TSA and signing mobile boarding passes
"NG NS" on ticket after airport security
How to get perfect UV sphere Mercator projection? I'm trying to unwrap a UV Sphere and I can't seem to get a perfect  projection. What process should I follow to get a perfect UV unwrap that looks like the black grid lines in this image?: Do the predictions of a Random Forest model have a prediction interval? What does [param: NotNull] mean in C#? A site URL changed and now its icon in SEDE is broken How to count derangements? I was going through .Suppose that there are n persons who are numbered 1, 2, ..., n. Let there be n hats also numbered 1, 2, ..., n. We have to find the number of ways in which no one gets the hat having same number as his/her number. Let us assume that the first person takes hat i. There are n − 1 ways for the first person to make such a choice. There are now two possibilities, depending on whether or not person i takes hat 1 in return:  A) Person i does not take the hat 1. This case is equivalent to solving the problem with n − 1 persons and n − 1 hats: each of the remaining n − 1 people has precisely 1 forbidden choice from among the remaining n − 1 hats (i's forbidden choice is hat 1).  B) Person i takes the hat 1. Now the problem reduces to n − 2 persons and n − 2 hats.  From this, the following relation is derived: !n = (n - 1) (!(n-1) + !(n-2))  I have a hard time understanding point B and the equation derived. I was trying to understand with an example of 4 people named A, B, C and D and the corresponding hats A, B, C and D. Everyone of them are supposed to wear any hat except their own matching hat i.e. A can wear B, C or D.  If suppose A wears B hat so we will be left with only 3 people and 3 hats. So I can understand "(n-1)!(n-1)" part but what i didn't understand is part B(marked above). Can anyone help? How do I manually install Adobe Flash player for Chromium? This thing came up in a combinatorics course I am taking.  Choose a fixed set of primes $p_1,p_2,\dots,p_k$ and let $A_n$ be number of integers in $\{1,2,\dots,n\}$ which are not divisible by any of the $p_i$'s. $A_n$ is given by $ n - \sum_{1\leq i_1 \leq k} \lfloor \frac{n}{p_{i_1}} \rfloor + \sum_{1\leq i_1 &lt; i_2 &lt; k} \lfloor \frac{n}{p_{i_1}p_{i_2}}\rfloor - \dots $. Now, if $n$ is divisible by each of the $p_i$'s then we have the simpler expression : $A_n = n \prod_{i=1}^{k}(1-\frac{1}{p_i})$(added later : note I am not assuming $n = \prod_{i=1}^{k}p_i$ here, this holds true whenever $n = c \prod_{i=1}^{k} p_i $ for some integer c, since each $\lfloor \frac{n}{p_{i_1} \dots p_{i_j}} \rfloor = \frac{n}{p_{i_1} \dots p_{i_j}}\ )$.  Another student pointed out that even if $n$ does not have $\prod_{i=1}^{k} p_i$ as a factor, the approximation $B_n = n \prod_{i=1}^{k}(1-\frac{1}{p_i})$ to $A_n$ is quite close in some specific cases. It is easy to see that $\lim_{n\to\infty}\frac{A_n - B_n}{n}=0$ as $\lim_{n\to\infty}\frac{1}{n}\lfloor \frac{n}{p_{i_1}p_{i_2}\dots p_{i_j}} \rfloor \to \frac{1}{p_{i_1}p_{i_2} \dots p_{i_j}},$ however that is not strong enough to imply that $A_n - B_n$ will be always close. Is there any way to analyze how well this approximation will perform in general? I am interested in the worst case for small to moderately sized $n$.  Just to give a feel of how close $A_n$ and $B_n$ can get, assuming the set of primes is $\{2,3,7\}$ we have (assuming my program is correct):  n     A(n)     B(n) 17    5    4.86   27    8    7.71   37    11      10.57   107   31      30.57   1111  318     317.43   3001  858     857.43   4007  1145    1144.86   5000  1429    1428.57 . Frequency encoding is a widely used technique in Kaggle competitions, and many times proves to be a very reasonable way of dealing with categorical features with high cardinality. I really don't understand why it works.   Does it work in very specific cases where frequencies are correlated with the target or is it more general? What's the rationale behind it? Consider a database table holding names, with three rows:  Peter Paul Mary   Is there an easy way to turn this into a single string of Peter, Paul, Mary? Table of Contents with Chapter I'm attempting to modify the Table of Contents in my document. Currently, chapter one in my document is listed as   1   Introduction   What I would like to see is  Chapter 1   Introduction   Seems like an easy enough thing to ask for, but can't seem to find a good way to do this. Any feedback would be most appreciative. I've been watching a lot of pro replays ever since the SC2 beta came out, and I've noticed that almost always, when Protoss research upgrades, the shields are the last research chosen. Why is that? Seems to me that if anything, shields should be the most important upgrade, as they affect all Protoss units and buildings. What should I do if I lost money in a scam? I live in New Jersey and my son wanted to order some toys from this guy who said he makes them in his house and he could give him the best deal, but before he could send these toys he needed my 16 year old son to put $200 into his bank account. The guy then gave my son his wells Fargo bank account info and told him as soon he deposits the money he will ship his toys. Well, that never happened.  My son called the guy up and he told my son, “I’m only the middle guy, and my boss is in Nigeria and you need to put another $200 in my account because now I have to ship the toys from elsewhere.” So my son deposited another 200 dollars into this guys bank account.  My son has sent these jerks a total of $650. Is there anything I can do to these individuals? At this point even if I don’t get the money back it’s okay but I don’t want this happening to other kids and I want to teach these guys a lesson that you’re not above the law. The guy is still calling my son up saying that he is pissed off that he didn’t get more money.  What can I do now? Bijection from $\mathbb R$ to $\mathbb {R^N}$ How does one create an explicit bijection from the reals to the set of all sequences of reals? I know how to make a .  I have an idea but I am not sure if it will work. I will post it as my own answer because I don't want to anchor your answers and I want to see what other possible ways of doing this are. C non-blocking keyboard input Prevent parameter expansion in shell script I often have to do a recursive search in files. Tired of typing the whole "find/grep" combination all the time, I just created a script with the following line:  find . -name $1 -exec grep $2 {} + 2&gt;/dev/null   The idea is that I should be able to run it as, for example:  myfind '*' hello   The problem is, when '*' gets passed into the script, the script is expanding it to each file in the directory.  I tried putting a quote around $1:   find . -name '$1' -exec grep $2 {} + 2&gt;/dev/null   However, this turns $1 into a literal string.  Would appreciate your help in finding the right syntax. Must be something simple that I am missing. Is the coefficient of friction always less than unity? What are the cases in which coefficient of friction is greater than unity? Proving that $\frac{\phi^{400}+1}{\phi^{200}}$ is an integer. How do we prove that $\dfrac{\phi^{400}+1}{\phi^{200}}$ is an integer, where $\phi$ is the golden ratio?  This appeared in an answer to a  I asked previously, but I do not see how to prove this.. Default class inheritance access arbitrary large finite sums of an uncountable set. C# has the keyword called . VB.NET lacks this keyword. How have the Visual Basic programmers gotten around the lack of this keyword? Do they implement they own iterator class?  Or do they try and code to avoid the need of an iterator?  The  keyword does force the compiler to do some coding behind the scenes.  has a good example of that.