Show that if any ten of eleven integers can be split into two sets with the same total, then the eleven integers must be equal.
After removing any part the rest can be split evenly. Consequences?
How can I efficiently drive an LED? I understand that I can not connect an LED directly to a battery because it will draw too much current. Thus, there must be something else in the circuit to limit the current. What options are there? Are some methods more efficient than others? How do I apply a patch file? How does linear regression use the normal distribution? How do I get permissions to delete files on Windows 7? I updated my laptop's OS from Windows XP to Windows 7. There are some leftover files from Windows XP on the computer now. If I try deleting them I get the following error:     You need permission to perform this action.      You require permission from S-1-.... to make changes to this folder.   What's weird is that I am logged in with the only user account on this machine and I have administrator privileges. I tried turning UAC off, but I still can't delete the files.  How can I force removal of these files? I would like to compare the contents of a couple of collections in my Equals method.  I have a Dictionary and an IList.  Is there a built-in method to do this?  Edited: I want to compare two Dictionaries and two ILists, so I think what equality means is clear - if the two dictionaries contain the same keys mapped to the same values, then they're equal. Why is there an emission of gamma rays? When a spontaneous radioactive reaction happens, there is an emission of gamma rays (in most cases) What causes this emission? Let's say that a player uses the ready action and says "If a character aims at me with a weapon, I'll use Teleport to move behind cover."  What happens? Does this work? If not, please cite the rules to explain why not. $\sum_{n=1}^\infty \frac{i^n}{n}$ converge? Generating x,y coordinates for an edge detection of image I saw this movie a while back. I don't remember how it starts, but from where I remember watching it, it may have not been too far from the start. Apparently, Earth has been conquered by some alien empire or something and humanity are basically cavemen being used as slaves. From what I remember, the main antagonist alien is seen taking one of the slaves to a room where a machine is used on him to make him smart; this is apparently a big no-no so the main antagonist and his sidekick have to keep it quiet. The idea was that by making one of the slaves smart, it could increase the work output of the others. Apparently the antagonist is using the slaves on Earth to gather gold bullion  which is apparently still very valuable to the aliens but he's doing it illegally (not the slave labor; that's apparently ok). The protagonist who had the machine used on him becomes the intermediary between the slaves and the aliens and begins teaching the other slaves. I remember him teaching them mathematics and I remember him saying that it was universally accepted (I think he may have been referring to algebra or trigonometry). At some point he becomes aware that they are slaves and organizes a plan to free not only his fellow slaves but the Earth. Some escape and find an old museum which has old flight simulators, and shows that humanity wasn't always a slave race and that it may have been modern times in which Earth was invaded (i.e. no lasers or starships). I think they also find Fort Knox as there is a huge collection of gold bricks and weapons. The protagonist comes up with a plan to destroy some sort of teleporter the aliens use to transport stuff to and from Earth, however that alone wont be enough as they could fight back, which will be bad for humanity, which is still undeveloped. So the plan also includes using the teleporter before destroying it to to transport and detonate a nuclear warhead on the alien home world which apparently cripples any attempt to immediately send a fleet but also as a show of strength. After executing their plan, the main antagonist is captured by the humans and as an insult is locked in a cage surrounded by the gold he sought. If I recall correctly the place is set to detonate as to destroy the precocious gold and that will be used against the aliens should they mobilize a fleet in the future (i.e. attack us and we destroy Earth's supply of gold). The antagonist's side kick for some reason I remember as a big black man from whom the antagonist had removed his hand at some point and also apparently the antagonist was cruel to him. After the antagonist is locked up, he is trying to appeal to his sidekick's loyalty, however the sidekick takes the humans' side, I'm also getting an image that apart from treating him kindly the sidekick's missing hand was restored. So, I'm working on a control station that has buttons. It is a one-mesh creation, that means, I don't want to create buttons and things like that separated from the main mesh, but as you can see, I have problems. I would like to make the highlighted parts to be one with the main part around them. I've tried everything, and I have this problem on multiple creations. Any idea?  Update: I've added another example of the problem. I want them to be one face, instead of two. (2nd picture) Show that $\tan{(\pi/7)} \tan{(2\pi/7)}\tan{(3\pi/7)}=\sqrt{7}$ I just bought a new HP Pavilion dv7t Quad Edition laptop that has HDMI out. I already have a couple of monitors that are VGA and I'd like to hook up one of these to dual monitors.  I've read some sketchy reviews of products that try to convert directly from HDMI (digital) to  VGA (analog), so I was wondering if someone has a good recommendation on how to hook these two together. I usually am able to render successfully to the c:\tmp folder, but when I came into work today, I rendered out the image on my work laptop, and everything seems to work, but I'm not getting an output to the tmp directory.  Does anyone know how to make this work? "Software Updater" & "Software & Updates" not working I havent used my Ubuntu for quite a long time.  Today, when I booted Ubuntu (14.04 LTS), the software updater and Software &amp; Updates (from Settings) are not working.  The software updater's window will show up for around 1 sec, but it will close automatically. Software &amp; Updates is never shown, no matter how many times I click the icon. Note that neither of them show any error message.  Those 2 features were working perfectly the last time I used Ubuntu. I want to do some system upgrade and update.  For now, I use sudo apt-get update &amp;&amp; sudo apt-get upgrade. This command runs very fast, meaning (I think) my Ubuntu is not updated properly. The update from software updater always has a big size hence the download should be slower.  What should I do?   Can I just uninstall and reinstall both of them? If I can, how to do it?  Just to clarify, I don't want to upgrade my Ubuntu version (I want the LTS one), I just want to upgrade the software/packages I used.  Thanks for your time. Is it correct to sometimes capitalize words mid-sentence in computer user interfaces? Currently, for all my commands that require root access, I have to type them out on a command line.  I would like for the GUI to prompt me to key in my password, when sudo is required, instead of having to type out the commands from command line.  Is there any way to enable this? Previously one version of Ubuntu desktop had this feature out of the box.  This version of Ubuntu (that I am now running) I upgraded from a server installation.  I will add, my user account is already added to sudo group. Thus I can run commands such as sudo gedit or sudo apt-get but I'm not able to install software in the Ubuntu Software Center. Prove the series $ \sum_{n=1}^\infty \frac{1}{(n!)^2}$ converges to an irrational number How can one prove that the series $\displaystyle \sum\limits_{n=1}^\infty \frac{1}{(n!)^2}$ converges to an irrational number? There's no need to use Taylor expansion, integrals or any advanced/professional techniques. It can be proved using only basic techniques. My first attempt was to assume that the series does converge to a rational number $ \frac{p}{q}$ and then it follows by definition that for every positive epsilon there exists an integer k such that $ {\sum_{n=1}^{k} \frac{1}{(n!)^2} -\frac{p}{q}}&lt;=\epsilon$ I tried to get a contradiction but I failed. How can I prove that $xy\leq x^2+y^2$? How can I prove that $xy\leq x^2+y^2$ for all $x,y\in\mathbb{R}$ ? Idea behind proof that $\frac{21n+4}{14n+3}$ is irreducible for all $n$