How many different ways can 200 coins be distributed among 10 people so that:  1)everyone gets 0, or more, coins?  2)everyone gets 5, or more, coins?  I know how to do question it they have an exact requirement like if they each need a certain amount. However, when it comes to 0 or more I don't know how to approach the question can someone teach me the way? Thank you.
How to use the  method?  Say I want to find number of combinations I can get with $x_1+x_2+x_3+x_4=22$,  where $x_i\in\mathbb{N}$.  Is this the correct time to apply the method?  This is being repurposed in an effort to cut down on duplicates, see here:     and here:
in questions, answers, and comments. Can we get something like this going on Stack Overflow?  I think it’d be appropriate as I at least pretty often want to write something like n^2 and would benefit greatly from prettier markup. My professor was lecturing today and he made this statement which I was unable to verify.  (I worded it nicer)  There is no map which is both smooth and onto from $S^1$ to $S^1$$\times$ $S^1$.  When he said this he included the original "one can clearly see" statement which is usually when the most people seem to be confused in his class.  Thus, I was hesitant to ask why.  So, please no one lecture me on the fact that I should have asked anyway.  If it is really that obvious, I would rather look stupid here than in class :) Passing an enum value as command parameter from XAML I want to pass an enum value as command parameter in WPF, using something like this:  &lt;Button      x:Name="uxSearchButton"      Command="{Binding Path=SearchMembersCommand}"      CommandParameter="SearchPageType.First"     Content="Search"&gt; &lt;/Button&gt;   SearchPageType is an enum and this is to know from which button search command is invoked.  Is this possible in WPF, or how can you pass an enum value as command parameter? I've always been one to simply use:  List&lt;String&gt; names = new ArrayList&lt;&gt;();   I use the interface as the type name for portability, so that when I ask questions such as these I can rework my code.    When should  be used over  and vice-versa? How can I disable the volume warning if you raise the volume too much? Ubuntu 18.04 not detecting full RAM size How can I make a part of a texture glow? I need to make a part of a texture glow slightly. Like Killer Crocs eyes (see image below)     How do I do this?  I added a black and white texture (white for the glow. But then this happened.     There are strange colors around the eyes. Also how do I change the white glow to red? What are the readline word separators? Basically the question is how to get from this:   foo_id   foo_name 1        A 1        B 2        C   to this:   foo_id   foo_name 1        A B 2        C Confused at + and ++ in TikZ I can't seem to figure out the difference between + and ++ relative coordinates in TikZ.   I understand ++. ++ specifies delta coordinates that are added to the last current point, the current point is then set to the new absolute current point (correct?):  \draw (0,0) -- ++(1,0) -- ++(0,1) means:  set Current Point to (0,0) add (1,0) to Current Point = (1,0) set Current Point to (1,0) add Current Point (1,0) to (0,1) = (1,1) set Current Point to (1,1)   I can't seem to figure out that + does, when I try it out it looks like the coordinates in the +(x,y) are absolute coordinates rather than delta coordinates, but the manual says otherwise The Start menu no longer shows up when I press the Start button Similar Matrices and Linear Transformations Can we use curved spacetime to measure the one-way speed of light? This is related to  and  The idea is to shine a beam of light from a clock towards a heavy mass, like a black hole, in some manner such that the curvature of spacetime around the mass is sufficient to &quot;bend&quot; the light directly back to the clock. That is, to send the light along a self-intersecting geodesic using a sufficiently curved spacetime. Note that in this case the source and the detector are the same object, so no clock synchronization is required. Hypothetically, this should measure the one-way speed of light. None of the given refutations from the similar posts on this site are convincing. Here are some of the main refutations, as I understand them, and my counter to them: (1) In being curved by spacetime, the light is actually changing direction, hence this is not the one-way speed. To my understanding of General Relativity, the light travels along a geodesic; that is, a curve such that, ignoring technicalities of Differential Geometry, its tangent direction is constant. There is no reflection or acceleration. So in this sense, how can the light with a constant tangent direction be said to change direction? One might say that the path deviates from a straight line in Euclidean space, but given that spacetime is not Euclidean, has no , and has no global notion of direction, this is the only definition of straight or &quot;one direction&quot; that makes sense. Thus, either the light does not change direction and is &quot;one-way,&quot; or we need to be clearer about what exactly we mean by &quot;one-way&quot; in the context of General Relativity. (2) Such an experiment would be impossible or impractical. I think some posters were saying this because the original questions implied that the clock would have to be at the event horizon of a black hole, which is of course impossible or impractical; however, I don't think such an extreme closeness to the black hole is required. Given that the  of a black hole, where light orbits in a circle, is outside of the event horizon, shining the light at some distance outside of the photon sphere should be sufficient to curve the light back to the clock, regardless of the distance of the clock from the black hole (see my rough illustration). At the extreme, we could place the clock directly on the photon sphere, which should be theoretically possible. Regardless, the question is not about practicality, but whether the one-way speed is theoretically measurable.  Update: Essentially what this argument boils down to, I think, is that the average speed of light along a single self-intersecting geodesic may differ from the average speed of light along a non-geodesic self-intersecting path, which is always c. Put that way, however, it does seem a little ridiculous. It is hard to see how the anisotropy of the speed could be defined in such a way as to be consistent with this pathological case. Presumably, we could approximate a single self-intersecting geodesic with a non-geodesic path arbitrarily closely, so, logically, the average speeds over each path should be approximately the same, i.e., c. Furthermore, how would the &quot;preferred direction&quot; of the speed of light behave around a black hole, for instance? Regardless, I still think this experiment does actually solve the problem for the given notion of &quot;direction&quot;. Though the problem is usually posed in the flat spacetime of Special Relativity, with a global notion of direction, so the apparent unanswerability of this question should be seen as a limitation of Special Relativity only, which is then solved by General Relativity. Possible Duplicate:          Most commands I use in linux behave exactly the same whether I include the trailing slash / character on the end of a directory name or not.  For example:  ls /home/cklein ls /home/cklein/  cp foo bar cp foo/ bar/   When does this trailing slash matter?  What is the semantic meaning of the trailing slash? Present-perfect-tense vs. Simple-past-tense Boy goes insane during space travel I'm trying to remember the name of a short story I read about 25 years ago or so. I'd also like to know of any collections it appeared in.   The details I recall involve a family who are embarking on a hyperspace journey. To undertake this journey you have to be put to sleep. One of the children pretends to be asleep, and when the jump is complete the child has gone insane. From the child's point of view the jump lasted for an eternity while in reality it was only a few seconds. Removing files with strange names Possible Duplicate:          Somehow I ended up with a file named "-r".  How do I remove it?  rm -r doesn't work.  I tried 'rm -i `ls -a`' to step through the file names, but it didn't prompt me to delete this one.  Edit A very hacky approach was to use python's os.unlink function.  That worked, but I'm curious to hear other ways. Can every even integer be expressed as the difference of two primes? Can every even integer be expressed as the difference of two primes? If so, is there any elementary proof? I'd like to install both Ubuntu 12.04 and Windows XP on a Dell laptop, and I was thinking about using a dual boot structure, and using the bulk of my hard drive as empty hard drive space to share files between the two operating systems (so choice of file system type is very important in this set-up).     The kind of partitioning structure I would like to use is  Partition 1 - Ubuntu 12.04 (root) (20GB)  Partition 2 - Ubuntu /home        (20GB)  Partition 3 : Free Space          (560GB)  Partition 4 : Windows XP          (35GB)  Partition 5 : SWAP                (3GB)  (Total Hardrive Capacity is ~640GB)    My question is; what is the best way to go about setting up this kind this system?   Should I install Windows XP first and setup the partitions, and then install Ubuntu which I believe will install the GRUB bootloader for OS booting choice   or   Do I install Ubuntu first, setting up the available partitions and then perform a WIndows install?  Please let me know if there is anything in this setup that I have left out and should know about, including things related to setting particular partitions as logical or primary, and whether the boot partition and the filesystem partition should actually be two separate partitions. There are 100 ropes in a bag. In each step, two rope ends are picked at random, tied together and put back into a bag. The process is repeated until there are no free ends. What is the expected number of loops at the end of the process?