The Question This question is a maths challenge and well to explain it better I will use an example. I have a number, say $20$ I can write this as $10 + 10$  (this is a make up of the number) Now I multiply the two numbers to get $100 = 10 * 10$ The challenge is to make the highest possible product in this manner and find a rule for this. Note : The composition (make up) can consist of a number of numbers. hehe. They have to be positive integers.  &quot;Let n∈N be a positive integer. Let m∈N and a1,a2,…,am be positive integers such that a1+⋯+am=n. For what m and what a1,…,am is the product a1a2⋯am maximal&quot; (Same, just rephrased, creds to SteamyRoot)  A solution Using the example $20$, to find the highest &quot;production&quot; number for this, we need to write out $20$ has a sum of as many as $3$ as we can use, so... $20 = 3 + 3 + 3 + 3 + 3 + 3 + 2$ Now we multiply them together $3*3*3*3*3*3*2 = 3^6 * 2 = 1458$
Suppose we have a natural number $n \ge 0$.  Given natural numbers $\alpha_1,\ldots,\alpha_k$ such that   $k\le n$ $\sum_i \alpha_i = n$   what is the maximum value that $\Pi_i \alpha_i$ can take?  I'm quite sure that there is a theorem telling me the result, but I cannot find it. For sure an upper bound is $n^k$ but I'm searching for a real upper bound. I'm pretty sure that upper the bound should be $n^2$, but I don't know I could prove it.
I'm trying to do something like the following:  enum E;  void Foo(E e);  enum E {A, B, C};   which the compiler rejects.  I've had a quick look on Google and the consensus seems to be "you can't do it", but I can't understand why.  Can anyone explain?  Clarification 2: I'm doing this as I have private methods in a class that take said enum, and I do not want the enum's values exposed - so, for example, I do not want anyone to know that E is defined as  enum E {     FUNCTIONALITY_NORMAL, FUNCTIONALITY_RESTRICTED, FUNCTIONALITY_FOR_PROJECT_X }   as project X is not something I want my users to know about.  So, I wanted to forward declare the enum so I could put the private methods in the header file, declare the enum internally in the cpp, and distribute the built library file and header to people.  As for the compiler - it's GCC. I'm trying to solve the following problem:  Given two CRHF $H_1:2^{4n}\to2^{2n}$, $H_2:2^{2n}\to 2^n$, construct the following hash function $H^{*}=H_2(H_1(x))$ compressing from $2^{4n}\to 2^n$. We want to demonstrate that if $H_1$ and $H_2$ are collision resistant then $H^*$ must be collision resistant too.  I made the following reduction  However I'm still unsure on how to calculate ”BAD event” in which $A^{H^∗}$ outputs a collision for $H_{s_1}$, in this case $x^∗=x′$ and the second part of the reduction doesn’t work. I know that an easy to handle formula for the CDF of a normal distribution is somewhat missing, due to the complicated error function in it.  However, I wonder if there is a a nice formula for $N(c_{-} \leq x &lt; c_{+}| \mu, \sigma^2)$. Or what the "state of the art" approximation for this problem might be. Shutdown Cause -128 SWR surname that in fact describes or applies to the human in question? There are (in real life) many amazing examples of this (Bill Gates, "gates" being the fundament of computers, Tiger "Woods", the greatest ever user of "woods" golf-clubs, etc) and it is a staple of fiction.  Is there a single-word for this, or a frequently-used term?  Note that in fictional usage, I observe there is literal "X", so, for example I just saw a children's movie where "Madame Work" was a taskmaster. However, authors often employ near-literal "X": for example, most of the minor character surnames in Harry Potter are 'kind of" "X".  So, is there an "X" for Bill "Gates", Tiger "Woods", an undertaken named Mr. Death, etc?  Sorry if this has been asked already, I couldn't find it.    Note - I've just found there's a "wikipedia" page claiming 'aptonym' or 'euonym' is sometimes used.  Wikipedia is often valueless, so I do not know if this is a meaningful claim. The escape velocity of earth is roughly $11 kms^{-1}$. However, what if a long ladder was built extending out of Earth's atmosphere and considerably more. Then if something was to climb up at much less than the escape velocity, what would happen when it reached the end?  And what if the object that climbed the "ladder" then fired some kind of thruster/rocket and was going fast enough so that it orbited the Earth. It would mean less energy required to get into orbit? If I downvote every competing answer, will I get flagged for vote abuse? I think everybody with a history of participation can't help but notice the explosive growth of repeated duplicate questions. The work of looking for duplicates and then closing questions has overtaken the work of actually answering questions.  It's become virtually impossible to ask something which hasn't been yet asked. Lately I feel boredom each time I see a new question and start answering it only to realize after the first written sentence that I have answered similar questions five times over or seen them answered some ten times or more. I know where it's going to be going and what answers with what votes it is going to receive before any answer is even written.  It's obviously not the administration's fault, it is simply so. The questions is, what to do about it? Engaging more moderators to close and close duplicates won't work because it's already starting to repel users who get mad at their questions closed and become afraid of asking more or perhaps just go away.  The original idea of Jeff stated the the site is for questions that can be answered. Meaning no open-ended discussions. When I first read this I had a casual thought - well, and what's gonna happen when they all are asked and answered? Will it become a museum, a monument of wisdom and knowledge or what?  I'm not sure what to do about it. Perhaps deprecation/versioning of older questions so that their new versions can sparkle the tiresome evening...  POSTSCRIPTUM.  I recall Star Trek Voyager episode  when another Q asked Captain Janeway for asylum. He was tired of immortality and wanted to die. They opened a hearing and went on to visit the continuum to evaluate the living conditions there which caused the suffering and the wish to escape it in death. A lifeless picture presented itself to the visitors... a house lone in an open space, two people going about their business, nobody talking. When asked why they were silent, the following was said. It's been so long, all has already been said, all stories told, all jokes are made... there is nothing left to do...  Are we there as well?  UPDATE: Just saw this answer in another question:       Also, some of the core questions got asked early on in the life of the site. Great questions still come around from time to time, but many have already been asked.   Doesn't that confirm my point? How do I write a cpp macro which expands to include newlines? Why does local fn=$(...) mask the $? status code Two function definitions, the only difference is that the first combines the local storage keyword with the assignment, while the second separates them:  function foo {     local fn=$(mktemp -p /path/does/not/exist 2&gt;/dev/null)     echo $? }  function bar {     local fn     fn=$(mktemp -p /path/does/not/exist 2&gt;/dev/null)     echo $? }  foo bar   This echoes "0" then "1". I expect it to echo "1" then "1". It seems like the value of $? is the result of the assignment to local, rather than the result of the command substitution.  Why does bash 4.2.46(1)-release behave this way? App crash when editing comment or uploading image This question arises when I try to describe my itinerary to ticket service in the UK. Take for example, I plan to buy a ticket from A to B. B is the terminal. How to say its counter part A? I cannot find a proper term. I have to say "I will depart from A" or "I plan to go to B from A". Or I even use "departure place" to refer to B. $a+b+c = 3$, prove that :$a\sqrt{a+3}+b\sqrt{b+3}+c\sqrt{c+3} \geq 6$ $a, b,c $ are positive real numbers such that $a+b+c = 3$, prove that :$a\sqrt{a+3}+b\sqrt{b+3}+c\sqrt{c+3} \geq 6$  Any ideas ? Revert new tab page behavior in Google Chrome 29+ I don’t like the behavior of the new tab page in Google Chrome 29+. How can I restore the old behavior?  The new tab page (if you have Google set as the default search engine) now shows the Google logo (or, apparently, the doodle of the day if there is one), a search box, and a few recently visited websites. It also added an Apps button to my favorites bar, seemingly the only way to access my apps page, which has easy access to things I use regularly (Calendar, Gmail, Docs, G+, Facebook, Feedly, Google News, Netflix, Play Music, Pandora, Drive, Keep, etc.) I don’t like this behavior. I actually don’t mind having the logo of the day and search box, but I want my apps linked to on my new tab page.  Is there any way to get the old behavior back? I checked the settings and it doesn’t seem like it’s possible to set chrome://apps to be the new tab page (which would restore the old behavior) or to configure the new new tab page to display apps instead of recently visited sites. Link broken on desktop but work on nautilus file manger I created a shortcut to a text file called &quot;imp&quot; on right-clicking it from the default file manager everything works well. But on clicking it on the desktop I get this  Any Idea why? $C_c^{\infty}(\mathbb R^n)$ is dense in $W^{k,p}(\mathbb R^n)$ I've been using mac for years, but prefer to do software development on windows. I'm really used to is using the folowing shortcuts on windows very much:  &lt;CTRL&gt;  + INSERT: Copy &lt;SHIFT&gt; + INSERT: Paste &lt;SHIFT&gt; + DELETE: Cut   Of late, I've taken to doing even my development work on the Mac. However, as a matter of habit, I'm missing these shortcuts very much. Actually, I find these a lot more convenient than COMMAND + (C/V/X) combo.  Is there a way to reassign these three shortcuts at least?   I've look all over the internet and in the "Keyboards" system preferences but I did not find anything.  PS: If you're wondering where I find the INSERT keys on a mac book pro, I use a wireless keyboard. Drush from GitHub stopped working I have a  that has been working since it moved there.  I did a git pull this morning, and am now getting errors:     $ drush      Warning: require(/home/mpd/drush/vendor/autoload.php): failed to open   stream: No such file or directory in   /home/mpd/drush/includes/bootstrap.inc on line 1007      Fatal error: require(): Failed opening required   '/home/mpd/drush/vendor/autoload.php' (include_path='.:') in   /home/mpd/drush/includes/bootstrap.inc on line 1007   How can I fix this? Beamer - create subsubsection page Solving multiple congruences by CRT = Chinese Remainder Theorem