How rare are magic items?
How rare are magic items and how many should I be handing out?
We have in and out degree of a directed graph G. if G does not includes loop (edge from one vertex to itself) and does not include multiple edge (from each vertex to another vertex at most one directed edge), we want to check for how many of the following we have a corresponding graph. the vertex number start from 1 to n and the degree sequence are sort by vertex numbers.  a) $d_{in}=(0,1,2,3), d_{out}=(2,2,1,1)$  b) $d_{in}=(2,2,1), d_{out}=(2,2,1)$  c) $d_{in}=(1,1,2,3,3), d_{out}=(2,2,3, 1,2)$  I want to find a nice way instead of drawing graph.  for (C): Repeat copies of array elements: Run-length decoding in MATLAB Do the same camera settings lead to the same exposure across different sensor sizes? Let's say I have a micro-4/3rd camera and a full frame camera, both set to 1/60 at f/2.8, taking a picture of the same scene in the same lighting. Will the exposure be the same across both cameras despite the different sensor sizes?  The reason why I'm asking is because of the difference in depth of field between micro-4/3 and full frame sensors. I'm finding that, in order to take a picture of certain scenes with the full frame camera at the same depth of field as the micro-4/3rd camera, I have to increase the aperture, which in turn forces me to crank up the ISO. Help needed with definite integral for $\lim_{n\rightarrow \infty}\sum_{k=1}^{n} \frac{1}{n+k}$ Why is the multiplicative group of a finite field cyclic? Why is the multiplicative group $(K\smallsetminus\{0\},\cdot)$ of a finite field $(K,+,\cdot)$ always cyclic? Regular expression for URL Say I have the following CSS and HTML code:    #header {   height: 150px; } &lt;div id="header"&gt;   &lt;h1&gt;Header title&lt;/h1&gt;   Header content (one or multiple lines) &lt;/div&gt;     The header section is fixed height, but the header content may change.  I would like the content of the header to be vertically aligned to the bottom of the header section, so the last line of text "sticks" to the bottom of the header section.  So if there is only one line of text, it would be like:   ----------------------------- | Header title | | | | header content (resulting in one line) -----------------------------   And if there were three lines:   ----------------------------- | Header title | | header content (which is so | much stuff that it perfectly | spans over three lines) -----------------------------   How can this be done in CSS? How do I use the chrome driver in Ubuntu 16.04? How to read value of variable, where the name of variable is the value of another variable I think an example is in order. Consider I have these two environment variables setup (by a Continuous Delivery tool): PACKAGE_VER=1.2.3 and USE_VERSION_FROM=PACKAGE_VER.  What I want now is a script that can't predict the name of the variable pointing out 1.2.3, only USE_VERSION_FROM. And so, I'm looking for a way to get my script to know the version to use (1.2.3) without knowing anything other than that USE_VERSION_FROM points out the name of the variable that holds the version number.  My naïve non-working first attempt:  #!/bin/bash VERSION_TO_USE="${${USE_VERSION_FROM}}" I am running 12.04 LTS. It's a pretty default installation and is the only OS on this machine.  I have two users one has administrator rights the other does not. I accidentally removed administrator rights from the "admin" user.  I tried to  but that requires reaching GRUB during boot but I cannot get there because my /etc/default/grub has GRUB_HIDDEN_TIMEOUT=0 and changing that to a positive integer requires admin privileges to save the changes and run sudo update-grub.  Should I boot from LiveCD? The  discouraged my a bit. Right now all I have handy is an install DVD from 11.10, but that did not help me much.  Not sure what to do now.  Any suggestions?  NOTE: 12.04 does not have an admin group and I have not enabled root Auto mount a disk drive in ubuntu 14.04 LTS (Bookmark directory not found) There is (there's) vs.There are What are the roots of the creeping usage of "there's" for both singular and plural predicates? (This seems to be more common in spoken English.) I have 2 theories.  Perhaps it is because spoken communication our society is becoming less formal by the day. Or perhaps it is a reflection of speakers of other languages having increasing contact with native English speakers.  I am aware of German  "es gibt" and Spanish  "hay" constructions. Please comment.  3/06/14 I ran a couple of Google Ngrams and was surprised to find a greater rise in the use of "there's" in English fiction than in general English language books, since the turn of the century.  This would seem to support my contention that informality is behind the shift. All group homomorphism from $ \mathbb{Z} _m $ to $ \mathbb{Z}_n $  How could I find every group homomorphism? I have a burning desire to install RPMs onto my Ubuntu installation - is this possible? Can I use Yum - or another RPM Package Management tool? Is there any way to set a MacBook Pro to not sleep when you close the lid? Could any one give an example of a bijective map from $\mathbb{R}^3\rightarrow \mathbb{R}$?  Thank you. What are the differences between a bridge camera and a DSLR? Is there a way to write binary literals in C#, like prefixing hexadecimal with 0x? 0b doesn't work.  If not, what is an easy way to do it? Some kind of string conversion? Make gnome-terminal show the command running as title I want the name of command running , e.g unzip to be visible through the title bar of gnome-terminal , but it seems to be impossible , if the application running doesn't set a title explicitly , even though I choose 'Replace initial title' option in the profile dialog. How is the derivative of $\textrm{Trace}\left\{ X^T A X B\right\}$ with respect to $X$ equal to $AXB + A^TXB^T$?