Having done a fair bit of contest- type math, I was interested in trying to write similar sorts of problems, only to find myself immediately stumped. How does one write "elegant problems" of the kind that are found in the IMO and comparable national mathematics olympiads? Is it a question of just investigating some simple system, finding an interesting problem and solving it, or does one somehow consciously design the "trick" to solving the problem beforehand?
The problems that appear in difficult math competitions such as the IMO or the Putnam exam are usually very difficult and require some ingenuity to solve. They also usually don't look like they can be solved by simply knowing more advanced theory and the such.  How do people typically come up with these problems? Do they arise naturally from advanced mathematics (the somewhat infamous 'grasshopper problem' from the 2009 IMO comes to mind - to my not exactly knowledgeable mind this problem looks like it popped out of basically nowhere)? What is the perspective that mathematicians take when seemingly "inventing" these problems with no theoretical motivation to them whatsoever?
I want to select the value from the dropdown I am testing www.paytm.com  In that I have filled in the mobile number but I am not able to focus and select the mobile operator which is present in the dropdown just after the phone number section.  I want to select 'vodafone' as the value from the dropdown.  How to do that using webdriver  Code I have written till now  `  public class MMT {   public static void main (String[] args)  {  System.setProperty("webdriver.chrome.driver","E:/som/chromedriver/chromedriver.exe");  WebDriver driver = new ChromeDriver();  driver.get("http://paytm.com");  driver.findElement(By.id("mobile-number")).sendKeys("9876543212");`   What should be my next steps? How to specify font size less than 10pt (or more than 12pt)? I'm trying to make a document that has a very small font throughout, I tried this:  \documentclass[0.5mm, a4paper]{article} \documentclass[7pt, a4paper]{article}   But it doesn't seem that they allow me to go anything below 10pt.  This hack make it work, but not for the section headers:  \fontsize{4mm}{5mm}\selectfont   Does anyone know any better ways to do this? What is the difference between can and could in 'Can/could you please explain this to me?' Mean Time to Failure (MTTF): When disk manufacturers post this, how should you interpret their numbers? Mean Time to Failure (MTTF) is usually given in terms of hours, and by doing some calculations, it seems that a disk should fail only after a good number of years have gone by.  It seems that disks need repair more often than that. Does anyone know why this is so?  I figured that there is something fishy about this metric. Am interpreting something wrong here? Vertically align text next to an image? Prove $(x+y) \text{ mod } n = ((x \text{ mod } n)+(y \text{ mod } n)) \text{ mod } n,\,$ and product analog For all $n \in \mathbb{N}$, $n &gt; 1$ and $x,y \in \mathbb{Z}$ prove that      \begin{equation}   (x+y) \text{ mod } n   = ((x \text{ mod } n)+(y \text{ mod } n))\text{ mod } n. \end{equation}   Would this be a proof if I say:  Let $x = x' \text{ mod } n$ and let $y=y' \text{ mod } n$. Then  \begin{equation}   x+y = x'+y' \text{ mod } n. \end{equation}  Now, if we look at the current thing we want prove, this will follow:  \begin{equation}   x+y \text { mod } n = (x \text{ mod } n + y \text{ mod } n) \text{ mod } n. \end{equation}    I'm not sure if this is allowed or will count as a "proof" at all. Maybe you can show me some other ways of doing this, more precise ones? How do you minimise hand washing between every step to keep tools clean? Say you cooking beef steak:  You have to unwrap the beef from its packaging, lay it down, get blood on your hands, wash hands, sprinkle salt, wash hands, grind pepper, rub the seasoning into the beef, wash hands, grab the tongs etc..  Is it normal to wash hands after every step or is there a trick to avoid getting all the tools dirty?  If you watch TV, they don't ever wash as much as I do. jQuery: Uncheck other checkbox on one checked I'm positive that vs I strongly believe that In general, which one is conveys a stronger conviction/opinion? I did some quick google search but didn't find any interesting results.      I'm positive that   or     I strongly believe that Am I being scammed by a sugar daddy? What is the best way to filter a Java Collection? I want to filter a java.util.Collection based on a predicate. A new version of Ubuntu has been released. I still can't find it on ubuntu.com. Where can it be downloaded from, or is it the only way to install it using update-manager to upgrade an existing installation? As in  I'm trying to use apa6e and biblatex-apa together and having problems.  Before I arrived at these problems, over the course of many hours of much reading, I first managed to get BibTeX working as expected in a simple input file (by modifying sample2e.tex). Then I managed to get apa6e working as expected based on the author's example in apa6e.pdf (which uses apacite). But when I try to get apa6e working with biblatex-apa, I end up with problems.  Here's my input file:  \documentclass{apa6e}  \usepackage[american]{babel} \usepackage{csquotes}  % biblatex \usepackage[style=apa]{biblatex} \bibliography{biblatex-apa-test-references}  \title{An Example Document} \shorttitle{Psychology: the end} \author{Silly Name}  \authornote{\dots} \abstract{\dots}  \begin{document}  \maketitle  This is an example input\cite{7.01:2} file.  Comparing it with the output it generates can show you\cite{7.01:3a} how to produce a simple document of your own.  \printbibliography  \end{document}   Attempting to typeset this in TeXShop by running LaTeX, then BiBTeX (which based on console messages, does seem to correctly call biblatex rather than BiBTeX), then LaTeX again, I get the following error message which I am having great difficulty (no doubt due to my lack of experience with TeX and co.) decoding.  (./test6.aux) (/usr/local/texlive/2011/texmf-dist/tex/latex/psnfss/ot1ptm.fd) *geometry* driver: auto-detecting *geometry* detected driver: pdftex (./test6.bbl) Underfull \hbox (badness 10000) in paragraph at lines 18--18  []\OT1/ptm/m/n/12 An Ex-am-ple Doc-u-ment   Underfull \hbox (badness 10000) in paragraph at lines 18--18  []\OT1/ptm/m/n/12 Silly Name   Underfull \hbox (badness 10000) in paragraph at lines 18--18  []\OT1/ptm/m/n/12 Author Note  [1{/usr/local/texlive/2011/texmf-var/fonts/map/pdftex/updmap/pdftex.map}] Underfull \hbox (badness 10000) in paragraph at lines 18--18  []\OT1/ptm/m/n/12 Abstract  [2] Underfull \hbox (badness 10000) in paragraph at lines 18--18  []\OT1/ptm/m/n/12 An Ex-am-ple Doc-u-ment   Underfull \hbox (badness 10000) in paragraph at lines 25--25  []\OT1/ptm/b/n/12 References  ./test6.tex:25: Undefined control sequence. &lt;argument&gt; \mkbibdateapalongextra  (/usr/local/texlive/2011/texmf-dist/tex/latex/psnfss/ot1pcr.fd) (/usr/local/texlive/2011/texmf-dist/tex/latex/psnfss/ot1ztmcm.fd) (/usr/local/texlive/2011/texmf-dist/tex/latex/psnfss/omlztmcm.fd) (/usr/local/texlive/2011/texmf-dist/tex/latex/psnfss/omsztmcm.fd) (/usr/local/texlive/2011/texmf-dist/tex/latex/psnfss/omxztmcm.fd) Overfull \hbox (8.03372pt too wide) in paragraph at lines 25--25 [][]  \OT1/ptm/m/n/12 Gilbert, D. G., Mc-Cler-non, J. F., Ra-bi-novich, N. E.,  Sugai, C., Plath, L. C., As-gaard, G., ... Botros,  ./test6.tex:25: Undefined control sequence. &lt;argument&gt; \mkbibdateapalongextra                                    {year}{month}{day}\iffieldundef {endyear}{... l.25   I tried many different sources in several different *.bib files before eventually trying the .bib database shown above and included with biblatex-apa. All trials gave a similar error.  Can someone help? I'm impressed that the poster above was able to do anything with apa6e and biblatex-apa, and if I only had her problem of having the reference page title show up in bold, I'd be really happy.  If you need to know, my tools are from a fresh installation of MacTeX that I immediately updated using the TeX Live Utility. I've checked my versions for apa6e (v0.3) and biblatex-apa (v4.2), and I think these are current. I am debating whether or not to get the Potato Sack (yes, I realize I've been debating for several weeks now) bundle through steam.  I already own: Defense Grid: The Awakening, Super Meat Boy, and Audiosurf, all of which are part of the sack pack. What happens if I buy the Potato Sack?  Do I get 2nd copies of the three above mentioned games to gift elsewhere?  Is the price of the bundle reduced by the games I already have?  Do I get nothing special for already owning those 3 games? WITH ROLLUP WHERE x IS NULL Automatically resize uploaded images Possible Duplicate:             Could large images of more then 640 pixels wide automatically be resized to reduce loading time and band width use? Not that I have a prehistoric internet connection here, but sometimes pages seem to need unnecessary time to load fully.  I just resized the image  from 179 kb down to 32 kb using a 15% compression rate. I think that is already worth it, although there have been much bigger downsizes in the past.  This feature then propably should/could be combined with , and uploading an image then would result in the following post addition:  [![enter image description here][2]][1]  [1]: http://i.stack.imgur.com/ZSBxw.gif "View &lt;image title&gt; full sized" [2]: http://i.stack.imgur.com/VXmBA.jpg "&lt;Image title&gt;"   Update:  I now understand from  that images áre resized already, but that post authors have to do some changes themselves. Could it then be automated to add the already resized image (that with the l suffix):  [![enter image description here][2]][1]  [1]: http://i.stack.imgur.com/ZSBxw.gif "View &lt;image title&gt; full sized" [2]: http://i.stack.imgur.com/ZSBxwl.jpg "&lt;Image title&gt;" Endofunctors of $\textsf{FinVec}$ which are not $C^n$ How to validate an email address in JavaScript Use of would in sentences Disabling sound output devices (e.g. Internal Speakers) in OS X Since my Cinema Display is both connected through mDP and USB, I can (stupidly enough) both choose “LED Cinema Display” or “Display Audio”.  Also, I never use the internal speakers since they sound extremely tinny.    How do I remove/delete/disable unwanted audio devices? It must be possible somehow!