Number of combinations of two numbers from a list with repeating numbers?
extended stars-and-bars problem(where the upper limit of the variable is bounded)
How to mount a NTFS partition in /etc/fstab? I have two partitions that I want to mount on startup: /dev/sda3   /mnt/devel  ext4    defaults    0   2 /dev/sda2   /mnt/excess ntfs    defaults    0   2  The ext4 partition mounts fine (owned by me, writable only by me), but the NTFS mounts owned by root with R\W permission for all. How to fix this? drwxr-xr-x  7 amanda amanda 4096 2012-03-14 19:07 devel drwxrwxrwx  1 root   root   4096 2012-03-14 22:38 excess I have connected speakers to the back panel of my computer at work and I would like to have them always enabled (I can switch them off on the speaker casing). However when I connect headphones on the front panel system automatically says that the rear output is unplugged.  I found a solution to disable auto detection with Alsamixer and it works almost ok except the fact that after system restart I need to reconfigure the settings again... How can I set this once and forget about it? How to properly render smoke on a transparent background? When rendering volumes with Film > Transparent enabled, the alpha appears to be the wrong type (premultiplied/straight). In the 3D view it works as expected:    This is a known .  Is there any way to work around this? Most properties of a single binary operation can be easily read of from the operation's table. For example, given $$\begin{array}{c|ccccc} \cdot &amp; a &amp; b &amp; c &amp; d &amp; e\\\hline a     &amp; e &amp; d &amp; b &amp; a &amp; c\\ b     &amp; d &amp; c &amp; e &amp; b &amp; a\\ c     &amp; b &amp; e &amp; a &amp; c &amp; d\\ d     &amp; a &amp; b &amp; c &amp; d &amp; e\\ e     &amp; c &amp; a &amp; d &amp; e &amp; b \end{array}$$ it is easy to check that it is closed (no elements occur in the table which don't occur as row or column index), commutative (the table is symmetric), has a neutral element (the row and column of $d$ are copies of the index row/column), and has an inverse element for each element (there's a $d$ in each row and column). In other words, almost all important properties can immediately be seen. The only part missing is associativity.  Therefore my question: Is there a simple way to see directly from the operation's table (i.e. without doing explicitly all the calculations) if an operation is associative? transpose columns to rows How do you integrate $e^{x^2}$? I know that $\int{\frac{1}{x}}dx$ is simply $\ln{(x)}+c$ (-which is clearly unrelated to the problem but I just thought I would share anyway) but I am not sure how to approach $e^{x{^2}}$. Perhaps a substitution? Redirect, Change URLs or Redirect HTTP to HTTPS in Apache - Everything You Ever Wanted to Know About mod_rewrite Rules but Were Afraid to Ask This is a  about Apache's mod_rewrite.   Changing a request URL or redirecting users to a different URL than the one they originally requested is done using mod_rewrite. This includes such things as:   Changing HTTP to HTTPS (or the other way around) Changing a request to a page which no longer exist to a new replacement. Modifying a URL format (such as ?id=3433 to /id/3433 ) Presenting a different page based on the browser, based on the referrer, based on anything possible under the moon and sun. Anything you want to mess around with URL   Everything You Ever Wanted to Know about Mod_Rewrite Rules but Were Afraid to Ask!  How can I become an expert at writing mod_rewrite rules?   What is the fundamental format and structure of mod_rewrite rules? What form/flavor of regular expressions do I need to have a solid grasp of? What are the most common mistakes/pitfalls when writing rewrite rules? What is a good method for testing and verifying mod_rewrite rules? Are there SEO or performance implications of mod_rewrite rules I should be aware of? Are there common situations where mod_rewrite might seem like the right tool for the job but isn't? What are some common examples?   A place to test your rules  The  web site is a great place to play around with your rules and test them. It even shows the debug output so you can see what matched and what did not. One of my favorite quotes is by Alvin Toffler which says:     The illiterate of the 21st century will not be those who cannot read   and write, but those who cannot learn, unlearn, and relearn.   The way I understand "relearn" in the quote is to learn something new that is different from what was originally learned.  I'm wondering in general if "relearn" convey learning the same thing again, or a different thing, or it depends on the context of the sentence. Is the same thing true for "learn again"? Visiting Greece with back-to-back Schengen visas (One from Germany, other from Italy) My cursor is moving by every selection by large increments!  Normally when I use Blender, I am able to select and move objects to any coordinate. Now, all of the sudden, when I select an object or mesh the selection moves by an inch or so in each direction.  How do I reset it to normal? Reputation graph not interactable with a touch screen How do I resolve samba share to IP address or host name I have a list of hosts in the network providing shares via SAMBA. How can I determine either IP address or the host name of one particular host, e.g. the one with the name “SASAK02”.  The output of smbtree is as follows  WORKGROUP     \\SASAK02                    \\SAURA-PC1                  \\PC-VAN-DAMME Which tool for fixing wobbly crank? Any idea what kind of tool should I but to fix the loose left crank on my bike? I found this  but not sure if it's gonna suit. Or is it enough to buy only nut driver? Is there a way to change the restrictions passcode on an iPhone without restoring the phone? I haven't forgotten the passocde; I just want to change it. Is infinity a real number?  If not, why not?  I want some very good arguments.   Thanks.  $$\rightarrow\leftarrow\Huge\Huge\Huge\boldsymbol\infty$$ If $\lim_{x\to\infty}(f(x)+f'(x))=L$ show that $\lim_{x\to\infty} f(x) = L$ and $\lim_{x\to\infty} f'(x) = 0$ Let $f:(0,\infty) \to R$ be differentiable. Suppose that $\lim_{x\to\infty}(f(x)+f'(x))=L$. Show that $\lim_{x\to\infty} f(x) = L$ and $\lim_{x\to\infty} f'(x) = 0$. (Hint: Write $f(x) = e^xf(x)/e^x$ and use l’Hopital’s Rule.)    My working for $\lim_{x\to\infty}f'(x)=0$:  For $\lim_{x\to\infty}f'(x) = 0$, I let $f(x) = e^xf(x)/e^x$ and applied quotient rule which then cancels off $e^{2x}$ and I'm left with $\lim_{x\to\infty}(f(x)+f'(x)-f(x))$. Can I then equate this with $\lim_{x\to\infty} \left(f(x)+f'(x)\right) - \lim_{x\to\infty}f(x)$ which then gives $L-L=0$? Is this step correct? Evaluating $\int_{-\infty}^{\infty}\frac{1}{(x^2+b^2)^2}dx$ Find $$\int_{-\infty}^{\infty}\frac{1}{(x^2+b^2)^2}dx$$   We see that the only poles are at $x=\pm bi$.  Integrating over the semicircular contour implies that it is equal to $2\pi i*Res_{(+bi)}$ because the integral over the circular arc is $0$.  So now I just need to calculate the residue at $+bi$. Can anyone give hints on how to do this?  I was thinking about multiplying by $(x-bi)^2$ and then evaluating at $bi$ but I'm not sure why this even makes sense. Creating controls within a Loop I have have some code which adds new cells to a table and fills them with text boxes.   The way I've coded it so far works fine:          TableCell tCell1 = new TableCell();         TableCell tCell2 = new TableCell();         TableCell tCell3 = new TableCell();         TableCell tCell4 = new TableCell();         TableCell tCell5 = new TableCell();         TableCell tCell6 = new TableCell();         TableCell tCell7 = new TableCell();          TextBox txt1 = new TextBox();         TextBox txt2 = new TextBox();         TextBox txt3 = new TextBox();         TextBox txt4 = new TextBox();         TextBox txt5 = new TextBox();         TextBox txt6 = new TextBox();         TextBox txt7 = new TextBox();          tCell1.Controls.Add(txt1);         tCell2.Controls.Add(txt2);         tCell3.Controls.Add(txt3);         tCell4.Controls.Add(txt4);         tCell5.Controls.Add(txt5);         tCell6.Controls.Add(txt6);         tCell7.Controls.Add(txt7);          tRow.Cells.Add(tCell1);         tRow.Cells.Add(tCell2);         tRow.Cells.Add(tCell3);         tRow.Cells.Add(tCell4);         tRow.Cells.Add(tCell5);         tRow.Cells.Add(tCell6);         tRow.Cells.Add(tCell7);   As you can see there's basically 4 instructions getting repeated 7 times. I'm sure there has to be a way to accomplish this with just 4 lines of code within a FOR loop and having all the names dynamically assigned but I just can't seem to find anything that would point me in the direction of how to do it.  Something like the following is what I'm after:      for (int i = 0; i &lt; 6; i++)     {          TableCell tCell[i] = new TableCell();         TextBox txt[i] = new TextBox();         tCell[i].Controls.Add(txt[i]);         tRow.Cells.Add(tCell[i]);      }    Any help would be much appreciated. Is it (theoretically) physically possible to project an image into thin air? Integral equation problem