Hello community! The problem you see above is a combinatorial problem that I could not solve. :c  This problem seemed easy to me at first like there are people $1,2,3, \ldots, n$ sitting on a circular table and I thought that it was easy using casework and stuff. However, when I really started doing this problem, this problem seemed harder than I thought. I thought about complementary counting but that clearly won't help. From the example given above, I tried first adding singleton sets: $n$. But how do I find out the number of sets with two elements and so on? Recursion?? I really don't know.  Any help would be much appreciated. Thanks.
I have asked this question before  The first guy solved it in a way, but  i would like to know is there any efficient way to do so, because i did the same for N = 13 and N = 15  which took long time.  This problem is from a pen and paper test, ZIO-2018 Can i solve it with an efficient algorithm, well i am pretty beginner in algos, so if there is one kindly descibe it how can i do so?  Thank you
Is Checksum to file back decoding possible? So, I was having this weird thought. If the checksums(MD5 or SHA...) are unique to any file and are modified if any part of the file is edited, why cant the checksums be decoded back to get the original file? That is if I want to send a large(say 700MB) video, instead I could send just the hash and the file be decoded locally in my friend's computer. I know the thought is stupid, but is it possible by any chance? Or am I missing some thing here? And forgive me if I'm wrong, I ain't a professional. If $P(x^5)+xQ(x^5)+x^2R(x^5)=(x^4+x^3+x^2+x+1)S(x)$ , then prove that $P(x)$ is divisible by $x-1$ $P,Q,R,S$ are polynomials such that: $P(x^5)+xQ(x^5)+x^2R(x^5)=(x^4+x^3+x^2+x+1)S(x)$ , then prove that $P(x)$ is divisible by $x-1$   I thought a lot on this but no result!! By the way,one idea is to insert some values for $x$ and try to produce a system of equations for the given polynomials,but I'm not sure it works. Why do people go to the Wall in Game of Thrones? Is the wall a bad or a good place to be? Some people are sent there as punishment, others go because they want to (Jon Snow), others to get away from harm (Arya).  If I am not completely correct, it is because I have only started watching the series recently, and it is a bit confusing!  Please also correct me if I am wrong with any facts! Symbolizing layer with graduated colors by date/time field? I've got a layer of polygons where each has a date associated with it.  I want to color the polygons with graduated colors, but I want the colors to start with the newest polygons and fade to the oldest polygons.  So far I haven't been able to find a way to do this in ArcMap (&lt;= 9.3.1) other than to create a new field and calculate some integer or float value based on the date.  Is it possible to use a date or time field directly?   The data is natively a date-time value There are far too many records to use any unique-value renderer Converting the date to a numerical field is an answer for a different question. Which transformations are canonical? Which transformations are ? How can I install firmware-b43-installer driver if I can't connect to internet by wire? Give each site a parallel site for polling, recommendations and subjective-ish stuff Stuff like polls, recommendations based on subjective constraints, puzzles, webcomics etc. do not belong on the serious main SE sites, where professionals should be considered at work and having just a few spare minutes ("code's compiling") to answer questions, so they should not be distracted by such things. However, I'd also like to have a home for these things still using the SE engine. For the reason I mentioned before, this needs to be a separate place though. Let's call it four.[sitename-here].com. Changing parameter values according to other parameter choice in Processing script using QGIS 3? How to display citations in text grouped as [1-3] in stead of [1,2,3] Prove that the function : $f(x) = x$ when $x$ is rational and $f(x) = 1 - x$ when $x$ is irrational is continuous at $x = \frac{1}{2}$  To prove the continuity it is necessary to prove that for every $\epsilon$ there exists a $\delta$ such that $|f(x) - f(\frac{1}{2})| &lt; \epsilon$ whenever $|x -c| &lt; \delta$ $- (1)$ Now if we choose $a  € (\frac{1}{2} - \delta, \frac{1}{2} + \delta)$ and also $a $ is rational and choose $\epsilon &lt; |a - \frac{1}{2}|$ then condition in $(1)$ is not satisfied. How to move from here? How can I solve "Be aware that removing the lock file is not a solution and may break your system"? Removing the Bracket from the First Line of bmatrix How can I write a matrix with a header line that is not bracketed? I have used the following code to produce the results below. In addition of being ugly, it is impractical when I need to align the first row, n1, ..., n6 with the matrix columns.  \documentclass{book}  \usepackage{amsmath}    \begin{document}    \[ \ \ \ \ \ \ \ n_1\ \ \ \ \ \ \ \ n_2\ \ \ \ n_3\ \ \ \ \ \ \ \ \ n_4\ \ \ \ n_5\ \ \ \ n_6\]     \[ \begin{bmatrix}         1 &amp; -1 &amp; 0 &amp; 0 &amp; 0 &amp; 1\\         0.960 &amp; -0.977 &amp; 0 &amp; 0 &amp; 0 &amp; 0.983\\         0 &amp; 1 &amp; -1 &amp; -1 &amp; 0 &amp; 0\\         0 &amp; 0.977 &amp; 0 &amp; -0.983 &amp; 0 &amp; 0\\         0 &amp; 0 &amp; 0 &amp; 1 &amp; -1 &amp; -1\\         0 &amp; 0 &amp; 0 &amp; 0 &amp; 0 &amp; 1\\        \end{bmatrix}        \begin{bmatrix}n_1\\n_2\\n_3\\n_4\\n_5\\n_6\end{bmatrix} =        \begin{bmatrix}0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 100\end{bmatrix} \]  \end{document} Where does Minecraft for Windows 10 store its data? I have searched in %appdata%, pulling up the list of files there, but there is no file labelled .minecraft. Searching %appdata%\.minecraft returns "no results found".   I also opened Minecraft to click on the resources button and could not locate that either. How to get apache to send a 404 based on no matching VirtualHost section (based on ServerName) being found? I am rebuilding an old server.  Only one of the five old sites need to go live and all five of the old sites point to the same IP address.  Unfortunately any time a request is made for one of the old sites via their own unique domain names they are passed the pages from the one site that I'm trying to make live.  I would just like the old sites to display a 404 instead of the one site that I'm actually trying to make live.  As an example:   Site 1 (192.168.0.1) [www.first.com] Site 2 (192.168.0.1) [www.second.com] Site 3 (192.168.0.1) [www.third.com]   I want to move site 1 live again.  So I turned on apache on the machine with the IP address of 192.168.0.1, with all of site 1's files in the /var/www directory.  When I browse to 192.168.0.1 or www.first.com I correctly see site 1. When I browse to www.second.com and www.third.com I also receive site 1 which is the problem.  Is there a way I can 404 any request which comes in without www.first.com?  Here is my sites-available:  NameVirtualHost *:80  LogFormat "%h %l %u %t \"%r\" %&gt;s %b" common  &lt;Files ~ "^\.ht"&gt;     Order allow,deny     Deny from all     Satisfy All &lt;/Files&gt;  &lt;Directory /&gt;   Order Deny,Allow   Deny from all   Options None   AllowOverride None   Options None &lt;/Directory&gt;  &lt;Directory /var/www&gt;   Order Allow,Deny   Allow from all &lt;/Directory&gt;  &lt;VirtualHost *:80&gt;         ServerName first.com         ServerAlias www.first.com         DocumentRoot /var/www         ErrorLog /var/log/first.com.err         CustomLog /var/log/first.com.log common &lt;/VirtualHost&gt;  &lt;VirtualHost _default_:*&gt;         ServerName unknown         DocumentRoot /var/www_404 &lt;/VirtualHost&gt; Travel in the Schengen area after my residence card was lost or stolen I have already booked my flight from Italy to the Netherlands through Ryanair. I'm staying in Italy legally and have a carta di soggiorno. However, after booking my flight, my wallet was stolen, which contains all my IDs except my passport. I filed a police report, and I'm trying to get a new residence card. However, I need to go to the Netherlands ASAP. Will Ryanair accept the police report and receipt of getting a new residence card from the post office?  UPDATE (17.07.2014)  Thanks for helping me out. BTW it's OK now. I went to our local CISL here in Florence, Italy, where they process your envelope for renewing your permesso di soggornio or carta di soggiorno (residence permit for foreigners) to be submitted to the post office. That's where you pay and get your postal receipt, and they make an appointment for you at the questura. Anyway, long story short, they processed a application for IMPROVISED residence permit which is good for 30 days to travel within the Schengen area, so all I have to do is go to the questura, bring my travel booking, the police report and copy of my passport. Now I can travel, and it's my first time to fly with Ryanair because I always use Transavia to go to Holland. =) Hope this helps for future persons who will have the same issue with lost or stolen residence permits...Just wish me luck that the questura will process my improvised residence permit immediately. Java reflection: how to get field value from an object, not knowing its class Does the following limit exist? $$\lim_{x \to 0} x\sin\left(\frac{1}{x}\right)$$  If yes, then I have to find it; if no, then I need to give reason why. I couldn’t figure out how to prove this formally, can someone please help me out. Practical hyperparameter optimization: Random vs. grid search Everything I've seen points to no (and I would love that to be true since applying for a visa online costs money) but I'm worried about getting refused due to the length of time I wish to stay, which is 6 months.  I went to university in the UK on a Tier 4 visa, but have never just been a tourist which is what I would like to do now. Since graduating, I have started working but am underwhelmed and would love to travel again. My original plan was Australia but now I would like to see the rest of the UK as well beforehand.  If I arrived with the following, would I be refused entry simply for not applying online?: an approved Australian work &amp; holiday visa, a mini itinerary, bank statements for the last 6 months. 90's book about children climbing a tree and visiting different worlds from there In the 90's I read a book about two children (I think they were siblings, boy and girl) who climbed a tree. At the end they found a door to another world. After some time the (fantasy) worlds switched to another one. Once they got stuck in a world, because the world went on traveling and therefore the door couldn't be reached anymore. They met many curious individuals during their adventures.  It's a completed novel for kids. I've read it in German, but I can't remember if the author was a German one, so it might've been available in English as well. It was a fairly thick book.  EDIT: After some thought I remember a pancake kind of person