During a Clash of Clans war, which team is determined to win when the star total is even and the total destruction is also even?
In Clash of Clans there was an update on 9/16 adding a Tie-breaker into the wars, can anybody explain in detail how this mechanism works?
It has been discussed before, but in light of some of the , I can't help but wonder what is accomplished by displaying the author of a given question or answer.  There is a , but if anything, I don't think it goes far enough.  If questions and answers are supposed to stand on their own merit, why do we need to show the author at all?  I'm not proposing any change to the way rep works; rep should still be accrued and abilities gained.  The only difference is that questions and answers would appear anonymous.  Does this better reflect the goals of SO?  If so, how far do you think the anonymity should be taken?  If not, what shortcomings am I missing? Let's consider a polynomial ring of single variable. One can define them informally by saying $P(X)=\sum_{i=1}^n a_n X^n$ while $X$ is an indeterminate variable. However, since mathematics is based on first-order logic, one can only talk about something that actually exists (as a set). So as its name says, indeterminate variable is not a sentence in $ZFC$. Nevertheless, we can formally define a polynomial ring $R[X]$ as a subset of $R^\omega$ whose support is finite. ($R$ is a commutative ring with unity) Just like a single variable, I want to know what would be the formal definition of a polynomial ring of several variables. What would be a formal definition? === I have figured out a candidate. That is,  Candidate for a &quot;Definition of a polynomial ring $R[X_1,...,X_n]$&quot;. ($R$ is a commutative ring with unity) Let $R[X_1,...,X_n]$ be the set of all functions $f:\omega^n \rightarrow R$ whose support is finite. Define $(f+g)(a,b,c)=f(a,b,c)+g(a,b,c)$ and $(f•g)(a'',b'',c'')=\sum_{a+a'=a''} f(a,b,c)•g(a',b',c')$ (Note that in this way, $+,•$ are well defined.) Then, it can be checked that $(R[X_1,...,X_n],+,•)$ is a ring.  Is this a formal definition of a polynomial ring? Hide and seek game $A$ and $B$ go to the Senate to play a game of Hide-and-Seek. There are $100$ rooms in the Senate, and $B$ picks one of them and hides there till the game ends.  $A$, at the beginning of every turn, picks one room and searches in it. Since he is human and thus fallible, he only has a $60\%$ chance of finding $B$ if she is in fact hiding in the room. If he fails to find her in the room, $B$'s score increases by one, and the next turn starts, whereupon $A$ must pick another room to check (he can also check the same room again). $B$ remains in the room she initially chose.  Given that $A$ and $B$ play with perfect strategies, what is the expected value of $B$'s score at the end of the game?  I tried with $1$ room. There is only one hiding place for $B$. So the expected score of $$B = \sum_{n=1}^{\infty}0.4^{n-1}0.6(n-1)=\frac{2}{3}.$$ This thought occurred to me earlier and I'm surprised I hadn't considered it previously. I get the feeling that no meaningful generalization can occur in a non-separable Banach space but on the surface it seems like a meaningful generalization can be had if the Banach space is separable. Even if it's possible, convergence and other issues likely severely complicate the matter. I'm trying to model my face on Blender using  and it gives links to reference photos.  The thing is, as I mentioned above, I want to try and model my face.  So I've decided to take photos of my face. But it doesn't seem to be working well (not symmetrical enough and stuff), so how exactly should I take my reference photos so that it would work well when I try to model it with the Mirror modifier?  Note: I only have the 'webcam' on my Macbook Pro and the camera on my Hongmi phone and I don't want to spend money on a new camera. Is there a way to substitute aliases such that it is appended or prepended to an existing command in the shell?   For example, defining the alias:  alias execloc='/home/user/'   Prepending this to a command in the bash terminal:  cd exeloc/temp/somefolder   Can something like this be done, or is there a way to do it? Any site that I visit can see my local IP (e.g. 192.168.1.102). Is there any reliable way to block this behavior? (browser setting, OS setting, router setting, etc.) I am particularity interested in Google Chrome and Mozilla Firefox, but any modern open source browser will do. If it is a browser plugin, it should be open source with a solid user base.  By reliable I mean, that I do not need to check the leakage again after every software update.  More info / what I have read so far:   There was a Chrome plugin that is not working anymore Local IP is obtained using JavaScript / WebRTC   Live Demo here:  Source code:   Firefox developers is not going to fix the leak (bug is open from 2014):  In Private / Incognito mode does not prevent this leak. If you use static IPs, and have non typical local IP (e.g. 10.66.77.88 or 192.168.212.121), then there is no need for . Your external IP + internal IP is perfect fingerprint.   Update 1: It is not duplicate of  - I want to prevent private / local IP leak, not disable all WebRTC.  Update 2: No, it is not related to header X-Forwarded-For (HTTP_X_FORWARDED_FOR), that is added when user/administrator chooses to do so. In my provided demo it is not your choice... It is Google's and Mozilla's choice to leak your private IP even when using private browsing mode.  Update 3: Ability to determine my local IP allows malicious JavaScript to quickly identify my local subnet and print on my local network printers from any website in the world without me doing anything.  This  finds my LAN printers using JavaScript.  Update 4: It is not a good idea to reveal private IP to every website. By seeing your private IP, for example 192.168.88.101, I can guess with very high probability that you are using MikroTik router. Also, I can track particular user event if user uses different browsers because local and remote IP stays the same for some time (hours or even days). I have some questions with string theory:   Why is it that there is exactly 4 large spacetime dimensions while the rest remain small? It is a nonlocal QFT. How could that fit in GR? I just watched Planet Hulk. At the end the Hulk ends up with someone seemingly almost as powerful as he is. Are the Hulks (Green, Red, and She-Hulk) able to have children? Including all the jars in a directory within the Java classpath biblatex: remove commas between last and first names in bibliography How would you categorize email subjects to find similar emails? I have a list of email subjects like:  &lt;XYZ&gt; commented on &lt;ABC&gt; Weekly review for &lt;Company&gt; Your account is ready    And I want to find patterns in them so I can group them.  Is there a well known algorithm I can use?    Preferably with wide language implementations or easy re-implementation. The algorithm should be unsupervised. The number of different emails is not known.   Update:  I think I can break this down into two problems:   Group subjects by the similar words they use, resulting in the following. Each group should be very distinct from the rest (they should be almost perfectly exclusive) and the algorithm should give relatively small number of groups with good length of the common words.  [commented, on] [weekly, review] [your, account, is, ready]  Once grouped, it should be easy to find a state automaton that accepts only the group's subject and thus eliminates variable Then I can go back and check if there are any intersections and tweak the variables.   Having said that, is it better to use a completley different approach like neural nets maybe? I have zero experience with those, but if it makes more sense, I am open to learning. It's been more than a month since I have started using . It has these users with user names in the format of "user-random number". I have observed them in some of the stack activities, most of the time asking questions.   Does the moderators create them for their own purpose. If yes what purpose do they serve?   I mean a user is free to have any user name. But it's just a hunch that such users are actually moderators. I may be wrong; just need some clarification. Levels or First Differences, VECM or VAR for Ultimate Impulse Response Functions? I am tired of always trying to guess, if I should escape special characters like '()[]{}|' etc. when using many implementations of regexps.  It is different with, for example, Python, sed, grep, awk, Perl, rename, Apache, find and so on. Is there any rule set which tells when I should, and when I should not, escape special characters? Does it depend on the regexp type, like PCRE, POSIX or extended regexps? A generic list of anonymous class How do I run 32-bit programs on a 64-bit Debian/Ubuntu? I have a 64-bit (amd64 a.k.a. x86_64) Debian or Ubuntu installation. I need to run 32-bit (i386/i686) programs occasionally, or to compile programs for a 32-bit system. How can I do this with a minimum of fuss?  Bonus: what if I want to run or test with an older or newer release of the distribution? Clicking leave closed shows the reopen pop-up Generating hatched filling using Region functionality How can we compute the following limit:     $$\lim_{n\to\infty}(1+1/n^2)(1+2/n^2)\cdots(1+n/n^2)$$   Mathematica gives the answer $\sqrt{e}$. However, I do not know to do it.