We're given a string $S$ with $N$ characters (the characters can be repeated). We can swap $2$ positions of two characters to obtain another string, and we can swap at most twice. How to find the number of distinct strings reachable by at most two swaps?
We are provided with a string A (may contain repeated characters as well ). One needs to make all possible permutations of A , and find out how many pairs of strings chosen from these permutations are not similar.  Two strings are similar if we can make both of them exactly same by carrying out at most 1 swap in each of them .  Example :- if we are provided with string abcd  , then for permutation abcd , the permutations which are not similar to it are bcda , bdac , cadb , cdba , dabc , dcab . Similar is the case for other permuations as well. So overall number of desired pairs are 24*6=144 .  I tried solving it for each possible pair by approach mentioned here     But as the permutations can be large enough , I need a better approach of solving this.
I just visited Ask Ubuntu (askubuntu.com) while logged into Stack Exchange, and noticed that "join this community" doesn't appear:    It is similarly broken on Math Overflow (mathoverflow.net). It works, however, on all sites that are subdomains of stackexchange.com, like Mathematics (math.stackexchange.com) and Academia.  I'm using Google Chrome version 46.0.2490.86 on Windows 8.1 Update 1.  (I don't know if this can actually be fixed, given how cookie security works, but I figured Stack Exchange should be aware of the issue.) How to best respond to a request to send a passport scan by unsecured email? It is not uncommon for travel or holiday accommodation companies to ask for a scan of your passport by email. Sometimes local laws require them to keep a record of the passport numbers of all visitors. I'm happy to provide that information but you usually have to send it in an unsecured email, which may have consequences .  Could these companies be more responsible, and provide a public cryptographic key at least?  Are there other steps you should take to protect yourself, if you do send by unsecured email? Book about a boy who travels to a parallel universe to get a book I can't remember the gender of the main character.  I remember bits and pieces from different books, but I think they're all part of the same series. The pieces may not be in order or from multiple books.   Boy somehow ends up in a mirror universe that's darker and seems to have no people. He has to travel to a certain office(?) building and steal a book. I think this is towards the end of the book (I can't remember the events leading up to it). I think he finds the portal in a forest or something behind his school. He goes into the ocean with mermaids or something and has to save the ocean from pollution. Aliens exist and are observing Earth, because they think it's undeveloped and are waiting for them to be advanced enough. His mother ends up in hospital and he does something to save her. He goes to Ireland(?) and enters a mountain or something to find a race of people. I can't remember who showed him how, but I'm pretty sure she used magic. He goes to Mars and saves a race from war with themselves(?). This place was hidden inside an illusion. He's also grouped with a linguist that learned their language. He travels to another world where there's a prince. I can't remember, but I think it might've been part of a tournament. His sister goes to a robot planet through a portal. I think the actual planet was a robot/AI and had lots of little robots on it. Can't remember what happens here, but he goes there and saves her from something.   It was set a few years ago, when computers weren't common (his family got one early in the first book, I think).  Thanks in advance if someone finds it. There are several unknown numbers in mathematics, such as optimal constants in some inequalities. Often it is enough to some estimates for these numbers from above and below, but finding the exact values is also interesting. There are situations where such unknown numbers are necessarily natural numbers, for example in Ramsey theory. For example, we know that there is a smallest integer $n$ such that any graph with $n$ vertices contains a complete or an independent subgraph of 10 vertices, but we don't know the exact value of $n$.  What kinds of unknown small (less than 100, say) integers are there? What are the smallest unknown constants which are known to be integers? Or, more rigorously, what is the smallest upper bound for an unknown but definable number that is known to be an integer?  I know that asking for the smallest unknown integer is ill-defined since we do not know the exact values. The more rigorous version of the question is well-posed, but I do not want to keep anyone from offering interesting examples even if they are clearly not going to win the race for the lowest upper bound.  An answer should contain a definition of an integer quantity (or a family of them) and known lower and upper bounds (both of which should be integers, not infinite). Conjectures about the actual value are also welcome. I have given one example below to give an idea of what I'm looking for. When should I use "didn't" instead of "haven't"? Is haven't supposed to mean something I may still do and didn't not?  Can I use didn't for something I might still do? executing web service using postman Capture characters from standard input without waiting for enter to be pressed I can never remember how I do this because it comes up so infrequently for me. But in C or C++, what is the best way to read a character from standard input without waiting for a newline (press enter).  Also ideally it wouldn't echo the input character to the screen. I just want to capture keystrokes with out effecting the console screen. Why would using higher ISO and faster shutter speed yield more noise than using lower ISO and slower shutter speed? Is there a deb package to install Firefox ESR? I would like to have  on my system but I would like to install it via apt-get. Is there a special package to install this?  Download link would be: How can I copy the contents of a folder to another folder in a different directory using terminal? I am trying to copy the contents of a folder to another folder in a different directory using terminal.  Would somebody be able to provide me an example of the command line syntax required to achieve this? BOOLEAN FUNCTIONS: generate a function $f: \{0, 1\}^n \rightarrow \{0, 1\}$ from a $n \times n$ S-Box I want to calculate the hamming weight of a S-Box using this formula: $\text{hw}(f) = \sum_{x=0}^{2^n-1} f(x)$. Where $f: \{0, 1\}^n \rightarrow \{0, 1\}$  My problem is that I don't know how to get the $f$-function.  I found that helpful paper: . At Page 9 (18) boolean functions are described. But she only prints the truth table (Table 2.1) without describing her $f$-function. She only says $f$ is a linear function, therefore I think $f$ depends on my S-Box?  For example, if I have this $2 \times 2$ S-Box:  0    1    2    3  1    3    0    2    $00 \rightarrow 01\\ 01  \rightarrow 11\\ 10  \rightarrow 00\\ 11  \rightarrow 10$  What are the $f$-functions and what is the hamming weight? How can I randomise the output of a redstone circuit? Is there a way to detach matplotlib plots so that the computation can continue? After these instructions in the Python interpreter one gets a window with a plot:  from matplotlib.pyplot import * plot([1,2,3]) show() # other code   Unfortunately, I don't know how to continue to interactively explore the figure created by show() while the program does further calculations.  Is it possible at all? Sometimes calculations are long and it would help if they would proceed during examination of intermediate results. How to vertically center content with variable height within a div? Does a linear operator obeying Leibniz rule imply it is a differential operator? Prove that if b is coprime to 6 then $b^2 \equiv 1 $ (mod 24) Let $\gcd(b,6) = 1$. Prove that $b^2 \equiv 1 $ (mod 24).  Now I have that as $\gcd(b,6) = 1$, we know that  $3\nmid b $ and $2\nmid b$ (else the GCD would be 3 or 2 resp.)  So as $2\nmid b$, $b$ must be odd. Hence $b^2$ is also odd.  Then I'm not sure where to take it from here? Maybe I've gone down the wrong path to start with, and should be looking more along the lines of the Chinese Remainder Theorem? I'm not sure. 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. :( Scenario: SQL Server 2014 CU6. 1 AG with 2 databases (compatibility level 100). Failover Cluster with 3 nodes on Windows Server 2012 R2. Primary Availability Replica on node 1 and node 2. Secondary Availability Replica on node 3 (no votes). Async commit, manual failover, readable secondary. Node 3 is used to run reports on these 2 databases (out of 8 databases running outside AG on node 1 and 2).   Problem: Looking to patch these from SQL 2014 to SP1 and latest CU. Not my build and no experience with AG or FC so far. My "test" environment is also used for development, so no room for mistakes.   Questions:  What's the best order to patch the 3 nodes ?   Do I first have to remove the databases from AG on the node I'm patching ?  Do I need to take the Secondary out when patching it ?  No experience on this, and I can't find clear answers for my scenario (maybe not supported?) in the docs: Does eating infected flesh have an effect? I don't remember what actually happends when people eat infected flesh. I have in mind :  Gareth and the cannibals eating bitten Bob's leg in . It seems that the cannibals survive for a while after eating Bob's flesh and they seem OK.  The Saviors eating pigs that ate walkers in . We don't know for how long this process has been on, but  has his routine and looks used to doing that. Can we assume that Saviors are eating infected pig flesh for a while now ?  Does it have negative effect in long term ? When I'm not exploring fresh caves or lands in minecraft, I'm busy trying to find deposits of diamond, gold and iron deep in the earth. So far I've just been digging around just above bedrock on a whim to look for these rare minerals but I've started thinking that I should be taking a more controlled, efficient approach to mining.  What is the optimal mining strategy that yields the most rare minerals while minimizing blocks removed and time spent digging and traveling?  Edit: The existing answers are great for mining, but no one has addressed travel time to and from the mine which is usually ~60 blocks downward and incredibly tedious. Solutions?