Problem statement  6 scientists are working on a secret project. They wish to lock up the documents in a cabinet so that cabinet can be opened when and only when 3 or more scientists are present. What is smallest number of locks needed? What is smallest number of keys each scientist must carry??  Let $n$ be the number of locks. Let us name each scientist as $1,2,3,4,5,6$.Let $S_i$ be the set of keys that scientist $i$ is carrying and each scientist carries $k$ number of keys.we would get following results  $|S_i|=k$ $|S_p \cup S_q \cup S_r|=n$ $n=3k-(|S_p \cap S_q|+|S_p \cap S_r|+|S_r \cap S_q|)+|S_p \cap S_q \cap S_r|$  I tried manipulating the above results in hope of finding solutions but failed.Is there anything I am missing or is this approach entirely wrong?
There are 8 crew members, The leading member wants that only a crew of 5 people or more could open a safe he bought, To each member he gave equal amount of keys, and locked the safe with several locks.  What's the minimal number of locks he should put:   at least 5 crew members would be required to open the safe? Any team of 5 crew members could open the safe, but none of the 4 team crew members.   1,2 stands individually of course.
How did this person gain possession of the Infinity Stones? Calculate the last digit of $3^{347}$ I think i know how to solve it but is that the best way? Is there a better way (using number theory). What i do is: knowing that  1st power last digit: 3 2nd power last digit: 9 3rd power last digit: 7 4rh power last digit: 1 5th power last digit: 3    $3^{347} = 3^{5\cdot69+2} = (3^5)^{69} \cdot3^2 = 3\cdot3^2=3^3=27 $ so the result is $7$. How can I prepend a tag to the beginning of several files? FasterCsv doesn't show any result in my view in Ruby on Rails? How quickly does the Ultimate Meter fill up? I went through a , but the answer was informing how to hide the monitor, but not how to disable it. I do not want any new windows to creep into the laptop display when the external display is connected. I could not find any in the Display Settings (under System Preferences). I don't want to close the lid because I think it impacts the air flow of the MacBook Pro. I don't want to close the lid because the sound quality is reduced. Grepping logs for IP addresses Is Ubuntu compatible with my hardware? Java code needs a system.out.println statement to run Show that $C[a,b]$ is a complete space under the metric $d(f,g)=\sup_{t\in [a,b]}|f(t)-g(t)|$. Installing Ubuntu 13.04 on a MSATA SSD I am trying to install Ubuntu 13.04 on my 24Gb MSATA SSD. In my laptop, I've also got a 500Gb SATA HDD. I realize that in order for this to work I need to put my /home directory on the 500Gb HDD.   I've tried installing it by creating a ext4 partition on the SSD and a 8Gb swap partition on my HDD. This resulted in an error saying something similar to Cannot install bootloader, please select an other location for the bootloader.   Now before I waste any more time trying to get it to work I'm going to ask a bunch of questions:   Where should I put the swap partition? How big should I make the swap partition? (I've got 12Gb RAM) My 500Gb HDD is currently in Raid mode. Should I change that (to AHCI or IDE)? Where should I put the bootloader if the error message occurs again? How do I make the home directory point to the HDD instead of the SSD? Can I configure Ubuntu to install software/packages on the HDD instead of the SSD? no cycles if and only if has $n-m$ connected components I want to create this:  Note that wire lay chaotically, so spiral object not the same thing.  There is a cool way to do this task in 3ds max:  Basically he deform straight spline/curve and then bend it couple iterations (over 9000 degrees angle in max).   Blender can't bend that way with simple deform as I know, only up to 360 degree. Is there any other way to make wire wrapping similar to photo? I use Chrome as my main browser.  I also spend a lot of time on a particular webapp that my company uses.  I'd like to keep those two things separate.  I can run the webapp in a separate window - but I'd like to go further than that.  I'd like to have it be identified by a different task in the Win 7 taskbar; ideally a different icon; and ideally a different title in Process Monitor.  How can I run a second, independent instance of Chrome, with a different title and icon, that won't merge with my main Chrome browser. Is there a way to see how the markup of a per-site meta answer is formed? I sometimes see a useful markup feature in a per-site meta answer. However, I cannot edit it to see how one did it, since editing (or suggesting edits) is disabled for users with less than 2k reputation on per-site metas.  Is there a way to see the source code of a per-site meta answer? Where were the cannons in final fight in Wakanda in Infinity War? In Black Panther, Ulysses Klaue describes his arm cannon as a leaf blower in comparison to the cannons/weapons that Wakanda has.  Infinity War comes after the events of Black Panther, so the weapons should exist. During the final fight with the children of Thanos and Space Dogs (as Rocket refers to them), Wakandans could have used these powerful cannons, pointing them at the opened section of barrier. Instead they chose a fist fight.  Even M'Baku says that it would be the end of Wakanda, so the magnitude is huge and risks are very high. Why were these powerful weapons not used?    Edit 1: I watched the movie again and planes are there in the fight. But they were only used to destroy the spaceships that crashed. Why does water take a "wet" path? Allow me to explain what I mean... ((I am asking this question in the physics section in hopes of finding a "physics" argument))  I shall make it clear what I mean by demonstrating an experiment...  Hold your hand upright with your index finger pointing up towards the sky. Now drop about 2-3 drops of water right on top of your finger. Water drop should (theoretically) stay there. Now tilt your hand ever so slightly towards one side. The water drop rolls down your finger down your wrist leaving a trail towards the tilted side right?  Now's here comes my question. Now if you bring your finger and the hand to the initial upright state and place another water drop on the same finger. Now we see that the water drop takes the same trail! Why does it happen?  My argument: The water trail which was previously left off reduced the friction in that path by filling the gaps between the molecules. Hence the new drop tends to slide more on that path and hence ends up travelling in it.  ((This "effect" is also observed when tear drops keep rolling down in the same path. But that could just be because that path is the steepest.)) unsigned int vs. size_t I notice that modern C and C++ code seems to use size_t instead of int/unsigned int pretty much everywhere - from parameters for C string functions to the STL.  I am curious as to the reason for this and the benefits it brings. JavaScript post request like a form submit Inheriting constructors