If I have only one front door, and only one back door, and they are both red.  Which is correct:         The front and back door are red;   The front and back doors are red.      I feel that (1) looks wrong and that (2) indicates that there are a plurality of both front and back doors.
I wonder which of the two is correct:        I have a red and a blue car.   I have a red and a blue cars.      or        Everyone has a left and a right arms.   Everyone has a left and a right arm.      My (non-native) inclination would be for option 1, as it sounds better.  On the other hand, in the following examples, the plural sounds better to me.    Everyone has left and right arms. I have old and new cars. (when I only have only one old car and one new car) The left and the right arms are...   But are they correct?
Should I postpone my trip to Paris in 2nd week of Jan in light of recent protests? I’ve a date and I really waited long to make this happen. My gifrfriend is a bit worried about the security issue in Paris. Which locals think that the media is exagerrating the issue and the issue is small and non-threatening for tourists? Migration stats not consistent between sites Apparently, as a result of  it appears that Yannis and myself see different statistics when going to the programmers.SE.com migration stats tool and the stackoverflow.com tool respectively.    :        while I see:        Why are the rejection rates so radically different?  Which is correct?  (Or am I simply misinterpreting the data somehow and these are representing different statistics) In respect to a larger proof I need to prove that $(n-m) \mid (n^r - m^r) $ (where $\mid$ means divides, i.e., $a \mid b$ means that $b$ modulus $a$ = $0$). I have played around with this for a while now but to no avail and would be grateful if you could help me. Say i have this PHP code:  $FooBar = "a string";   i then need a function like this:  print_var_name($FooBar);   which prints:  FooBar   Any Ideas how to achieve this? Is this even possible in PHP? Story is in a medievalish setting and starts with a woman who has been falsely accused of being a witch being taken by 2 men to be sacrificed to a dragon.  She ends up befriending the (male) dragon, who is able to transform into various forms, including human, and can speak only the language of whatever form he is in. e.g. can speak English in human form, but can't in dragon form.  He needs to return to his dragon form every day at sunrise or he dies.  Contact with iron or steel causes him pain and prevents him from transforming.  Near the end of the book, he's been put in handcuffs by one of the two men from the start and the woman has to get the assistance of the other one (village blacksmith?) to remove them before sunrise, which they manage to do just in time.  I think I read it maybe 10 years ago.    I also remember it was a very short book, probably only about 100 pages. Why won't my YN-568EXII work with a flash trigger? I have a Canon 5DMk2 and have just bought 2 Yongnuo YN568EXII speed lights. I have an existing Yongnuo RF-603CII trigger, but I cannot get them to work together! Does anyone have any suggestions, as the manual is no use :( Thanks Steve If a Matrix Has Only Zero as an Eigen-Value Then It Is Nilpotent If $S$ is a nonempty subset of group $G$, then $S^{|G|}$ is a subgroup of $G$. Let $G$ be a group with $|G| = n$ and let $ \emptyset \ne S \subseteq G$.   I want to show that $S^n$ is a subgroup of $G$ where by $S^n$ I mean the set $\lbrace s_1\cdots s_n \; | \; s_i \in S\rbrace$. How can I get multiple stacked plots (ybar stacked, stack plots=y) in one diagram, such that there are multiple stacked bars for the same x-coordinate, each slightly shifted? Is there a way to reset pgfplot's zero levels after an \addplot command, such that the next \addplot[xhshift=...] doesn't add something to the current stack, but rather starts a fresh stack?  FWIW, overlaying two plots with scale only axis won't help; I need this to work with groupplot \mathcal(O) and font size I use the following mystic TeX so as to display the Landau's notations for big and small O.  There is one partial solution to improve the scriptscriptstyle so as to not use a small o : see the secund answer below. The problemen with \smallOBis is the wrong spacing, contrary to \smallO. How can I do this ?  % Sources : %     1) http://forum.mathematex.net/latex-f6/bonnes-commandes-de-base-t12278.html %     2) http://tex.stackexchange.com/questions/30944/mathcalo-and-font-size  \documentclass{article}     \usepackage{amsmath}     \usepackage{amsfonts}     \usepackage{amssymb}      \usepackage{graphicx}      \newcommand{\bigO}[1]{\ensuremath{\mathop{}\mathopen{}\mathcal{O}\mathopen{}\left(#1\right)}}      \newcommand\smallO[1]{         \mathchoice             {% \displaystyle                 \ensuremath{\mathop{}\mathopen{}{\scriptstyle\mathcal{O}}\mathopen{}\left(#1\right)}             }             {% \textstyle                 \ensuremath{\mathop{}\mathopen{}{\scriptstyle\mathcal{O}}\mathopen{}\left(#1\right)}             }             {% \scriptstyle                 \ensuremath{\mathop{}\mathopen{}{\scriptscriptstyle\mathcal{O}}\mathopen{}\left(#1\right)}             }             {% \scriptscriptstyle                   \ensuremath{\mathop{}\mathopen{}{o}\mathopen{}\left(#1\right)}             }     }      \newcommand\smallOBis[1]{         \mathchoice         {% \displaystyle             \scriptstyle\mathcal{O}\left(#1\right)         }         {% \textstyle         \scriptstyle\mathcal{O}\left(#1\right)         }         {% \scriptstyle         \scriptscriptstyle\mathcal{O}\left(#1\right)         }         {% \scriptscriptstyle         \scalebox{0.8}{$\scriptscriptstyle\mathcal{O}$}\left(#1\right)         }     }   \begin{document}  \[     \renewcommand{\arraystretch}{1.2}%     \begin{array}{llll}          \textbf{Style}            &amp; \verb!\bigO!         &amp; \verb!\smallO!                          &amp; \verb!\smallOBis!         \\ \hline         \verb!\displaystyle!      &amp; \displaystyle      \bigO{\frac{1}{n}}         &amp; \displaystyle      1 + \smallO{\frac{1}{n}} - 2 &amp; \displaystyle      1 + \smallOBis{\frac{1}{n}} - 2         \\         \verb!\textstyle!         &amp; \textstyle         \bigO{\frac{1}{n}}         &amp; \textstyle         1 + \smallO{\frac{1}{n}} - 2 &amp; \textstyle         1 + \smallOBis{\frac{1}{n}} - 2         \\         \verb!\scriptstyle!       &amp; \scriptstyle       \bigO{\frac{1}{n}}         &amp; \scriptstyle       1 + \smallO{\frac{1}{n}} - 2 &amp; \scriptstyle       1 + \smallOBis{\frac{1}{n}} - 2         \\         \verb!\scriptscriptstyle! &amp; \scriptscriptstyle \bigO{\frac{1}{n}}         &amp; \scriptscriptstyle 1 + \smallO{\frac{1}{n}} - 2 &amp; \scriptscriptstyle 1 + \smallOBis{\frac{1}{n}} - 2     \end{array} \]  \end{document} I'd like to user a FIDO2 key to log into Windows 10. There are various guides explaining how to add a key to a Microsoft web account, or to Windows 10 sign in options, but neither result in showing up as an option when I try logging into Windows.  How can I configure windows to use my FIDO2 key to log in? Flag and close my own question Why is it possible to flag and close my own question?   The only realistic usage I could think of is when I see that my question is a duplicate, but it has already got some great answers. So instead of deleting the question, I would vote to close it as a duplicate.   But still, I can't see how flagging my own question would be useful. Am I going to have trouble flying without my full name on the ticket? Number of integer solutions of $x^2 + y^2 = k$ I'm looking for some help disproving an answer provided on a  I posted about computing the number of double square combinations for a given integer.    The original question is from the Facebook Hacker Cup       Source: Facebook Hacker Cup   Qualification Round 2011      A double-square number is an integer $X$   which can be expressed as the sum of   two perfect squares. For example, 10   is a double-square because $10 = 3^2 + 1^2$.   Given $X$, how can we determine the   number of ways in which it can be   written as the sum of two squares? For   example, $10$ can only be written as $3^2 + 1^2$   (we don't count $1^2 + 3^2$ as being different). On the other hand,   $25$ can be written as $5^2 + 0^2$ or as   $4^2 + 3^2$.      You need to solve this problem for $0 \leq X \leq 2,147,483,647$.      Examples:      $10 \Rightarrow 1$      $25 \Rightarrow 2$      $3 \Rightarrow 0$      $0 \Rightarrow 1$      $1 \Rightarrow 1$   In response to my original question about optimizing this for F#, I got the following response which I'm unable to confirm solves the given problem correctly.       Source:       Again, the number of integer solutions   of $x^2 + y^2 = k$ is four times the   number of prime divisors of $k$ which   are equal to $1 \bmod 4$.      Knowing this, writing a program which   gives the number of solutions is easy:   compute prime numbers up to $46341$ once   and for all.      Given $k$, compute the prime divisors of   $k$ by using the above list (test up to   $\sqrt{k}$). Count the ones which are   equal to $1 \bmod 4$, and sum. Multiply   answer by $4$.   When I go through this algorithm for $25$, I get $8$ which is not correct.          For each prime factor (pf) of $25$ ($5$, $5$ are prime factors of $25$)         if pf % $4$ = $1$ (true for both $5$'s), add $1$ to count      return $4$ * count (count would be $2$ here).          So for $25$, this would be $8$ Show that any prime ideal from such a ring is maximal. Let R be a commutative ring with an identity such that for all $r\in$ R, there exists some $n&gt;1$ such that $r^n = r$. Show that any prime ideal is  maximal. (Atiyah and MacDonald, Introduction to Commutative Algebra, Chapter 1, Exercise 7.)    Any hints? What should be in the sources.list for Kali Rolling Linux? This is exact content from my sources.list:  #  # deb cdrom:[Debian GNU/Linux 2016.1 _Kali-rolling_ - Official Snapshot amd64 LIVE/INSTALL Binary 20160830-11:29]/ kali-rolling contrib main non-free #deb cdrom:[Debian GNU/Linux 2016.1 _Kali-rolling_ - Official Snapshot amd64 LIVE/INSTALL Binary 20160830-11:29]/ kali-rolling contrib main non-free   I couldn't install the Synaptic package manager and was told to modify sources.list.  I googled a lot and added some repos into it and ran update and upgrade command only to see Kali crash... I had to recover it.  Please mention the exact content that should be there to ensure that Kali Linux works. I know that the Windows copy dialog (in Windows&nbsp;XP) stores the copy in memory first, and it is still copying after the dialog closes, so the time is off, but why is the estimation of the time it will take to make a copy so inaccurate, even when memory copying has been disabled (in Vista and Windows&nbsp;7)? It seems so arbitrary! How does the whole copy procedure work, and why can't Windows estimate it correctly? Center figure that is wider than \textwidth How to reset the terminal properties and preferences? I fooled around with the colors and stuff, in the terminal, and now want to go back to the maroon and white default config of the the terminal. What files do I have to delete? Regression Proof that the point of averages (x,y) lies on the estimated regression line How do you show that the point of averages (x,y) lies on the estimated regression line?