The police have three suspects for the number of Mr. Boddy: Professor Plum, Colonel Mustard, and Mr. Green. Professor Plum, Colonel Mustard, and Green each declare that they did not kill Boddy. Mustard also states that he did not know Boddy and that he was out of town the day Boddy was killed. Green also states that he saw both Plum and Mustard with Boddy the day of the killing and that either Plum or Mustard must have killed him.  Assume one of the three men is guilty and that innocent men do not lie. The statements of the guilty man may or may not be true. Determine who killed Mr. Boddy and prove it.
I’m trying to solve a logic puzzle that goes like this:     The police have three suspects for the murder of Mr. Cooper: Mr. Smith, Mr. Jones, and Mr. Williams. Smith, Jones, and Williams each declare that they did not kill Cooper. Smith also states that Cooper was a friend of Jones and that Williams disliked him. Jones also states that he did not know Cooper and that he was out of town the day Cooper was killed. Williams also states that he saw   both Smith and Jones with Cooper the day of the killing and that either Smith or Jones must have killed him. Can you determine who the murderer was if one of the three men is guilty, the two innocent men are telling the truth, but the statements of the guilty man may or may not be true?   When i was young, i used to solve such puzzles graphically, drawing vertices and arrows and excluding impossible cases. But now i want to do that formally. How can i express this puzzle definition using proposition calculus notation, inference and truth tables? Or, in other words, when you stumble upon a logical puzzle and you want to solve it formally, what is your algorithm?  What i tried. I extracted several propositions from the definition:   S: didn't kill C S: J knew C S: W disliked C J: didn't kill C J: J didn't know C J: out of town W: didn't kill C W: S with C W: J with C   There are 3 groups of propositions, two of them are always true, the third may contain either true or false statements. Let be $A = 1 \land 2 \land 3$, $B = 4 \land 5 \land 6$, $C = 7 \land 8 \land 9$. Then from  by using truth tables and Karnaugh maps i deduct that the statement “some two of A, B, C are true” looks like $(A \land B \land \neg C) \lor (A \land \neg B \land C) \lor (\neg A \land B \land C)$. But wait, “may or may not be true” means that all statements might be true, not that at least one is false (hence the NAND is not appropriate here). So the sentence should be reformulated as “at least some two of A, B, C are true”. Am i going in the right direction?
Is It Possible to NSLog C Structs (Like CGRect or CGPoint)? I want to be able to debug C structures without having to explicitly type every property that they consist of.  i.e. I want to be able to do something like this:  CGPoint cgPoint = CGPointMake(0,0); NSLog(@"%@",cgPoint);   Obviously the '%@' won't work, hence the question. In transformers, the ratio of the voltages equals the ratio of the turns - so double the output coil's turns and the output voltage doubles. Then, in order to conserve energy, current halves.  This makes perfect sense in terms of $\mathrm{P=VI}$, but what happened to $\mathrm{V=IR}$? Doubling voltage and halving the current seems to completely contradict this basic law. That is, of course, unless the resistance in the output circuit changes, with R proportional to $\mathrm{V^2}$ - but I don't see how this is possible.  So how can a transformer obey both laws? Can resistance change or am I missing something else? This question led to a new package:      I want to reference to citations from other file. Similar to what xr package does to labels, but I want to apply it for the bibliography.  If I'm able to do \cite{someone} in the main file, and it creates let say the number [4], I want to do the same \cite{someone} in a second file, and also create the same number [4]. Similar to what xr does with the labels.  By the way, I tried to add the main.bbl file from the main file. However, that adds all the references to the end of the second file. I want to avoid this.  Is there any package that accomplish this? Let $D$ be a , and let $a,b,x \in D \setminus \{0\}$. Then is it true that $\gcd (ax,bx)=x \cdot \gcd (a,b)$ ?    Let $c=\gcd (a,b)$ and $d=\gcd(ax,bx)$, then as $cx|ax$ and $cx|bx$ so $cx|d$. We would be done if we could show $d|cx$, but I am unable to show that. Please help me to solve this problem. Finding distance between consecutive points using ArcGIS Desktop? From Euler we've learned that $z=re^{i\theta}$.  And it's easy to see that $|z|^2=r^2$, since $re^{i\theta}\times re^{-i\theta}=r^2$.  Why must we use e to represent these numbers correctly? It seems that I could arbitrarily choose a different exponent $z=r\pi^{i\theta}$ and get the same size for $z$ as I did before: $|z|^2=r\pi^{i\theta}\times r\pi^{-i\theta}=r^2$  What did I miss? Pokemon GO isn't working at all for me right now. I'm in one of the following circumstances and can't do anything:   My game is displaying a "Try Again" message I'm stuck on the Loading Screen When I sign in I get a message that the servers are experiencing problems. I see the map but nothing is loaded, and my team color is wrong The "loading" Pokeball just ends up spinning and I can't catch or interact with things When I try to catch a Pokemon, the Pokeball just sits on my screen doing nothing Gym opponents will drop to 1 HP and won't take any more damage or attack When I open a pokestop, the pokestop image and the name of the pokestop does not load.   What's causing this? Is there a way to fix it? Name of short sci-fi story involving a musician who is punished for listening to Bach I'd like to know whether, given a system, there's a way to obtain all the conserved quantities. For instance if the system consists of electric and magnetic fields, the fields must satisfy Maxwell's equations. These equations are invariant under many transformations (Lorentz transformation, rotations, spatial and temporal translations, etc. By the way is there a way, maybe from group theory, to find all the possible transformations that leaves the equation(s) invariant?) which imply as many conserved quantities thanks to Noether's theorem. In wikipedia I can see an equation that seems to give all the conserved quantities () but it involves the Lagrangian and I'm not sure whether the formula is valid for all systems whose Lagrangian is possible to obtain. Are InnoDB Deadlocks exclusive to INSERT/UPDATE/DELETE? "Agree" vs. "concur" Let $n$ be a nonnegative integer, and $k$ a positive integer. Could someone explain to me why the identity $$ \sum_{i=0}^n\binom{i+k-1}{k-1}=\binom{n+k}{k} $$ holds? I'm trying to do an incremental backup using cpio but it seems that the busybox version doesn't work the same as the normal one? This is what I've got so far:  find data/Backup -mtime -2 | cpio -cm media/USB_FLASH_2  I origianlly used:  find . -mtime -2 | cpio -cm /media/USB_FLASH_2  However, I've seen people say busybox doesn't like definitive paths while using cpio. Unsure about that though.   It returns an error that basically says I'm using cpio wrong. I can't find anyone using the busybox cpio to do things like this, does that mean i can't do it? I've looked at using rsync as well but again, it doesn't do what i would expect.  For reference I'm using PuTTY to connect through SSH to a ReadyNAS 102.  After using find . -mtime -2 | cpio -o | { cd /media/USB_FLASH_2 &amp;&amp; cpio -imd; }  i get the output:   BusyBox v1.20.2 (Debian 1:1.20.0-7) multi-call binary.  Usage: cpio [-dmvu] [-F FILE] [-H newc] [-tio] [EXTR_FILE]...  Extract or list files from a cpio archive, or create an archive using file list on stdin  Main operation mode:         -t      List         -i      Extract EXTR_FILEs (or all)         -o      Create (requires -H newc)         -d      Make leading directories         -m      Preserve mtime         -v      Verbose         -u      Overwrite         -F FILE Input (-t,-i,-p) or output (-o) file         -H newc Archive format Distribution of $-\log X$ if $X$ is uniform. Why is the potential energy equal to the negative integral of a force? Why is the potential energy equals to the negative integral of a force? I am really confused with this negative sign. For example, why there is a negative sign in the gravitational potential energy and what does it mean?   I read that the negative sign means you do the same force but in the opposite direction.  Doesn't that mean the object shouldn't move? Where do object file "Version References" come from? Dual boot windows 8 and Ubuntu with Windows 8 Boot manager I have two partitions on my hard-didk , I have installed ubuntu on my 1st partition and windows 8 later on another partition.Now i can only boot into windows 8 because it doesn't recognize Ubuntu.  How would i dual boot my PC without using grub . I would like using Windows 8 boot manager as its pretty neat.  This is what i have tried :  I tried using easyBCD but it doesn't work.It causes the boot manager to switch to windows 7 Boot Manager .  EasyBCD creates a C:/NST/AutoNeoGrub0.mbr file .  As EasyBCD was causing the boot manager to switch i created a manual entry to the BCD store uisng windows bcdedit command and point it to the C:/NST/AutoNeoGrub0.mbr file created by EasyBCD. This gave me the Windows 8 Boot-Manager with Ubuntu Entry,but grub is unable to find the root partition.  Is there any other work around or solution for this ?  Any help would be appreciated.  Note: The windows 8 boot Manager is sky blue color interactive menu with mouse and other options and windows 7 boot manager is the normal black and white one where you can only use your keyboard  I don't want to install grub because it would prevent my windows 8 from updating as its a genuine MSDN version and various other reasons Systemd is really slow in comparison to upstart I have been using Ubuntu for a long time now, this is what happened when I use:  Systemd: It performs really bad using systemd: it uses 95% of the CPU all the time and the PC gets really hot. Also it takes a really long time to boot (about 1.5 min, and sometimes it does not boot at all as it has a black screen at boot.)  Upstart: When I tried the upstart options at boot, it performs as expected, booted in seconds, and it was awesome as it should be.  Laptop:   AMD A8 Radeon SSD   Questions:   Why does upstart perform better than systemd? How can I debug systemd? Should I switch to upstart? If yes, how do I do it? What is an efficient way to implement a singleton pattern in Java? What is an efficient way to implement a singleton pattern in Java? I'm writing up some notes that will be displayed on an overhead projector. The standard time-derivative \dot{x} produces a dot that is hard to see. Does anyone know of a package or have a macro that produces a (nice looking) larger dot? Similarly with \ddot{x}.  At the moment, I've been supplied with some ugly code that produces an ugly output:  \def\dt#1{{\buildrel  {\hbox{\LARGE . }} \over {#1}}}    % dot-over  \def\ddt#1{{\buildrel {\hbox{\LARGE ..}} \over {#1}}}    % double dot