Travelling in the Kingdom of Crystal Skull, Indiana Jones discovered a small box with notation  $$ 3 x^2 - 25 x + 66 = 0 \implies  x_1 = 4,\; x_2 = 9, $$ which seems to be incorrect. However after some reflection he realised a number system other than the decimal was used to determine the roots of the quadratic equation. What is the base of that number system?
Try to solve this puzzle:     The first expedition to Mars found only the ruins of a civilization.   From the artifacts and pictures, the explorers deduced that the   creatures who produced this civilization were four-legged beings with   a tentatcle that branched out at the end with a number of grasping   "fingers". After much study, the explorers were able to translate   Martian mathematics. They found the following equation:   $$5x^2 - 50x + 125 = 0$$   with the indicated solutions $x=5$ and $x=8$. The value $x=5$ seemed   legitimate enough, but $x=8$ required some explanation. Then the explorers    reflected on the way in which Earth's number system developed, and found   evidence that the Martian system had a similar history. How many fingers would    you say the Martians had?      $(a)\;10$      $(b)\;13$      $(c)\;40$      $(d)\;25$   P.S. This is not a home work. It's a question asked in an interview.
Is there a way to determine which features / variables of the dataset are the most important / dominant within a k-means cluster solution? I'm trying to determine the best way to truncate or drop extra decimal places in SQL without rounding.  For example:  declare @value decimal(18,2)  set @value = 123.456   This will automatically round @value to be 123.46, which is good in most cases.  However, for this project, I don't need that.  Is there a simple way to truncate the decimals I don't need?  I know I can use the left() function and convert back to a decimal.  Are there any other ways? I can't find Karliah at the Ragged Flagon During the 'Hard Answers' Thieves Guild quest, Karliah asked me to meet her at the Ragged Flagon.  However, it seems that she doesn't show up at the rendezvous point.  Where do I find her? How to make sure one understands each and every detail while reading a textbook/research paper without leaving any gaps? I am a physics Master's student.  I have good grades, with CGPA above 9(/10)(However, all courses in my university are graded on a curve so the actual marks are significantly lower than 90%). This has been my marks throughout my undergraduate and graduate courses and I was happy because this was above average. Also, my summer projects in UG were usually computational and any difficulty I had in theoretical aspects I attributed it to my inexperience in advanced Physics.   However, recently I have started to work on pure theoretical project and while reading for the project I realized that I consistently miss some details from each topic. I understand the general idea, can re-derive most of the equations(with some effort) however when I discuss things with my professor or when I read further topics I realize that I have missed certain key-details. This is exactly similar to the case of me missing a few key questions in my exams and getting that 9 grade point instead of 10(or at-least I think so). I was not worried about this before but now I realize that there is some flaw in the way I study (but I do not know what).   Since I want to apply for Physics PhD I realized that I will need to have solid concepts and it would be best to correct my mistakes but I do not know how or even what could be the reason for my imperfect understanding.  Any direct suggestion would help or even certain general guidelines on what I can do.    Things I've tried recently -   1) I've started to written down almost everything I read. This is slightly laborious but is certainly helping. It also helps me to gloss over the things I read previously when I come back the next day.  2) I completely avoid smartphone when I'm library/study room so that I won't get distracted. Not sure if it helps me solve the above problem but certainly helps me study better in general.  3) I've tried to read the topics from several sources. The books I am reading is somewhat like a collection of research papers and hence does not have a exercises. So I though reading from various sources might help get better ideas but it's not really helping because most other sources are too high level as an introductory text. But this will probably help me in cases where it's practical to do this.  4) Somewhat similar to point (1)- I am trying reread, whenever I can, what I've done until that point. But not sure how much this will help me in filling the gaps. Are mounts proficient in armour (barding)? Bring all planes in mesh to same level I have added a plane in top view. I have then extruded the plane according to a floorplan in topview.  I don't know what happened, but when I switched my view, I could see that some parts of it are for some reason high up in the air.  I would like to ask how I can bring everything back down onto the grid / floor.  And if somebody could tell me how this might have happened, I would also be glad. What if 'kill -9' does not work? I have a process I can't kill with kill -9 &lt;pid&gt;. What's the problem in such a case, especially since I am the owner of that process. I thought nothing could evade that kill option. Expectation of truncated normal This started to happen immediately after I had rebooted the first time after doing a system upgrade. It first starts with a dialogue that says "System program problem detected". Then when I try to hit 'report problem' not much happens. I am led through a dialogue that always ends up the problem cannot be solved.  I am aware this is not a lot of information, however I'm not sure which information I need to publish and how should I obtain it to debug this problem.  Here's a screenshot! I'd like to be able to easily transfer large files wirelessly, fast, between Android devices - preferably without requiring root.  As a secondary objetive, it wouldn't hurt if the same solution could be used, to transfer files between the Android devices and a Windows PC.   Specifically, I'm trying to exchange files between my Nexus 7 (Android 4.2.2) and Samsung Galaxy S2 (Android 4.0.4).   Bluetooth is simply too slow, so that's out of the question Transfer via the Internet is also not an option, hence so is cloud-based solutions Only Nexus 7 supports NFC, so that's out too  looked promising and very simple, but does not work on "Devices that don't have WiFi Tethering setting, such as the Nexus 7"   Wi-Fi direct ( and up) seems to be a decent lowest common denominator between my two devices, however...  Galaxys S2's native Send via Wi-Fi Direct sees the Nexus, but seems to get stuck in the "Connecting..." most times. When there finally seems to be breakthrough, I get "Waiting..." and a spinning circle. Even if it worked, it would only allow me to send from the Galaxy S2 to the Nexus 7, as a similar option os not present on the Nexus 7.  J4velin's  is no longer available in the Play Store, with the following explanation:     WiFi Direct drivers are broken on many devices, which led to users leaving negative reviews for this app. As I don't see any sense in keeping a free app published when only getting 1-star-ratings (for an issue which only your device manufacturer can fix), the app is no longer available at the Play Store.   Nick Adams'  seems flaky at best. Invations from Nexus 7 to Galaxy S2 are never received. Invitations from Galaxy S2 are mostly received, but even when accepting promptly, the peers doesn't always show as connected. When they finally do, usually after quite a long wait, I can select a file to send but it's never transferred -  "Transfer failed" it says almost immediately in the notification bar.  budius inc's  is working slightly better, but still very unreliable. I actually managed to (occasionally) send files both ways, but never when attempting connection from the Nexus 7. To send from the Nexus 7 to the Galaxy S2, I had to go through this akward manoeuvre:   Share the file on the Nexus 7 via the WiFi Shoot intent Start the Receive WiFi Shoot app on the Galaxy S2 Invite the Nexus 7 from the Galaxy S2 (never the other way around!) Accept the invitation on the Nexus 7 Press the Shoot button on the Galaxy S2   Take the whole switching back and forth between devices, and garnish with random delays or failures in any step of the process...  Is there really no easy, reliable, fast way to transfer files directly between different Android devices?  Generally, my experience with Wi-Fi Direct is all but positive...   A device often won't even see a device lying next to it Sometimes, it will see the other device, only to have it disappear from the list, before I have the chance to connect When I do have a chance, invations are not realiably received (from Galaxy S2 to Nexus 7 mostly reliable, but never worked the other way around) When invitations are received (and accepted), a partnership rarely manages to be setup ("invited" or "connecting") And even when that happens, some apps can't seem to transfer files through it...   *Sigh*  Maybe J4velin's explanation pretty much sums up the sad state of Wi-Fi Direct on Android, which otherwise seemed as the best solution to my quest? Biblatex + Xelatex does not display accents How do the tens­es and as­pects in English cor­re­spond tem­po­ral­ly to one an­oth­er? Non-na­tive speak­ers of­ten get con­fused about what the var­i­ous tens­es  and as­pects mean in English. With in­put from some of the folk here I've put to­geth­er a di­a­gram that I hope will pro­vide some clar­i­ty on the mat­ter.  I of­fer it as the first an­swer to this ques­tion. Con­sid­er it a liv­ing doc­u­ment. In­put is wel­come, and good sug­ges­tions will be  in­cor­po­rat­ed in­to the di­a­gram.    No­ta bene: What this is not is a dis­cus­sion of whether there are  more than two tens­es in English. , to which this ques­tion is not in­tend­ed to sup­ply ar­gu­ments one way or the oth­er.  Here, the aim is to pro­vide an overview of what con­struc­tions English-speak­ing peo­ple use for con­vey­ing in­for­ma­tion about ac­tions re­fer­ring to past, present, and fu­ture, and to pro­vide it first and fore­most to pre­cise­ly the peo­ple who are like­ly to use "tense" as a catch-all term in their search, rather than to lin­guists who know bet­ter.  Break­ing News There is now an ex­cel­lent ELU blog ar­ti­cle ti­tled  . It is high­ly rec­om­mend­ed read­ing. I think it would be nice to have a "friends list" on Stack Overflow. This would allow us to be able to follow the questions and answers that are posted by users that we want to watch/monitor.  I suggest it be implemented in the same fashion as DotNetKicks.com; where you can add someone to your "friends list" without them needing to approve you the way that other social networks do it. It should be completely open for us to add anyone to our "friends list" that we like. Selling a car with a lien I own a car personally, but it is mortgaged to a bank. I want to sell it to an individual. I haven't the funds to repay the loan until I'm paid for the car. The buyer doesn't want to pay me without a lien release (or guarantee that one is coming). The bank won't release the lien until it gets the funds. What do people do in a case like this? It must be a common case. What should I do? Proof that every polynomial of odd degree has one real root I want to prove that every real polynomial of odd degree has at least one real root, using  the intermediate value theorem.  Let $P(x) = x^{2n+1} + a_n x^{2n} + . . . + a_0$ for each $a_i \in \mathbb{R}$ and $n \in \mathbb{N}$.  By the fundamental theorem of algebra I know that $P(x)$ has exactly $2n+1$ complex roots, so  $P(x) = (x+r_1)(x+r_2) . . . (x+r_{2n+1})$ for each $r_i \in \mathbb{C}$  I do not know how to complete this but I do know that, at some point, I probably have to show that each root with imaginary part non zero has to come in conjugate pairs, and since $2n+1$ is odd there is at least $1$ root that is imaginary part $0$ and thus real. What is a simple way to create a binary relation symbol on top of another? What is a simple way to have \ll on top of \gg with equal size and vertically center aligned and have them work as a binary relation symbol like \lessgtr? The commands \underset and \overset cannot be used because they do not treat the two symbols equally, and they do not vertically center. How to backup settings and list of installed packages If I want to make a backup of everything I have done since the fresh install of Ubuntu, what are the possible options? What all should I backup? I want to get all the settings that I changed, all the packages I installed, etc. Error handling in C code Leave Convert to Edit button enabled all the time in the moderator flag list In the moderator flags list, there is a &quot;Convert to Edit&quot; button on answers which are posted by the person who posted the question. This button is disabled at times, and I am not sure that the algorithm used is useful. My proposal is that the Convert to Edit button in the flag list should always be enabled, as it seems fairly frequent that it's disabled when it would be useful. Justification When the button is disabled, it is required that we pop open the answer view in the flag list, and use the regular Mod menu and choose convert to edit there. When we do that, however, we experience this issue:  (that should also be fixed, by the way!) Here are two items currently in the queue:    Note that one has the button enabled, while the other does not. The only differences I can see in those two answers is the age and the number of answers. Neither question has an accepted answer, but the one with the button disabled only has that single answer. I've only just now noticed that difference with these two posts, so I'm not 100% sure if that's the determining factor. 1 It is perhaps coincidental, but these buttons being (dis)abled are reverse of the action needing to be taken. The one with the disabled button needed to be converted to an edit; the one with the enabled button was an attempt to answer their own question. If I'm right about the determining factor here (that the answer is the only one), I'm not sure that's useful. A good bit of the time, an asker will post an answer due to people requesting additional information. In such cases, it seems like it will be likely there are no other answers. 1  Note 1: I was looking to create a userscript to enable these buttons, and I found something that I think is related as to the reason. It looks like the ones which are disabled are on answers which have comments on them. I noticed the title attribute of those buttons says, &quot;There are comments on the post. Please review&quot;. That does seem to make some sense in theory. However, it still seems like I am often converting them, anyway. With the above-linked, separate issue regarding how the 'mod' link on the expanded view works, this is still a bit of an impediment to our workflow. It occurred to me to check if the button was reenabled once you expanded the view, but it does not. Maybe that's an alternate solution. My plan for my userscript is to enable the button, but change the text color (and leave the title attribute), to point out that there are comments. Is there an intuitive explanation for why Lorentz force is perpendicular to a particle's velocity and the magnetic field?