How many possibilities are there to arrange the letters of the word MISSISSIPPI, such that no S is next to another S?  Here are some possible examples:   SMSISISIPPI MSISISISPPI MISISISPPIS   Note that there is never something like SSS.  Or in other words: No S touches another S!
How many arrangement of the letters in MISSISSIPPI have at least 2 adjacent S's?  I was thinking that I can glue two of the S's together, so there will be 9 letters plus the special letter SS, and the number of arrangements will be $10!/(2!2!4!)$, this is not the correct answer, but what is wrong with my reasoning.  (the correct answer is $11!/(4!4!2!)-7!/(4!2!)\binom{8}{4}$, I understand the solution)
Category Theory textbook (learning through guided discovery Dummit and Foote) How to enable assembly bind failure logging (Fusion) in .NET How do I enable assembly bind failure logging (Fusion) in .NET? I'm calculating the covariance of a distribution in parallel and I need to combine the distributed results into on singular Gaussian. How do I combine the two?  Linearly interpolating between the two almost works, if they are similarly distributed and sized.   provides a forumla at the bottom for combination but it doesn't seem right; two identically distributed distributions should have the same covariance, but the formula at the bottom of the page doubles the covariance.  Is there a way to combine two matrices? While I'm aware of  it does not quite answer my question. I have a simple sentence:     If any of the devices was not switched off, do something.   Is there supposed to be was or were? I was thinking about was since it could be rephrased as:     If any one of the devices was not switched off, do something.   But maybe that does not make any sense at all. Also, this is for a technical documentation where more formal language is preferred, not sure if that makes any difference. Let $f,g:X\to Y$ be maps of spaces such that $f\simeq g$. Is it true that the mapping cones $\operatorname{cone}(f)$ and $\operatorname{cone}(g)$ are homotopy equivalent?  Can we write down an explicit homotopy equivalence? It ought not to be too hard to get a map $\operatorname{cone}(f)\to \operatorname{cone}(g)$ from the existence of a homotopy $H:X\times I\to Y$, but I haven't been able to find a sensible candidate, despite trying for quite a while. Showing the norm' is non-negative error with inner class object Installing QGIS on Ubuntu 14.04? Following the QGIS installation guide I have tried both UbuntuGIS and QGIS stable, but both fail with the error message:  The following packages have unmet dependencies:  python-qgis : Depends: python-qgis-common (= 2.6.1.1+trusty1) but it is not going to be installed             Depends: libqgispython2.6.1 but it is not going to be installed            Depends: libqgis-analysis2.6.1 but it is not going to be installed            Depends: libqgis-core2.6.1 but it is not going to be installed            Depends: libqgis-gui2.6.1 but it is not going to be installed            Depends: libqgis-networkanalysis2.6.1 but it is not going to be installed   qgis : Depends: libgdal1h (>= 1.8.0) but it is not going to be installed      Depends: libqgis-analysis2.6.1 but it is not going to be installed     Depends: libqgis-core2.6.1 but it is not going to be installed     Depends: libqgis-gui2.6.1 but it is not going to be installed     Depends: libqgis-networkanalysis2.6.1 but it is not going to be installed     Depends: qgis-providers (= 2.6.1.1+trusty1) but it is not going to be installed     Recommends: qgis-plugin-grass but it is not going to be installed     Recommends: qgis-plugin-globe but it is not going to be installed   E: Unable to correct problems, you have held broken packages.    I had QGISv.2.4 running on my machine with Ubuntu 12.04. After upgrading to Ubuntu 14.04 I was getting error message that pyqgis could not be loaded.  So I uninstalled QGIS using the Ubuntu Software Center and also run  sudo apt-get purge qgis   After that I tried to install the latest version of QGIS Debian Stable and UbuntuGIS unstable but getting the error messages described above.  The weird thing is that neither Ubuntu Software Center nor apt-get list have QGIS listed as installed, but if I run a search for qgis on my file system qgis and all its dependencies are still there. That's why I getting told to have broken packages. How run a .jar file with a double-click? Tempdb Add files require Restart Does adding Tempdb files require a restart? We would like to Add files on the same drive, Not Delete and Not modify. We tested in Dev and QA environment, restart was not required. However for production I would like to be sure everything works properly. Some are stating conditions, not always necessary, sometimes necessary, I am reading resources below:  ALTER DATABASE [tempdb] ADD FILE ( NAME = N'tempdev2', FILENAME = N'G:\tempdb2.ndf' , SIZE = 12288000KB , MAXSIZE = UNLIMITED, FILEGROWTH = 0 ) GO ALTER DATABASE [tempdb] ADD FILE ( NAME = N'tempdev3', FILENAME = N'G:\tempdb3.ndf' , SIZE = 12288000KB , MAXSIZE = UNLIMITED, FILEGROWTH = 0    Do You Need an Outage to Add tempdb files? Brent Ozar  "Technically, not always. But practically speaking, yes. If you have to shrink files, that’s very difficult while SQL Server is in use, and we’ve seen cases where anti-virus/file control tools didn’t act up until SQL Server was restarted after the files were added."   "Once the additional files have been created, it’s not always necessary to perform a service restart.  However, in many production environments, simply modifying the filesize of the existing TempDB datafile (tempdev) is not possible without restarting services first. "  The following resources are saying no restart required: How does reflection work? Applications of complex numbers to solve non-complex problems Recently I asked a question regarding the diophantine equation $x^2+y^2=z^n$ for $x, y, z, n \in \mathbb{N}$, which to my surprise was answered with the help complex numbers. I find it fascinating that for a question which only concerns integers, and whose answers can only be integers, such an elegant solution comes from the seemingly unrelated complex numbers - looking only at the question and solution one would never suspect that complex numbers were lurking behind the curtain!  Can anyone give some more examples where a problem which seems to deal entirely with real numbers can be solved using complex numbers behind the scenes? One other example which springs to mind for me is solving a homogeneous second order differential equation whose coefficients form a quadratic with complex roots, which in some cases gives real solutions for real coefficients but requires complex arithmetic to calculate.  (If anyone is interested, the original question I asked can be found here: )  EDIT:  I just wanted to thank everyone for all the great answers! I'm working my way through all of them, although some are beyond me for now! My bibliography (made with biblatex) has all items close to each other. I would like to introduce some space between them, e.g. half a line.  How can I do this? When are "if" and "whether" equivalent? Are if and whether equivalent in sentences like the ones below?     How to determine if my saddle is too high?   How to determine whether my saddle is too high?         We should check if everything is okay now.   We should check whether everything is okay now. Matrices $B$ that commute with every matrix commuting with $A$ can I change value of $_SERVER['DOCUMENT_ROOT']? I'm trying to find out why my application is very slow on a certain machine (runs fine everywhere else). I think i have traced the performance-problems to hard-disk reads and writes and i think it's simply the very slow disk.  What tool could i use to measure hd read and write performance under Windows 2003 in a non-destructive way (the partitions on the drives have to remain intact)? How can I bake the cloth simulation into keyframed vertices or shape keyed vertices? I'm simulating a cloth. How can I bake the cloth simulation into keyframed vertices or shape keyed vertices? If $\omega \in \Omega^q(M)$, and $(\omega|_{U})_p = 0$, is $\omega_p = 0$? How should we handle downvote retaliation?