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 Aug 29 comment Knight on a chessboard moving from a1 to h8 Please explain your solution in a language that can be most of us. Aug 29 comment Knight on a chessboard moving from a1 to h8 @AndréNicolas Are you considering the squares excluding a1 or h8? Aug 29 comment Knight on a chessboard moving from a1 to h8 I think that my argument could be wrong if we are considering all the squares and not just ones that will only visited. In fact, even if I consider 63 squares ( including h8 ), I am still having one white square in excess and hence the pairing won't be possible. Mar 24 comment LOVES+LIVE=THERE. How many “loves” are “there”? and hence I can also say that $S\neq0$. I am so sorry for this mistake. Mar 2 comment Bayes' Theorem: Detection of bomb in a box Thanks for the answer. So, from your answer I take it that it not possible to calculate the probability that is required by me. I can say that it is not possible to calculate $P(d_1|{p_1}^c)$ without knowing the threshold and the distribution. Is that right? Also, does you theory also apply if replace bombs with something more safe( say letters ) and boxes with envelopes? If yes, then what will be threshold ( in that case ) ? Feb 27 comment Find the solution $x(t)$ satisfying initial value problem $\frac{dx}{dt} = e^x e^t$ sorry, problem in writing LATEX. It is now rectified. Feb 26 comment Bayes' Theorem: Detection of bomb in a box In the problem itself it is mentioned that the bomb is equally likely to be present in any of the three boxes. So,I think that$P(p_i)=\frac{1}{3}$. Also, you are right that $\alpha_i$ is the probability that the bomb is detected, provided it is present in the the box i ( i=1,2,3). $P(d_i)$ is indeed denoting just the detection. So ,when I say $P(d_i|p_i)$, I mean detection when it was present and hence, $P(d_i|p_i)$ = $\alpha_i$. Feb 26 comment Bayes' Theorem: Detection of bomb in a box The bomb is supposed to be detected, not seen. There might be issues with the detector that it is doing so. It might happen that the bomb is pressure sensitive and opening the box might trigger. So, the bomb is to be detected and it might happen that the detector was unable to detect it. Think of the medical cases where a patient is said to free of a disease when , in fact, he has that disease. Feb 26 comment Bayes' Theorem: Detection of bomb in a box I apologize for the inconvenience. Please free to edit the question to make it more understandable. By the way, what was I unable to convey properly? Jan 9 comment Estimate the given sum. Thanks for the help. I just didn't consider the asymptotic behavior ( even though I was considering large values of N ). Dec 12 comment Combinatorics with repetitons Thanks for the answer. Multiset really elucidated the concept. Also , the thought that I presented in my questions ( about total number of permutations when we have many objects but those can be divided into two types ) can be used to understand this concept,yes? Jun 28 comment Mathematics in the “ The Art of Computer Programming” @AndréNicolas this is also one of the reasons. Jun 28 comment Mathematics in the “ The Art of Computer Programming” i am learning it for fun Jun 28 comment Mathematics in the “ The Art of Computer Programming” So, I can study it just for the sake of maths and the analysis of algorithms and completely forget about the implementation of algorithms on computer? Jun 28 comment Mathematics in the “ The Art of Computer Programming” I am not trying to learn mathematics from this book. I have learnt the required topics from Concrete Mathematics. I am just studying the TAOCP to get anexperience of the real-life applications of the math that I've studied. By "right", I meant studying only the analysis of algorithms given in the book and not implementing them on the computer. Jun 24 comment Calculate the limit at x=0 This is my approach:- We have \begin{align} f(x) & = \dfrac{\sqrt{a^2-ax+x^2}-\sqrt{a^2+ax+x^2}}{\sqrt{a-x} - \sqrt{a+x}}\end{align} \begin{align} lim_{x\to0}f(x) & = lim_{h\to0}\dfrac{\sqrt{a^2-ah+h^2}-\sqrt{a^2+ah+h^2}}{\sqrt{a-h} - \sqrt{a+h}}\end{align} \begin{align}& = \dfrac{\sqrt{a^2-0+0}-\sqrt{a^2+0+0}}{\sqrt{a-0} - \sqrt{a+0}}\end{align} \begin{align}& = \dfrac{\sqrt{a^2}-\sqrt{a^2}}{\sqrt{a} - \sqrt{a}}\end{align} . Here I carried out the usual algebraic manipulations and got $2\sqrt{a}$ Jun 24 comment Calculate the limit at x=0 @Cocopuffs. How is it $\sqrt{a}$. This is my main problem. Please elaborate. Jun 24 comment Calculate the limit of the given function at $x=0$ so what you suggested was just to avoid confusion due to the presence of a negatuve number, right? This means that if there was some other postive number in place of -1, then I could have used logarithm? Jun 24 comment Calculate the limit of the given function at $x=0$ Thanks. Its just like $cosx$ when $x\to \infty$. It oscillates between 1 and -1. Here the Greatest integer function doesn't oscillate but still it can hold either of the two values - 1 or -1. right? Jun 24 comment Calculate the limit of the given function at $x=0$ When $x$ approaches 0, $\frac1x$ approaches infinity. Then what can we say about $[\frac1x]$ ? You are claiming this to be 1 or -1. Why?