Why is it not possible to cover the chess board with 3X1 dominoes if one of the corner squares is missing (e.g. the top right square)?
If we remove the square in the upper right corner of a $8\times 8$ chessboard.  The question is: Is it possible to cover the entire remaining area, with $1\times 3$ chocolate bars? (they can be laid on the chessboard vertically and horizontally aswell)  For the answer: We know that there will be $63$ squares left on the chessboard, of which $32$ are white and $31$ are black, since the one in the upper right corner was black. $63$ is divisible by $3$, so it could be possible to cover the area, but that doesn't prove that an arrangement exists to do it. I'm not sure how to continue and am seeking help. Thanks.
What do you call someone who pretends to be your friend but is actually your enemy?  A friend suggested spy for me, but that does not nearly describe the word I need for an English project. The character is very good at manipulating how people see him. He's a good liar. And pretends to be your friend but actually is your enemy. Convert .sdf database to .mdf database Which B2C option to choose? A stock Salesforce org is geared toward B2B companies, but I work in Higher Ed and we're B2C-focused.  There seem to be three main B2C options available:   Person Accounts Nonprofit Starter Pack (NPSP) 1-to-1 model NPSP bucket model   Why would I choose one option over the other? Why does println(array) have strange output? ("[Ljava.lang.String;@3e25a5") Can I get the "Diamonds to you!" achievement in singleplayer? How can one get the "Diamonds to you!" achievement in singleplayer? The achievement list cannot be completed without it. Perhaps it can be possible by passing a diamond to a zombie? Do lure modules and incense cause new pokemon to spawn near you, or existing pokemon to be drawn to you? What fallacy dismisses problems by presenting "bigger" problems? Wasn't really sure how to phrase this, but I'm thinking of an instance in which someone diminishes a problem by presenting one of larger scope - as a rather shoddy example, "x political problem in America doesn't matter because half the world's population is starving."  I honestly have no idea if this is considered fallacious or not, but for some odd reason I can't shake the feeling that someone has described it to me as a fallacy before. Am I crazy or is there something to this (or something similar)? Is my proof of convergence for $\sum\limits^{\infty}_{n=1} \frac {2^n} {n^n}$ true? I want to prove that $\sum\limits^{\infty}_{n=1} \frac {2^n} {n^n}$ is convergent.  Therefore I want to use that it will be convergent if $\lim\limits_{n \to \infty}|\frac {2^{n+1}} {n^n}| &lt; 1$ is true.  But I am not sure if all of my steps are legal to do in order to do it. Here is what I came up with:  $$\lim_{n \to \infty}|\frac {2^{n+1}} {n^n}| &lt; 1$$ $$\lim_{n \to \infty}|\frac {\sqrt[n]{2^{n}} \sqrt[n]{2}} {\sqrt[n]{n^n}}| &lt; \sqrt[n]1$$ $$\lim_{n \to \infty} \frac {2 \sqrt[n]2} {n} &lt; 1$$ $$0&lt;1$$  $\Rightarrow$ It is true. Full List of inventory items After beating the game, I still have several empty inventory spots.  I most likely missed several items in my addicted frenzy to finish the game.  What are all the items that can be found in the game? And where can they found? Is there really a way to make a true toon shader material in Cycles? How many times more than $0$? If a group satisfies $x^3=1$ for all $x$, is it necessarily abelian? I know that any group satisfying $x^2=1$ for all $x$ is abelian. Is the same true if $x^3=1$? I don't think it is, but I can't find a basic counterexample. Covariant derivative ambiguity I'm studying general relativity and am running into an ambiguity with the covariant derivative. The covariant derivative acting on a scalar is, in a co-ordinate basis, simply $$\nabla_X f = X^a \nabla_a f = X^a \partial_a f $$ whilst when acting on vectors or tensors, the covariant derivative includes extra terms involving the connection coefficients $\Gamma$. My problem is that I'm not sure what happens when the covariant derivative acts on the components of a vector. So the $X^a$ in the above expression are each scalar functions, and so when we write $\nabla_Y X^a$, do we assume the covariant derivative acts on $X^a$ as scalars, or do we include connection coefficient terms?  To clarify, consider $$ \nabla_X Y = X^a \nabla_a(Y^b e_b) = X^a (\nabla_a Y^b) e_b + X^a Y^b (\nabla_a e_b) = X^a (\partial_a Y^b) e_b + X^a Y^b \Gamma^c{}_{ba} e_c $$ As you can see, when the covariant derivative acts on the $Y^b$, it acts as a simple partial derivative, since the $Y^b$ are here considered functions premultiplying the vectors $e_b$.   However, in this equation from  page: $$(\nabla_X \nabla_Y Z)^a = X^c \nabla_c Y^b \nabla_b Z^a = X^c Y^b \nabla_c \nabla_b Z^a + (X^c \nabla_c Y^b) \nabla_b Z^a = (\nabla^2_{X,Y} Z)^a + (\nabla_{\nabla_X Y} Z)^a$$ When the covariant derivative acts on the $Y^b$ term it treats it like a vector.  What's going on here? Thanks. ESTA approved on the same day as B-1/B-2 visa refused I am writing because I have a question regarding my ESTA application and because I could not find a similar case online that would help me at this stage. I have never been to the U.S. so this would be my first visit.    I am a German citizen, hence eligible for the Waiver Program. I applied for an ESTA in June 2014 and got approved. After further research on the Internet I learned that the passport should be valid until 6 months after the planned return date. My passport was due to run out in Feb 2015 - which still should have been fine but because I didn't want to take chances I applied for a new passport which was issued August 2014 and is now valid until August 2024. My passport number has been changed also.    After I received my new passport I was advised by a friend to apply for a B-1/B-2 visa as it would allow me to extend my stay and it seemed like a good idea at first. On the day of my interview I also applied for a new ESTA with my new passport number (just in case) which again was granted.   Unfortunately for me the interview for the B-1/B-2 visa was unsuccessful and I got rejected. I was not aware then that after a rejected interview one could not travel with ESTA, otherwise I would have never risked it!  Now I am very concerned, can I still use my ESTA and enter the U.S.? as I read everywhere that once you get rejected the chances of getting through are very slim and any visa rejection will result in not being able to use the waiver program.  It might be important to note that both the B-1/B-2 interview and the waiver application were on the same day, 21st of August 2014, so depending on how one might look at it that might present a problem too I suppose.  I guess the frustration lies in the fact that I did not need to apply for a B-1/B-2 visa to begin with, and had I not I would now not have these problems. I would like to know how likely it is that I can still travel under the waiver program, if at all, and what my options are at this point. Dependence of Friction on Area Is  really independent of area? The friction force, $f_s = \mu_s N$. The equation says that friction only depends on the normal force, which is $ N = W = mg$, and nature of sliding surface, due to $\mu_S$.   Now, less inflated tires experiences more friction compared to well inflated tire. Can someone give clear explanation, why friction does not depend on area, as the textbooks says? Mute conversations on Skype I'm in a conversation and I don't really want to leave because the people there keep adding me back so it's just whatever. But I would like to mute the conversation or something like I do on Facebook so I won't take notifications or anything from there unless I press on the group and see what's going on. Because for now I have my Skype having a new notifications every half a second.  Any solutions to that? If the dual spaces are isometrically isomorphic are the spaces isomorphic? Related questions with over 99 score display incorrectly How general is the Lagrangian quantization approach to field theory? Why align and equation environment do not tolerate empty lines?