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Is it theoretically possible that every person in this village has a different jar of coins? A village has about $1$ million residents. Suppose each resident has a jar with $100$ coins in it.Two jars are considered to be “equivalent” if they have the same number of 10c, 20c, 50c, $\$$1 and $\$$2 coins in them. How many different (i.e. nonequivalent) jars of coins exist? Is it theoretically possible that every person in this village has a different jar of coins?  I understood that if we have $k_1$ 10 coins in the jar where $k_1$ is between $0$ and $100$ inclusive, then there are $100-k_1$ coins of other denominations in the jar. Likewise, we also have $k_2$ 20c coins in the jar where $k_2$ is between $0$ and $100$ inclusive, so the combined number of 50c, $\$$1, and $\$$2 coins in the jar is $100-k_1-k_2$. And we always have some $k_1, k_2, k_3, k_4, k_5$, let's say, so that the sum of those $k$'s is $100$.  I got stuck since I don't know how to 'compare' the number of coins in jars for different residents. Why multiplicative group $\mathbb{Z}_n^*$ is not cyclic for $n = 2^k$ and $k \ge 3$ I found the .bashrc file and I want to know the purpose/function of it. Also how and when is it used? Does it make sense to get a PhD if a person does not want to be in academia and prefers to stay in business? Most statements regarding Riemann integrals (at least the ones that I have encountered) begin with the statement "for $f(x)$ bounded on $[a,b]$." I am wondering if Riemann integrability implies boundedness. I think that this has to be the case, but I am not sure. If Riemann integrability does imply boundedness, are improper integrals considered Riemann integrals? I would think that improper integrals wouldn't be Riemann integrals since improper integrals are allowed to be equal to $+\infty$ or $-\infty$. Or are improper integrals that are not equal to $\infty$ considered Riemann integrals?   I am confused. How to decide whether to replace or repair? Matlab - Function taking no arguments within a class How do I download a YouTube video? Google Spreadsheets: IF not working I have problems with my IF command in Google Sheets. If gives #ERROR! all the time. See this simple test:    Not even if I put in the number directly and avoid references:    Am I using the IF wrong? Or what could such a problem be? This example is from a new document. Why can't Chromium suddenly access any partition except for /home? I just upgraded to Ubuntu 19.10 and to my horror I discovered that the default browser Chromium can no longer access other partitions than /home.  This means that my partitions containing music and videos (/multimedia) for instance are no longer accessible e.g. to upload into Google Drive. This includes USB partitions.   I found another description of this phenomenon here:  where it says  "Also, while we acknowledge that most users will only need to access their home folders, it’s worthy to mention that you no longer can access system files &amp; folders from inside Chromium (You can’t access anything except your home folder). This means that if you are to upload a file or an image for example into the Internet using an uploading website, then this file/image must be in your home folder, as you can not access directories such as /usr, /etc or other directories located in your root partition. In fact, you no longer can access any other partition at all, this includes USB sticks and other booted partitions:"  I wonder why this behaviour been introduced? it violates the whole idea of multiple disks, partitions and symlinks. Btw, this still works for Firefox.  My questions are   Are there any plans to fix this? I expect one reason for this behaviour is about security. If so, is it possible to explain why and how that makes for better security? The files on other partitions are legitimately accessible by the user anyway e.g. through symlinks. But with this change, I'll have to move them to /home before uploading so still accessing them although more slowly and cumbersome.  If this behaviour is now permanent, the question is how should we incorporate multiple disks in our filesystem?  Alternatively, can someone tell me how to find and install the debian package. I haven't been able to locate it?   This is not a duplicate of  because that is about a specific error during installation that I didn't get. My question is about the access chromium has in Ubuntu 19.10.  Anyway, I solved the problem via the following command by using the original debian package from Google:  sudo apt-get install google-chrome-stable   After that I can now access my other partitions again. I know this is hacky in the sense that the package isn't native to Ubuntu so I would really like to get some advice on how to incorporate multiple disks and partitions with this new restricted behaviour of Chromium.  Thank you very much Adverb sentence query He is arguably the best actor of his generation   In the above sentence the adverb is placed just after "be" Can we use adverb after "be"? If we can use then please explain properly because I have studied that adverb can be used before adjective and adverb . What would you call someone who imposes on other people's generosity? What would you call someone who isn't afraid to ask for money or any kind of favor or who misinterprets someone's generosity for a consistent resource for what they need? Proof that the One-Dimensional Simple Harmonic Oscillator is Non-Degenerate? Zsh says "no matches found" when trying to download video with youtube-dl I downloaded youtube-dl using pip on CrunchBang (a Debian Wheezy distro). When I run   youtube-dl {video URL}   I get  zsh: no matches found: {video URL}   I guess it has something to do with zsh, because I found some users on Arch forums complaining about it. When I switched to bash it worked. I am currently working my way through "A Concise Introduction to Pure Mathematics" by Martin Liebeck, and have been stuck on an excersise for a couple of days now. The question reads:  "Show that for an integer n $\geq2$, the period of the decimal expression for the rational number $\frac{1}{n}$ is at most $n-1$."  I've been trying to solve this without making any substantial progress. And yes, I have seen explanations that when performing a long division the decimal expression either terminates to $0$ or eventually repeats. But I haven't seen any proof of this that I've been satisfied with, even less do I know how to formalise this type of proof. I've tried to write out long division with arbitrary digits, but that obviously turns out to be too much of a hassle and basically impossible to draw any conclusions from. Why light moves sideways? Greatings!  I'm trying to understand special relativity and have one question bugging me.  In almost every book or video about the subject there is a thought experiment with moving light clock. I hope I need not elaborate on the sutup and the outcome of the experiment.  So the question is this: When a light source on the MOVING light clock emits a photon of light the path of the photon is triangular.   How this can be?   I thought since light speed is constant in every reference frame the movment of the "emmiter" can't affect the movment of the light so light should shoot right up (from the point of stationary observer) and thus move backward and up from the point of moving observer.  So you see my logic is: light speed is invariant => you can't make it move UP &amp; FORWARD only UP. i.e. you can't change it's direction once it's emited in UP direction. Why the hell light moves sideways then?  And I'm puzzeled. There is flaw in the logic but I don't see it.  Thanks for help. Is there a better way than the following to check to see if a string is nil OR has a length of 0 in Ruby?  if !my_string || my_string.length == 0   return true else   return false end   In C# there's the handy  string.IsNullOrEmpty(myString)   Anything similar to that in Ruby? Infinite series $\sum _{n=2}^{\infty } \frac{1}{n \log (n)}$ I have interesting bug that I have experienced before but has gone away on its own. This one is not going away though.  I have a giant stripe or chunks missing from my desert biome, I would say probably 7 chunks long.  I'm guessing the chunks are corrupted or something, what was hoping to figure is whether it can repaired or reverted.  Here is a picture of the problem. Just noticed the "meta user" link under the picture and reputation on the Stack Exchange user's page. It doesn't seem to work for all users. Error is "Page Not Found".   Not working:  /  Working:  /    My guess is this is because they've never logged into the meta site.