How many draws to collect all items?
The coupon collectors problem
No custom off topic message when flagging on SO I have less than 3000 rep on StackOverflow. Now that the new closing changes are live, I cannot supply a custom off topic message:    I can enter a custom off topic flag message without issue here on meta, though it only has three canned off topic reasons, rather than five.  I'm not sure if this is the same for users with enough rep to vote to close directly, but the lack of a custom message eliminates the ability to use the correct flag reason in some cases.  For example, I wanted to flag , which is simply off topic on SO. However, I can't use a custom message, and none of the canned ones are appropriate.    appears to be the most up to date official information on custom reasons, and indicates that they are remaining in play for now.  supports that.  If this is by design, how should I flag such questions? This is not a case worth bothering the mods over, so I don't want to use a custom diamond attention flag. What do \makeatletter and \makeatother do? Many LaTeX “hacks” begin with \makeatletter and end with \makeatother. What do these commands do? Java Equivalent to Python Dictionaries Why are place names in some old books a capital letter followed by dashes, and what is this phenomenon called? This is something very odd I have noticed in some older books, most recently in "Crime and Punishment" by Dostoyevsky.  Place names, when not specifically essential or well-known, are made up of one letter followed by a line of underscores (i.e. "X_____").  I think I recall reading something similar in another older work, possibly by Jane Austin?  Apologies if this is a duplicate; I've searched quite extensively and can't seem to figure it out.  I don't know a name for this, so can't search easily for it. "I saw him crossing" vs. "I saw him cross" I saw him crossing the road.   I saw him cross the road.   Which one is correct and why? There are many cards that can put multiple permanents onto the battlefield simultaneously, such as , , or .  How do these interact with the following types of abilities?  As [this permanent] enters the battlefield... You may have [this permanent] enter the battlefield as... [This permanent] enters the battlefield with... When [a permanent with certain characteristics] enters the battlefield...   Justification There have been many questions already about particular instances of this situation.  This question is intended to be a canonical question and answer to all questions such as:      Note to moderators: three of these five questions have already been marked as duplicates pointing to this one.  Can we do the same for the remaining two? Can magnetic fields be "blocked"? For example, in the game, TitanFall, a robot stop bullets with ( presumably ) a magnetic shield.  I wish to calculate the magnetic force required to stop a bullet within a few microseconds.  But the problem I have is that my entire electronic system or the vehicle ( most likely even a building ) will be subjected to massive fields most likely destroying it as well.  Does any know of a way to "block" or divert the field around my vehicle? Is it even possible? My knowledge in magnetic fields are quite limited at this time. Suppose that $\hat{x}$ is the least squares solution of $Ax = b$.  That is, $\min{|r|}, r = Ax - b$ with respect to $x$.  Is $\hat{x}$ also the least squares solution of $JAx = Jb$?  I suspect so, but I'm not sure how to prove it.  If $J$ is invertible, it's easy enough to prove as you can just cancel it out from both sides.  But what if it's not invertible? When I'm using  find . -type f -name "*.htm*" -o -name "*.js*" -o -name "*.txt"  it finds all the types of file. But when I add -exec at the end:  find . -type f -name "*.htm*" -o -name "*.js*" -o -name "*.txt" -exec sh -c 'echo "$0"' {} \;  it seems it only prints .txt files. What am I doing wrong?  Note: using MINGW (Git Bash) For my MAC laptop, I only have 250GB and out of this 250GB MAC is taking up 129GB in the other section. I looked everywhere to the best of my knowledge. Please note my home directories is only 45GB. Can you somehow please help me? What does it mean for two objects to "touch"? If you've ever been annoyingly poked by a geek, you might be familiar with the semi-nerdy obnoxious response of      "I'm not actually touching you! The electrons in the atoms of my   skin are just getting really close to yours!"   Expanding on this a little bit, it seems the obnoxious geek is right. After all, consider Zeno's paradox. Every time you try to touch two objects together, you have to get them halfway there, then quarter-way, etc. In other words, there's always a infinitesimal distance in between the two objects.   Atoms don't "touch" each other; even the protons and neutrons in the nucleus of an atom aren't "touching" each other.  So what does it mean for two objects to touch each other?   Are atoms that join to form a molecule "touching"? I suppose the atoms are touching, because their is some overlap, but the subatomic particles are just whizzing around avoiding each other. If this is the case, should "touching" just be defined relative to some context? I.e, if I touch your hand, our hands are touching, but unless you pick up some of my DNA, the molecules in our hands aren't touching? And since the molecules aren't changing, the atoms aren't touching either?  Is there really no such thing as "touching"? How to add a progress bar to a shell script? When scripting in bash or any other shell in *NIX, while running a command that will take more than a few seconds, a progress bar is needed.  For example, copying a big file, opening a big tar file.  What ways do you recommend to add progress bars to shell scripts? How to attach CGPDFDocument/CGPDFPage to MFMailComposeViewController Make the chat link one click away in the new top bar An instructor has an exam of 5 questions and a question bank of 50 questions. Are there $50\choose 5$ or $(50)_5$ possible exams? Where $(50)_5 = 50! / 45! $ and $50\choose 5$ $= 50!/(5!45!)$   I've narrowed it down to these two possibilities (though even these may be wrong), but I think I'm confusing myself as to which one I use. Can anyone suggest a good way of thinking of this problem that will make it apparent whether I need use use the falling factorial or the binary coefficient?   Edit: thank you for all the answers! Indeed, I meant $50!/45$ as the falling factorial. Also, the question doesn't specify whether it was meant to be ordered or unordered, but I think I understand my confusion now! Consider this picture of sun beams streaming onto the valley through the clouds.    Given that the valley is only (at a guess) 3km wide, with simple trigonometry and the angles of the beams, this gives the result that the position of the light source is being a few tens of km away at most.   What is wrong with the analysis? Node access based on view mode "World's Hardest Easy Geometry Problem" Existence in ZF of a set with countable power set Is it consistent with ZF for there to exist a set $S$ such that the power set $P(S)$ is countable? If so, what is the weakest form of the axiom of choice needed to prove that no such set exists? Why $\sqrt{-1 \cdot {-1}} \neq \sqrt{-1}^2$? I know there must be something unmathematical in the following but I don't know where it is: \begin{align} \sqrt{-1} &amp;= i \\\\\ \frac1{\sqrt{-1}} &amp;= \frac1i \\\\  \frac{\sqrt1}{\sqrt{-1}} &amp;= \frac1i \\\\  \sqrt{\frac1{-1}} &amp;= \frac1i \\\\  \sqrt{\frac{-1}1} &amp;= \frac1i \\\\  \sqrt{-1} &amp;= \frac1i \\\\  i &amp;= \frac1i \\\\  i^2 &amp;= 1 \\\\  -1 &amp;= 1 \quad !!? \end{align}