A lot of games I've been in have had either enemies with player levels or straight up PvP. How should XP be awarded when facing enemies like that? Should you attempt to calculate the CR of the enemies based on the DMG tables or is there a guideline on how XP should be awarded based on the class levels?
As part of an early quest, my PCs are likely to face off against a wizard.  The problem here is that the stat block for Mage NPCs listed in the Basic Rules has a Challenge Rating of 6, while the PCs are going to be five Level 1s. So, instead of messing with the stat block and risk weakening it too much/too little, I'm choosing to create a Level 1 Wizard PC and use it as an NPC for this quest.  The problem with that is that, as far as I can tell, there aren't any designated rules for assigning either Challenge Ratings or XP values to a PC. So, should I just give the wizard a Challenge Rating equal to his level (and thus have him give 200 xp when killed), or is there a better way to do this?  (This is different from , because he's asking for a way to assign a level to an NPC, while I'm asking for a way to assign an XP value/Challenge Rating to a PC (for use as an NPC). Similar questions, but different.)
Why is a geometric progression called so? Just curious about why geometric progression is called so. Is it related to geometry? How to find the number of automorphisms on $\mathbb Z_2\times \mathbb Z_4$ Well, I was trying find out the number of group homomorphisms from $U(20)$ onto $U(15)$ which I reduce to the problem of finding the number of automorphisms for $\mathbb Z_2\times \mathbb Z_4$. But don't know how shall I proceed.   Any help will be appreciated. Integral $\int_{\frac{1}{2}}^1 \frac{\ln x}{\sqrt{x^2+1}}dx$ Iterate a list with indexes in Python Theory behind partial least squares regression Can anyone recommend a good exposition of the theory behind partial least squares regression (available online) for someone who understands SVD and PCA?  I have looked at many sources online and have not found anything that had the right combination of rigor and accessibility.    I have looked into The Elements of Statistical Learning, which was suggested in a comment on a question asked on Cross Validated, , but I don't think that this reference does the topic justice (it's too brief to do so, and doesn't provide much theory on the subject).  From what I've read, PLS exploits linear combinations of the predictor variables, $z_i=X \varphi_i$ that maximize the covariance $ y^Tz_i $ subject to the constraints $\|\varphi_i\|=1$ and $z_i^Tz_j=0$ if $i \neq j$, where the $\varphi_i$ are chosen iteratively, in the order in which they maximize the covariance.  But even after all I've read, I'm still uncertain whether that is true, and if so, how the method is executed. While explaining to my nephew about the physics of light, I told him we cannot see infrared color, and he kicked back with a very simple question: why can't we see it? I could not tell him. Is the human eye unable to sense such light or can it indeed but the brain can't understand the signal? any other reason? WPF TextBox and Scroll behavior I have a problem. I need to host grid with controls in ScrollViewer to prevent textbox from being either truncated or collapsed to zero-with at the UI. Also I want the with of textbox to be expanded when user change windows width. I'm setting Window's content to following code  &lt;DockPanel&gt;     &lt;TreeView DockPanel.Dock="Left" Width="150"/&gt;     &lt;ScrollViewer VerticalScrollBarVisibility="Auto" HorizontalScrollBarVisibility="Auto"&gt;         &lt;Grid&gt;             &lt;Grid.ColumnDefinitions&gt;                 &lt;ColumnDefinition Width="Auto"/&gt;                 &lt;ColumnDefinition /&gt;             &lt;/Grid.ColumnDefinitions&gt;             &lt;Grid.RowDefinitions&gt;                 &lt;RowDefinition Height="Auto"/&gt;             &lt;/Grid.RowDefinitions&gt;             &lt;TextBlock Text="Name"                         Margin="5"                         VerticalAlignment="Center"/&gt;             &lt;TextBox Grid.Column="1"                      Text="Some Name"                      Margin="5"                      VerticalAlignment="Center"                      MinWidth="200"/&gt;         &lt;/Grid&gt;     &lt;/ScrollViewer&gt; &lt;/DockPanel&gt;   All work fine, but when user types very long text in TextBox it is being expanded and horizontal scroll appears. Is there any easy way to limit TextBox maximum width and allow it to be expanded only when user changes window size. $ \tan 1^\circ \cdot \tan 2^\circ \cdot \tan 3^\circ \cdots \tan 89^\circ$ How can I find the following product using elementary trigonometry?     $$ \tan 1^\circ \cdot \tan 2^\circ \cdot \tan 3^\circ \cdots \tan 89^\circ.$$   I have tried using a substitution, but nothing has worked. pain of browser back button Upcasting is allowed in Java, however downcasting gives a compile error.   The compile error can be removed by adding a cast but would anyway break at the runtime.   In this case why Java allows downcasting if it cannot be executed at the runtime? Is there any practical use for this concept?   public class demo {   public static void main(String a[]) {       B b = (B) new A(); // compiles with the cast,                           // but runtime exception - java.lang.ClassCastException   } }  class A {   public void draw() {     System.out.println("1");   }    public void draw1() {     System.out.println("2");   } }  class B extends A {   public void draw() {     System.out.println("3");   }   public void draw2() {     System.out.println("4");   } } Could it be that Goldbach conjecture is undecidable? header and footer of the first page of every chapter It maby be weird, I want to make header and footer for every page including the first page of each chapter, how can I do this? Say I have two normal distributions A and B with means $\mu_A$ and $\mu_B$ and variances $\sigma_A$ and $\sigma_B$. I want to take a weighted mixture of these two distributions using weights $p$ and $q$ where $0\le p \le 1$ and $q = 1-p$. I know that the mean of this mixture would be $\mu_{AB} = (p\times\mu_A) + (q\times\mu_B)$.  What would the variance be?    A concrete example would be if I knew the parameters for the distribution of male and female height. If I had a room of people that was 60% male, I could produce the expected mean height for the whole room, but what about the variance? Is there BitTorrent software that runs in a terminal? I want to deploy it on my VPS server to download resources quickly.  This could save me a lot of time since some resources are in a foreign country, Invalid characters for XML parsing in posthistory.xml from Stack Overflow We got the April 2011 data dump from Stack Overflow and, while trying to put everything into a database, we got      SyntaxError: reference to invalid character number: line 1105549, column 5445   in the middle of the posthistory.xml file. It seems that there are sets of characters (&amp;#xC I believe) within a few posthistory entries which break our XML parser.  Is there a solution besides manually changing all the C's? Breaking single polygon into multiple polygons? I created voronoi polygons after which I dissolved them on the basis of one attribute. Now there are cases where in for one single attribute "abc" I have3 polygons at different places with same object id. I would like to break these into 3 polygons as they are at different locations.  Is there any tool in ArcGIS Desktop or QGIS which can help me in doing that? There seems to be some bug where mac os is constantly contacting . You can prevent it by turning off the wifi, but then your computer is nothing more than a fancy calculator. Is there a program, vpn, or even the firewall option, to block this site from the whole os? Installing node with apt-get or downloading the Linux Binaries (.tar.gz) Program counter goes to the end of code and 8051 Restarts I have an 8051 MCU which I use keil to program it with C. My problem is that the micro-controller restarts at the end of some functions while they should return.  Using a debugger I tried to check it line by line. And I figured out the the MCU is not restated right after the end of the function. The PC(progam counter) goes to somewhere else (sometime somewhere that there is not any code to execute) and then it increases one by one until the end of code. It is very strange for me because I write my code in C and never seen the type of error previously.    I think this problem might be related to the compiler settings and thus I post the settings here:   Assembler settings: XR GEN DB EP NOMOD51  Compiler settings:  DB OE BR LARGE OPTIMIZE(11, SIZE) DEFINE(SILABS_PLATFORM_WMB912) DEFINE(SILABS_WMCU_SI106x)  Linker settings: CODE REMOVEUNUSED CLASSES(BIT(0x20.0-0x2F.7), DATA(D:0-D:0x7F), IDATA(I:0-I:0xFF), XDATA(X:0-X:0xFFF), CODE(C:0-C:0xFBFF), CONST(C:0-C:0xFBFF))  I tried both large and small settings but the problem remains. Kindly help me if you know the reason. The top bar is showing (again) the suggested edits count and 10K flags count, like it was before.  On Stack Overflow it looks like this: (that's the original color, same as in old top bar)        And on this very Meta site:        Same top bar. But different colors! Consistency broken.  I've just noticed the suggested edits count on Meta:        Black on black, I can see just a floating number - really confusing and out of any context.  In the name of Consistency, can we please have the same color on all sites?