In how many ways can $4$ books be removed from a bookshelf with $15$ books such that no two adjacent books are chosen?
In how many ways can you choose $k$ numbers out of $\{1,2,3,\dots,n\}$ so none of them is consecutive?
Name tikz pic as if it was a node I'm confused about tikz pics. I can freely define them without issue, and even add coordinates inside that will be available by name inheritance like (-A) as for example in \pic (S) at (0,0) {myPic}; \draw (S-A) -- ++(0,0);. This is all documented around p. 255 of the pgf manual.  However I don' understand why it is not possible to give a name to a pic like the one above if no coordinate is defined inside it. By default it would be great if it could behave like a normal node.  MWE:  \documentclass{minimal} \usepackage{tikz}  \tikzset{     myBlock/.pic = {         \node[draw,minimum width=1cm,minimum height=0.5cm] at (0,0) {};     },     myBlockNamed/.pic = {         \node[draw,minimum height=1cm,minimum width=0.5cm] (-m) at (0,0) {};     }, }  \begin{document} \begin{tikzpicture}     \pic () at (0,0) {myBock}; % can't give it a name     \pic (S) at (3,0) {myBlockNamed}; % can give it a name     \draw (S-A) -- ++(2,0); \end{tikzpicture} \end{document}   The underlying point is I'm working on a control blocs library (so that we can stop the chat below with @Alenanno). For example here is the definition of a math operator  \tikzset{     mySum background/.style = {         circle, minimum size=1.5em, fill=white,     },     mySum edge/.style = {         draw=black, circle, minimum size=1.5em, line width=.5pt,     },     pics/bOp/.style = {     code = {       \node [mySum background] {};       \foreach \t [count=\i] in {#1}{         \pgfmathsetmacro{\angle}{\i*90}         \node[anchor=center, font=\tiny] at (\angle:0.45em) {$\t$};       }       \node [mySum edge] {};     },   }, } Rising edge pulse detector from logic gates The circuits I describe are entirely made of 7400 series logic gates (7402, 7404 and 7408 ic). I'm trying to build a rising (positive) edge pulse detector using logic gates.  The following circuit should work in theory:   (see )  I do not expect the short output to be seen through a LED so, to test it, I make it trigger an SR latch to its up state:    However, it doesn't have effect on the latch. So I added an inductor to delay the input to the NOT gates in the pulse detector circuit and it worked:   But now I can see the short flashing output through a LED which I should not because it would mean it is too long to work with a circuit like that:   Which intends to toggle the D Latch output on each clock rising edge (Note that this is a D Latch not a D Flip-flop)  And anyway there is no place for inductors in integrated circuits so there must be a way to do this only with logic gates. Can someone solve this mystery?  BTW It does not show in my schematics but I did put 10K pull-down resistors where there might be floating pins. List the files containing a particular word in their text Derived template-class access to base-class member-data What do the symbols on the main menu mean? If you swipe all the way to the left on the menu and then some, this sequence of symbols appears. (Do not pay any mind to the white circles: it's where I was holding my finger. The space between the first few and the last three symbols is also not present in game.)    What gives? Is there a good way to determine the value of magic items in 5e? In 5e, magic items aren't as common or as varied as in older editions, but that also means it is hard to place prices on them.  As DM, NPC's can't really sell a magic item because we don't know the prices for these items. While it is stated that they are rare and usually unpurchasable and unsellable, but I still have to have some basis on what to price them.  So is there a way to find buying and selling prices for magic items in 5e? Regression for an outcome (ratio or fraction) between 0 and 1 I am thinking of building a model predicting a ratio $a/b$, where $a \le b$ and $a &gt; 0$ and $b &gt; 0$. So, the ratio would be between $0$ and $1$.  I could use linear regression, although it doesn't naturally limit to 0..1.  I have no reason to believe the relationship is linear, but of course it is often used anyway, as a simple first model.  I could use a logistic regression, although it is normally used to predict the probability of a two-state outcome, not to predict a continuous value from the range 0..1.  Knowing nothing more, would you use linear regression, logistic regression, or hidden option c? How do I access the terminal without logging in to the desktop? Series with denominator that is square of product of consecutive numbers Is there a way to spellcheck the word under the cursor with a keyboard shortcut? How to show that there is an element of order $51$ in the multiplicative group $(Z/103Z)^∗.$  I can't use Cauchy's theorem since $51$ is not prime. HDMI over cat extender video We have a few cases of chat accounts remaining without valid parent account:  and  for example. What should mods do when that happens:  delete the chat account notify the SE team so they can reattach or clean it up leave it as is: it's a normal situation Clicking community promotion ad renders an instance of SO within the frame of that ad Today I came across an ad on this question on SO:  (I don't expect it to stay very long).   There was a community promotion ad on the right hand side of the site, I think for one of our English sites. It had a sentence that I only partially remember:     Idiom ... poor or even poorer   I found it interesting, so I clicked that ad. Which caused a new instance of SO to open within the ad space. Unfortunately I failed to take a screenshot. I've been refreshing the page like crazy, but can't get the ad to appear again.  Edit: I managed to get a new community add, for the photography site, and captured a screenshot:   Edit2: This bug still persists, I saw it today with an OOP add from CodeReview, and an area 51 add. How do I have no default web browser, so the system asks what browser to use when I click on a link? I use Internet Explorer for some things and Chrome for others. I'd like to have a choice when I click on a link of which browser to open the link in. Is this possible in Windows? I am currently running Windows 8, although there should be similarities between versions.  To the best of my knowledge this isn't possible. If I see an answer that involves some illegal activity, such as breaking license agreements, should I then mark this as Offensive or should I simply down-vote it? given value of matrix, getting it's coordinate Why don’t I have the Get Windows 10 icon? I want to get Windows 10, but I do not see this icon in the notification area (tray):    How do I get the icon to get Windows 10? When is mapping $g$ to $g^{-1}$ a group homomorphism? It just means that the map maps the identity to the identity and inverses to inverses. So does that mean it's only a homomorphism if the inverse is itself? How can I repair a toilet that is leaking at the base? Flushing the toilet causes a small amount of water to leak out from under the base of the toilet on one side. Stops after 2-3 seconds. Also noticed there is a higher pitch dripping of water which sounds like it is coming from the top part of the toilet. Lastly, the base of the toilet is slightly loose due to one of the bolts attaching it to the floor coming loose. How bad does this sound? I'm concerned this could cause some rotting to the floor (upstairs) - obviously needs to be fixed but do I really need a plumber or can I unscrew the toilet and fix this myself? I know zilch about plumbing.