I have an enum defined like that:  [Flags] public enum Orientation {     North = 1,     North_East = 2,     East = 4,     South_East = 8,     South = 16,     South_West = 32,     West = 64,     North_West = 128 }   Is there a generic way to tell if exactly one flag is set, multiple or none? I don't care for what the value of the enum is, I just want to know how many flags are set.  This is not a duplicate for counting the number of bits. If I initialize the enum like this and count the number of bits I get 10. But the number of set flags would be 8.  GeographicOrientation go = (GeographicOrientation) 1023;
8 bits representing the number 7 look like this:  00000111   Three bits are set.     What are algorithms to determine the number of set bits in a 32-bit integer?
Can we really not tell if we are moving? It has been a while since I've thought about physics, however, I remember something about how if you are on a train with no windows that is going perfectly straight and is perfectly smooth, there is no experiment that you could perform to prove that you are in motion or at rest. So I have a couple of questions related to this.   Is this still held to be true? I was just wondering if anything in physics has come to light since I learned about this (about 10 years ago) that would allow an observer on the train to tell if they are moving. If this is true, why couldn't you accelerate a particle in different directions to a certain mass and measure how much energy it took to get it up to that mass. If you were moving in any direction, wouldn't you measure less energy in your direction of travel? Would having an outside observer affect the aforementioned experiment in any way? Derivation of the general forms of partial fractions I'm learning about partial fractions, and I've been told of 3 types or "forms" that they can take  (1) If the denominator of the fraction has linear factors:  $${5 \over {(x - 2)(x + 3)}} \equiv {A \over {x - 2}} + {B \over {x + 3}}$$  (2) If the denominator of the fraction has quadratic factors that don't factorise:  $${{2x + 3} \over {(x - 1)({x^2} + 4)}} \equiv {A \over {x - 1}} + {{Bx + C} \over {{x^2} + 4}}$$  (3) If the denominator has a factor that repeats:  $${{5x + 3} \over {(x - 2){{(x + 3)}^2}}} \equiv {A \over {x - 2}} + {B \over {x + 3}} + {C \over {{{(x + 3)}^2}}}$$    I'd appreciate it if someone could explain to me how these equivalence relationships are derived, essentially how do they take the forms that they do? I sort of understand the first one, but the other two I don't.  Thank you Where did Harry's parents get all of their money from? How to Install Virtualbox on Windows 10 host? How to tell M2Eclipse to install jar file as a maven dependency What is the advantage to crushed garlic over minced garlic beyond texture? I use a lot of garlic in my cooking, especially minced garlic.  But lately I've been doing some more recipes with crushed garlic and while I love the texture of cooked garlic, I can't see how it could be better than minced garlic for the overall taste.  Is there an advantage to crushed garlic over minced garlic, beyond texture? When is it okay to exceed the absolute maximum rating on a part? How do I suppress the whitespace above an equation block at the page top? How do I suppress the whitespace above the equation block at the page top ? It is added to the top margin, and I don't want that to happen. I know that \abovedisplayshortskip controls this for the whole document, but how can I change this for this particular equation block and NOT for any others ? Negative vspace doesn't work.  \documentclass[pdftex,12pt,a4paper,english,dutch,leqno]{article} \usepackage[top=1cm,right=1cm,bottom=1cm,left=1.5cm,noheadfoot]{geometry}         \usepackage{babel} \usepackage{amsmath} \usepackage{amssymb} \usepackage{empheq}  \begin{document}  \abovedisplayskip=6pt \abovedisplayshortskip=3pt % This should NOT be changed \belowdisplayskip=6pt \belowdisplayshortskip=3pt  \begin{equation*} \left.\begin{array}{r} a_{31}'=a_{11}\cdot a_{31}-a_{31}\cdot a_{11}=0\\ a_{32}'=a_{11}\cdot a_{32}-a_{31}\cdot a_{12}\\ a_{33}'=a_{11}\cdot a_{33}-a_{31}\cdot a_{13}\\ a_{34}'=a_{11}\cdot a_{34}-a_{31}\cdot a_{14}\\ b_{3}'=a_{11}\cdot b_{3}-a_{31}\cdot b_{1} \end{array}\!\!\right\} \Longrightarrow\; \begin{matrix*}[l] \text{Pseudo-code :}\\ a_{11}\cdot b_{3}-a_{31}\cdot b_{1}\mapsto b_{3}\text{.}\\ \forall\;i\in\{4,3,2,1\} : a_{11}\cdot a_{3i}-a_{31}\cdot a_{1i}\mapsto a_{3i}\text{.} \end{matrix*} \end{equation*}  \end{document} How do I handle the window close event in Tkinter? How do I handle the window close event (user clicking the 'X' button) in a Python Tkinter program? As a(n) noun vs as only I tried a couple of substitutions but have so far gotten nowhere. Can anyone guide me in the right direction? Thanks for your time. Why was Peeves in Hogwarts? Peeves was a poltergeist. It generally irritated people and rather then helping them as well as making fun of them.   Why was Peeves in the school? What is/was the job or work assigned to Peeves? How do you turn off Bluetooth on startup using MacBook Air and macOS Sierra? Every time I turn on my laptop (from a completely off state) the Bluetooth is on by default. How can I prevent it from turning on at startup and then only turn it on (manually) when I want to connect any Bluetooth devices like mouse and keyboard? Can $\sqrt{n} + \sqrt{m}$ be rational if neither $n,m$ are perfect squares? Can the expression $\sqrt{n} + \sqrt{m}$ be rational if neither $n,m \in \mathbb{N}$ are perfect squares? It doesn't seem likely, the only way that could happen is if for example $\sqrt{m} = a-\sqrt{n}, \ \ a \in \mathbb{Q}$, which I don't think is possible, but how to show it? Combined flair not updating with badges I've got 28 bronze badges on Stack Overflow, 10 on Astronomy and 15 on Software Recommendations, making it a total of 53. Yet, my combined flair doesn't show that. It just shows the combined badges from my SO and Astronomy SE sites. The reputation has no problem. I can see the correct combined rep. Why is it happening? Is it because Software Recommendations is in private beta?  Here are the flairs (Combined and that from Software Recommendations):     The rep on my combined flair is the sum total of my rep from all three sites. But the badges aren't. I'm a bit familarized with conditional sentences. But the following sentences with 'should' and 'happen to' are quite confusing too me. They are:   If it should rain, I will stay at home. 2.If it should happen to rain, I'll stay at home   If it happens to rain, I'll stay at home.    What are the meaings of those sentences ? Do they all mean the same ? Thank you a lot in Advance for your answer. My website title shows up slightly different from what's in my title tag, only in Google search Show that for any prime $ p $, there are integers $ x $ and $ y $ such that $ p|(x^{2} + y^{2} + 1) $. So we obviously we want $ x^{2} + y^{2} + 1 \equiv 0 ~ (\text{mod} ~ p) $.  I haven’t learned much about quadratic congruences, so I don’t really know how to go forward. I suppose you can write it as $ x^{2} \equiv -1 - y^{2} ~ (\text{mod} ~ p) $, but again, I’m not sure where to go. I know about the Legendre symbol and quadratic residues, which I know are involved in this question, but I don’t know how to apply what I know. :( Efficient way to check collision with potentially hundreds of objects I am trying to make a top down shooter that could potentially have hundreds of objects at once at one point. I need to check collision with projectiles, walls, and enemies. I am currently using ArrayLists which probably won't suffice later on and was wondering if someone had a good method or knows a good method for checking all of those objects at once. This is going to be a game for smartphones and is built in java. Any ideas would be great or if you could point me in some direction that would be fantastic.  Thanks in advance! In Star Trek canon, what's the range of operation of Transporters? By "range of operation" of the transporter, I mean "distance up to which it could transport" or "distance from which it could transport something to its own location". The range of operation would have increased with time without a doubt but I want to know the average range at any period. It'll be better if you provide full stats of all times.