Say I have a string that I want to keep hidden. You can then enter a known string which is added to the end of the hidden string and you are given the sha256 hash of the combined string. If you were to do this many times with whatever strings you wanted and the hidden string remained fixed, would there be a practical way to determine the hidden string?
To be clear, I have access to $H(S)$ and as many $H(S||K)$ as I want. Every string $K$ is known. Can I use the extra information to my advantage and try to deduce $S$, without requiring bruteforce? Or do you still have to bruteforce but try less combinations since you have more information?
How to input open intervals I want to write open and half-open intervals using the following notation:  ]a, b[ ]a, b] ]-∞, b]   When writing them just like that in the LaTeX source, the spacing doesn't come out right. For example, for this equation:   \(X = ]-\frac{π}{2}, +\frac{π}{2}[\)   the minus sign is typeset as a binary operator. I can solve this by surrounding the whole value in braces, but then the spacing around the equal sign is still not correct. For other combinations of intervals and operators, different spacing inconsistencies arise.  What is the correct and easy  way to input intervals in order to avoid having to take care of this at all? Why could the dwarves only enter Erebor with the secret passage? Please bear with me as I've never read any of the LOTR books or the Hobbit, only seen the movies so far...  But when the sunlight fades and the dwarves think they've lost their only chance to enter Erebor using the secret passage and the key, they turn around to head home. Why is it that the dwarves would be unable to enter Erebor the way they did years ago, using regular doors to get inside? I'm assuming that's how they entered Erebor years ago? When using data.stackexchange.com I fail to remember if as [post link] is the correct alias to get the url for the post. Luckily the site has an  link. Unfortunately it is now broken. Can this be fixed? Given a collection of sets $\mathcal{C}$ and $E$ an element in the $\sigma$-algebra generated by $\mathcal{C}$, how do I show that $\exists$ a countable subcollection $\mathcal{C_0} \subset \mathcal{C}$ such that $E$ is an element of the $\sigma$-algebra, $\mathcal{A}$ generated by $\mathcal{C_0}$?    The hint says to let $H$ be the union of all $\sigma$-algebras generated by countable subsets of $\mathcal{C}$....although I don't know why. There are several ideas on hard determinism, but the core seems to be that in an interconnected existence, there can be no "actions" (free will), but only "reactions" (determinism). An action of free will would have to be a separate entity outside of existence, so we'd say it can't occur.   Now fast forward to Joe Schmo the robbing/murdering/rapist.  Joe wasn't born in some infinite bliss utopia, then decided one day to invent the concept of scumbaggery.  He's a product of an incomprehensible number of variables - maybe some are apparent like his dad was a violent alcoholic or whatever, but most likely it's far more complicated than that.    So that's fine - I get all that - but if that's the case, then how can you ethically deal with people like that?  You can't hardly let them do what they please at the expense of society, but then how can you get medieval on them when they're basically riding a wave?  I think that's a big reason why people fight concepts of determinism that mitigate or eradicate the concept of free will - now everyone has a license to do what they want and how can you punish them, it's not their fault!  How would/could/should you consolidate hard determinism with responding to criminal acts? let $a,b,c$ be postive real numbers ,and such $$ab+bc+ac=3$$   show that   $$\dfrac{a^2}{a+2b^2}+\dfrac{b^2}{b+2c^2}+\dfrac{c^2}{c+2a^2}\ge 1$$   This problem is from Secrets In Inequalities volume 1  page 30,example 1.24. the comment.the  author this case is a bit more diffcult,But this author can't post solution.Thank you What is the current state of apple device (iPhone, iPod, etc.) support? Why multiplying fractions is equal to multiply the tops, multiply the bottoms? $$\frac{a}{b}\times \frac{c}{d}=\frac{a\times c}{b \times d},$$ And why $$\frac{a}{b}\times \frac{c}{c}=\frac{a}{b},$$ Also why $$\frac{a}{b}+\frac{c}{b}=\frac{a+c}{b}.$$ I understand it, but I want a mathematical approach as a math student proves it. Also I want to know the mathematics topic of this question (number theory, logic, etc). A full answer is not necessary. Just a reference. How can I split an equation over two (or more) lines I am having the following equation:  \begin{equation}   Q(\lambda,\hat{\lambda}) = -\frac{1}{2} P(O \mid \lambda ) \sum_s \sum_m \sum_t \gamma_m^{(s)} (t) \left( n \log(2 \pi ) + \log \left| C_m^{(s)} \right| + \left( \mathbf{o}_t - \hat{\mu}_m^{(s)} \right) ^T C_m^{(s)-1} \left(\mathbf{o}_t - \hat{\mu}_m^{(s)}\right) \right) \end{equation}   which does not very well fit on one line. How can I split this over two lines? What I have in mind is that I specify the splitting place, and that the first line is left aligned and the second line right aligned to make clear that it is still the same equation.  The linebreak \\ does not work. New UI encourages askers to confirm or dispute duplicate votes Is it permissible to use somebody else's words (without quotations) to describe a concept once their work is cited? Quite often one comes across a really succinct and precise explanation of a concept. I'm wondering if it is permissible to use this explanation verbatim, if the source work is cited in your paper (next to the explanation)? What's in question here is at most 3 sentences. Is it possible to use Matcap materials as an actual material for a model so that I can render with it? There are certain parts that I want to apply specific Matcaps textures to but I want to actually use them to render and not just for sculpting purposes.  Is this at all do-able? How does this wiring work? I have a Trane XV90 and XL 14i. The wiring looks a little strange as in the picture bellow.                    _____________                   |           |   BK W2  W1   R  G  Y  B/C  YLO O     |___||   |__|  ||   |          |   |     ||   |_____>|----------|         |   |     ||_________>|other wire|         |   |     |           ------------         V   V     V     ---------------     |thermostat   |     ---------------  The R and G are jumpered together and the G wire is connected on the board  but is actually not connecting to the thermostat on the other end. So people told me that means the furnace fan is always on! (In my diagram above, I switched the location of Y and B/C to make diagram easier to draw. You can refer to the photo added below to see the details) My questions are the following  is the jumper between O and Y doing anything? I don't think I have heat pump I need to install Honeywell wifi thermostat and I am thinking of doing either one of the following:   remove jumper between R and G, and use G to connect B/C and then to thermostat C and put jumper between G and Y  leave jumper between R and G, and use G to connect B/C and then to thermostat C and put jumper between G and Y  remove jumper between R and G, connect G on control board to thermostat G, and finally have the spare wire to connect B/C and then thermostat C  leave jumper between R and G, does not connect G to thermostat,  and just use a spare wire to connect B/C on board to thermostat C   Can anyone comment on those plans? Thanks a lot! Why can a 1 element set be a member of another set but not a subset of it? I have just updated to Minecraft 1.7.4 and now all of a sudden there are barely any mobs spawning.  I checked to make sure that I was in normal difficult and I saw 1 creeper but that is all.  Also I tried different difficulties. Another thing - mobs seem to to spawn normally in the nether and all other mobs except aggressive mobs spawn like they should.  Please if you know how to fix this, please help! What is the difference between the memory usage report in System Monitor and the one by free? I am using System Monitor 2.28.0.  When I look in the Resources tab, I see a nice graph with for memory and swap.  Memory is about 60% 2.3 GiB of 3.8.  When I type the command free, I got :               total       used       free     shared    buffers     cached Mem:       3994908    3962396      32512          0     100852    1477032 -/+ buffers/cache:    2384512    1610396 Swap:      8000328      28468    7971860   cat /proc/meminfo | grep MemFree give  MemFree:           34536 kB   The situation has remained the save for several minute.  I started a lot of process with a script and the script is waiting for the free memory to get lower.  According to what I am seeing in the Process tab (or with top), the number in System Monitor seem a lot closed to the total of the memory of the process that the one reported by free.   Thanks Have you used any of the C++ interpreters (not compilers)? I am curious if anyone have used UnderC, Cint, Cling, Ch, or any other C++ interpreter and could share their experience. When a permanent magnet attracts some object, lets say a steel ball, energy is converted into for instance kinetic energy and heat when attraction happens, and they eventually collide. Does this imply that energy is drawn from the magnetic field and the magnet is depleted, making it weaker and weaker for each magnetic attraction performed?  (if the answer requires Quantum Mechanical explanations, please elaborate :)) Cannot set LC_CTYPE to default locale: No such file or directory Convert IEnumerable to DataTable