If George had stocked on some of his hairs before his ear got cut off by Snape, could he have used polyjuice potion to turn into a version of himself with both the ears?    From Goblet of Fire we know that polyjuice replicates deformities of the target, when Barty Crouch Jr Changes into Moody and has all his scars and fake leg.    We also know it replicates better body conditions from Chamber of Secrets, when Harry no longer needed his glasses after turning into Crabbe.  Would this be true if the body part had been cursed off by dark magic as well?    (In fact, in case of the twins George probably didn't even need to have a stock of his own hair, he could just polyjuice himself into Fred and no one would know the difference.)
Suppose you cut a five year old's hair, save it for 10 years, and then use it for a Polyjuice transformation. What age do you turn into: The toddler or the teenager?
How do you sort du output by size? using a:hover to change the color of an image I'm confused about why we should change door in the Monty Hall Problem, when thinking from a different perspective  gives me equal probability.   Think about this first: if we have two doors, and one car behind one of them, then we have a 50/50 chance of choosing the right door.   Back to Monty Hall: after we pick a door, one door is opened and shows a goat, and the other door remains closed. Let's call the door we picked A and the  other closed door B. Now since 1 door has already been opened, our knowledge has changed such that the car can only be behind A or B. Therefore, the problem is equivalent to: given two closed doors (A and B) and one car, which door should be chosen (we know it's a 50/50 thing)? Then, not switching door = choosing A, and switching door = choosing B. Therefore, it seems that switching should be equally likely, instead of more likely.   Another way to think: no matter which door we choose from the three, we know BEFOREHAND that we can definitely open a door with a goat in the remaining two. Therefore, showing an open door with a goat reveals nothing new about which door has the car.   What's wrong with this thinking process? (Note that I know the argument why switching gives advantage, and I know experiments have been done to prove that. My question is why the above thinking, which seems legit, is actually wrong.) Thanks. Run a command on all subfolders If you have a series of subfolders (like from a to z) and want to run a command on each one of them (like rm *.pdf or ls *.pdf), how do you do that? The "manual" approach would be cd a, rm *.pdf, or ls *.pdf, cd .., cd b, ... That seems too complicated, so I believe there must be an easier approach. Difference between administrative and user mode of MiKTeX How does $e^{i x}$ produce rotation around the imaginary unit circle? 'Possible duplicate' comment not appearing for questions with deleted comments containing the link apt-get update fails to fetch files, “Temporary failure resolving …” error A very compact list in Beamer I would like to make a very compact list (e.g., itemize) in Beamer.  has been asked for an article-type document class; the answer uses the enumitem package, known to be .  My question is: How do I make the same compact list in the Beamer document class? As in the above linked question, I would like the list to have   No whitespace before list No whitespace after list No whitespace between lines Less indent before the bullet points how to make some border lines of a table thick and colored Error "Power::infy: Infinite expression 1/0 encountered". Why do I get this? How to copy the complete folder structure one location to another location include all files and sub folders I have folder structure like in Shared documents/East using CSOM and C# Main Folder   Folder1   Folder2      File1      File2  I have to copy all folders with files to Shared documents/West .... Open existing file, append a single line Let $G$ be a finite abelian group and let $\phi: G \rightarrow G$ be a group homomorphism. I am trying to show that there is a positive integer $n$ such that $G \cong \ker(\phi^{n}) \times \phi^{n}(G)$.  I know that since $G$ is abelian we have that $\ker(\phi^{k})$ and $\phi^{k}(G)$ are normal subgroups of $G$ for any $k$  I also suspect we have the following towers which stabilize at $m$ and $m'$  $$\phi(G) \unrhd \phi^{2}(G) \unrhd \cdots \unrhd \phi^{m}(G)=\phi^{m+1}(G)=\cdots$$  $$\ker(\phi) \unlhd \ker^{2}(\phi) \unlhd \cdots \unlhd \ker^{m'}(\phi)=\ker^{m'+1}(\phi)=\cdots$$  I know that if given a group of the form $HK$ where $H$ and $K$ are normal subgroups of $HK$ and $H\cap K=1$ then $H \times K \cong HK$. I want to apply this to this situation but I am unable to show how write $G$ as a product $HK$  Resolution One of the comments directed me to the following article:  The last part of which answers the question. Below is what is says:  Choose $n=\max(m,m')$, then we have for $x \in \ker^{n}(\phi) \cap \phi^{n}(x)$, this means that $x=\phi^{n}(y)$ for some $y \in G$. This gives:  $0=\phi^{n}(x)=\phi^{2n}(y)$ which means that $y \in \ker^{2n}\phi=\ker^{n}{\phi}$. and then we have that $0=x=\phi^{n}(y)$.  The answer below kindly points out that every element $x$ is contained in one of the cosets of $G/\ker^{n}(\phi)$, this means that $x=k+g$ for some $k \in \ker^{n}(\phi)$ and $g \in G$. We also have that $g=\phi^{n}(h)$ for some $h \in G$. Writing $x=k+\phi^{n}(h)$ essentially shows that $G=\ker(\phi^{n}) + \phi^{n}(G)$. Using the fact above, the claim follows. I have to maintain a large number of classic ASP pages, many of which have tabular data with no sort capabilities at all. Whatever order the original developer used in the database query is what you're stuck with.  I want to to tack on some basic sorting to a bunch of these pages, and I'm doing it all client side with javascript. I already have the basic script done to sort a given table on a given column in a given direction, and it works well as long as the table is limited by certain conventions we follow here.    What I want to do for the UI is just indicate sort direction with the caret character ( ^ ) and ... what?  Is there a special character that is the direct opposite of a caret?  The letter v won't quite cut it.  Alternatively, is there another character pairing I can use? Updating a field programmatically, hook_node_update Currently trying to update a field every time a node is created or updated. However the value is not being populated within the node, do I have access to the node object with this particular hook? What could I be missing?    function vbtoken_node_update($node) {         entity_get_controller('node')-&gt;resetCache(array($node-&gt;nid));         $types = node_type_get_types(); //What are the current Node Content Types?       $yes = ($types['volunteer_project']-&gt;type);        if($node-&gt;type === $yes){           $hash = md5($node-&gt;title . $node-&gt;nid . $node-&gt;nid);         $hashed = substr($hash, 0, 6);         $node = node_load($node-&gt;nid);         $node-&gt;tcode[$node-&gt;language][0]['value'] = $hashed;         node_save($node);          watchdog('vbtoken', 'Added a new Token code to %nid', array('%nid' =&gt; $node-&gt;nid));          }         else          {           dpm('not working dude');         }      } How can I chain implicits in Scala? Creating bash scripts that take arguments Skype window problem in Ubuntu 14.04 I have a conjecture that any two positive coprime integers $a$ and $b$ can be added to form any integer greater than or equal to $(a-1)(b-1)$.   This is true for $3$ and $5$, which can form any integer greater than or equal to $8$, where $8=3+5, 9=3+3+3, 10=5+5; k=3n+8$ or $3n+9$ or $3n+10$.  It is true for $4$ and $7$, which can form any integer greater than or equal to $18$, where $18=4+7+7, 19=4+4+4+7, 20=4+4+4+4+4, 21=7+7+7$, etc. How can it be proven that this will work for any two coprime numbers?