysis? I am taking a course in Mathematical Methods for physicsPhysics (Junior Level).   We are working from   > Mathematical Methods for physicists, George B.Arfken .    I just need online resources covering ( Matrices, Determinants, Vector Analysis, Tensors and differential forms and Vector spaces...etc) to study and understand from. What can I do to give the players the same feel their characters would have about wilderness travel? I find that in a lot of our group's games, traveling long distances through wilderness is too easy.  In real life, it's quite arduous traveling overland.  No one who's just walked a hundred miles is eager to repeat the trip.  But here's the problem -- for the players, it's trivial to travel a long way.  You just say "then we walk over the Groblick Hills to Dorridge", and you get there.  The players find it easy, but there's no way the characters would be eager to set out on a long stretch across the wilderness.  What can I do to give the players the same feel their characters would have about wilderness travel?  One thing I'd like to avoid (if possible) is to just make it perilous by throwing in a bunch of fantasy monster encounters.  Imagine some hobbits off in Gondor -- sure, they'd love to go home to the Shire, but it's mighty tempting to stay an extra day in the inn before setting off on the journey. Imported CSV data is not displayed in QGIS When I try to bring down the Achievements tab in Area 51, it's showing an error dialogue.  Strangely enough, the global inbox dropdown works just fine.  Could be connected to .  Screenshot: Selection of logical connectives {¬,∨,∧,⇒,⇔} in set theory? How can I model flips until N successes? You and I decide to play a game where we take turns flipping a coin. The first player to flip 10 heads in total wins the game. Naturally, there is an argument about who should go first.  Simulations of this game show that the player to flips first wins 6% more than the player who flips second (the first player wins approx 53% of the time).  I'm interested in modelling this analytically.  This isn't a binomial random variable, as there are no fixed number of trials (flip until someone gets 10 heads). How can I model this?  Is it the negative binomial distribution?    So as to be able to recreate my results, here is my python code:  import numpy as np from numba import jit   @jit def sim(N):      P1_wins = 0     P2_wins = 0      for i in range(N):          P1_heads = 0         P2_heads = 0         while True:              P1_heads += np.random.randint(0,2)              if P1_heads == 10:                 P1_wins+=1                 break              P2_heads+= np.random.randint(0,2)             if P2_heads==10:                 P2_wins+=1                 break     return P1_wins/N, P2_wins/N   a,b = sim(1000000) I am using Sql Server 2008 on Small Business Server 2003; client is using WinXP.   I added a user to my Active Directory Security Group; Why can't this user immediately access the database? It seems there is a delay before the user is recognized in Sql Server.   I am using AD Security Groups for permissions expressly so that I don't need to add individual users in Sql Server. So effectively I don't need to do anything but add the user to the AD Security Group in order to grant access.  But for some reason Sql Server doesn't immediately recognize the addition. I've seen this a number of times. I add the user to the group but that user can't access data until the next day. It seems that it doesn't query the Active Directory in real time. Can you confirm that is so?  What do I need to do so that Sql Server "refreshes" the list of users from Active Directory? As I understand it, anything created with an alloc, new, or copy needs to be manually released. For example:  int main(void) {     NSString *string;     string = [[NSString alloc] init];     /* use the string */     [string release]; }   My question, though, is wouldn't this be just as valid?:  int main(void) {     NSAutoreleasePool *pool;     pool = [[NSAutoreleasePool alloc] init];     NSString *string;     string = [[[NSString alloc] init] autorelease];     /* use the string */     [pool drain]; } Posts linked in deleted answers still show up under "Linked" E.g. see . Do I need a visa for Paris, if my connecting flight stops for 24 hours in Paris? Do I need visa for Paris, if my connecting flight stops at Paris for 24hrs and I want to visit Paris during that 24hrs? I have US B1 visa. I'll be travelling from San Francisco to Bangalore (India) via Paris. I hold Indian passport. If yes, what is the procedure for that visa? I'm trying to measure the execution time of a process that I call via the command line (i.e., I want to find out how long it takes to for the process to finish). Is there any command that I can add to the command calling the process that will achieve this? UIToolbar tint on iOS 4 It is a known fact that if $R$ is a UFD, then $R[X_1,X_2,\dots]$ is also a UFD, but there is a subtlety that is making me uncomfortable.  The standard approach essentially goes something along the lines of...let $f$ be a polynomial, so it only involves finitely many variables, say up to $X_1,\dots,X_n$. Then since $R[X_1,\dots,X_n]$ is a UFD, $f$ has a factorization into irreducibles. Then $f$ cannot have a factorization involving indeterminates $X_N$ not in $R[X_1,\dots,X_n]$. If it did, then $f$ would have two factorizations in the UFD $R[X_1,\dots,X_n,\dots, X_N]$, a contradiction.  This seems to assume that the prime factorization in $R[X_1,\dots,X_n]$ is still a prime factorization in $R[X_1,\dots,X_n,\dots,X_N]$. But how can you see that irreducibles in $R[X_1,\dots,X_n]$ are still irreducibles in $R[X_1,\dots,X_m]$ for $m&gt;n$? This does not seem obvious.  Let $R_k=R[X_1,\dots,X_k]$. The explanantion I found is this: Suppose $p\in R[X_1,\dots,X_n]$ is irreducible in $R_n$. Suppose $p=ab$ for $a,b\in R_m$. Evaluating $X_1,\dots,X_n$ at $1$, you get  $$ \bar{p}=\overline{ab}\in R[X_{n+1},\dots,X_m] $$ But $\bar{p}\in R$, which implies that $a$ and $b$ do not involve any variables $X_{n+1},\dots,X_m$. So $a,b\in R_n$, and thus one is a unit, hence a unit in $R_m$.   The part I don't follow is how evaluation at $1$, implies $a$ and $b$ do not have indeterminates other than $X_1,\dots,X_n$. Isn't it possible that some of the higher indexed indeterminates disappear when you evaluate? Suppose for instance $p\in R_1$, and $a\in R_2$ is $a=-X_1X_2+X_2$. Then evaluting at $1$ gives $\bar{a}=0$ so we may not get the desired contradiction since $\overline{ab}=0\in R$? I want to select the value from the dropdown I am testing www.paytm.com  In that I have filled in the mobile number but I am not able to focus and select the mobile operator which is present in the dropdown just after the phone number section.  I want to select 'vodafone' as the value from the dropdown.  How to do that using webdriver  Code I have written till now  `  public class MMT {   public static void main (String[] args)  {  System.setProperty("webdriver.chrome.driver","E:/som/chromedriver/chromedriver.exe");  WebDriver driver = new ChromeDriver();  driver.get("http://paytm.com");  driver.findElement(By.id("mobile-number")).sendKeys("9876543212");`   What should be my next steps? command to display time (duration) in human readable form I spent 3 hours trying to write a command to format a time (duration) expressed as a floating number (in seconds) in a nice form as follows:  if the time is &lt; 60 write as a float with 3 decimals (i.e. milliseconds)  else let h,m,s be the hours, minutes and seconds corresponding to the time      if h=0 then write as m:ss (ss always with 2 digits, m can have only 1)      else write h:mm:ss (mm and ss with 2 digits, h can have only 1)   So 1.25678 gives 1.256, 125.35 gives 2:05, 18249 (which equals to 5*3600+4*60+9) gives 5:04:09.  I tried several packages for the comparison/formatting. No success. Can someone help me ? Thanks !