So here is the deal:  There is a team of 16 people. There are 16 rooms and there is another room with a box with gold in it. The team knows that the box is closed at the beginning. After that each team member is locked in a room and they do not have any contact with each other. Randomly one player is picked, he can go to the room with the box in it and he can decide if he wants to open it, close it or leave it so that it was when he entered the room. After that this player have to go back his room and a next player is picked randomly. The procedure repeats itself until somebody claims that now all of the team member were at least once in the room with the box in it. If it is true they win the gold form the box, if not they don't. Which strategy should the team apply to win?  Can anybody give me an idea how should I start to think? Is it possible to solve it as a model of a Turing-machine?
100 prisoners are imprisoned in solitary cells. Each cell is windowless and soundproof. There's a central living room with one light bulb; the bulb is initially off. No prisoner can see the light bulb from his or her own cell. Each day, the warden picks a prisoner equally at random, and that prisoner visits the central living room; at the end of the day the prisoner is returned to his cell. While in the living room, the prisoner can toggle the bulb if he or she wishes. Also, the prisoner has the option of asserting the claim that all 100 prisoners have been to the living room. If this assertion is false (that is, some prisoners still haven't been to the living room), all 100 prisoners will be shot for their stupidity. However, if it is indeed true, all prisoners are set free and inducted into MENSA, since the world can always use more smart people. Thus, the assertion should only be made if the prisoner is 100% certain of its validity.  Before this whole procedure begins, the prisoners are allowed to get together in the courtyard to discuss a plan. What is the optimal plan they can agree on, so that eventually, someone will make a correct assertion?    I was wondering does anyone know the solution for the 4,000 days solution. Also, anyone got any ideas on how to solve this?   Just wanted to know if anyone got any ideas how to solve this.  is offering prize money for a proof of a optimal solution for it. I suppose to make it clear the people want a plan that would mean on average it would take least amount of time to free the prisoner. The point is the average run time is as low as possible.
Trying to overwrite ... which is different from other instances of package I tried to upgrade Intel graphics in ubuntu 16.10 using the official installer. The last stage of unpacking libcairo2 produces an error (see figure).  When I do upgrade I get the same error also:   Preparing to unpack .../0-libcairo2_1.15.2-0intel1_amd64.deb ... Unpacking libcairo2:amd64 (1.15.2-0intel1) over (1.15.2-0intel1) ... dpkg: error processing archive /tmp/apt-dpkg-install-aYhdFd/0 libcairo2_1.15.2-0intel1_amd64.deb (--unpack): trying to overwrite shared '/usr/share/doc/libcairo2/changelog.Debian.gz', which is different from other instances of package libcairo2:amd64 Preparing to unpack .../1-libcairo2_1.15.2-0intel1_i386.deb ... Unpacking libcairo2:i386 (1.15.2-0intel1) over (1.15.2-0intel1) ... dpkg: error processing archive /tmp/apt-dpkg-install-aYhdFd/1-libcairo2_1.15.2-0intel1_i386.deb (--unpack): trying to overwrite shared '/usr/share/doc/libcairo2/changelog.Debian.gz', which is different from other instances of package libcairo2:i386 Errors were encountered while processing: /tmp/apt-dpkg-install-aYhdFd/0-libcairo2_1.15.2-0intel1_amd64.deb /tmp/apt-dpkg-install-aYhdFd/1-libcairo2_1.15.2-0intel1_i386.deb E: Sub-process /usr/bin/dpkg returned an error code (1)   It seems that there is a conflict in thelibcairo releases; if yes, how to resolve it ? Updating inherited property Relative log file matching with linux? Let $g_n= {2^2}^n +1 $. Prove $g_0 · g_1 · · · g_{n−1} = g_{n} − 2$.    I'm not sure how to start this proof, if it should be done algebraically or if I should try to use a proof by induction. What are some typical LuaTeX gotchas? Commas with "so" I am confused with the usage of so.  Consider some examples from Oxford and Meriam-webster        It was still painful so I went to see a doctor (Oxford).   We were bored with the movie, so we left (MW).   There are no more chairs available, so you'll have to stand (MW).      So is a conjunction in all the above sentences. But I don't understand when to place a comma before it. So is one of FANBOYS. Thus, we have use a comma when it connects two independent clauses, which I think contradict the first sentence.  Is the placement of comma before so depends on a style guide? For example, Americans prefer a comma while the British doesn't. I am quite new to DSLRs and one of the first things I noticed was the incredible focus points and appearance of depth that you can achieve. That is great in a lot of scenarios, but not in all. When filming a landscape as a whole, I do not want to have the focus on that single tree, but on the whole skyline.  Is there a way by which you can sort-of "disable" the focus, so that the raw image is recorded without any added blur? I suppose something as simple as this is only a small function you can turn off, but I can't seem to find it in the manual of my camera. root@SERVER ~$ df Filesystem  512-blocks  Free    %Used   Iused   %Iused  Mounted on /dev/YXCV   655360      365632  45% 6322    13% / /dev/ASDF   3801088     670648  83% 41759   32% /usr /dev/ASR    1048576     500496  53% 5555    9%  /var   How can I pipe the df command's output to only display lines that have more usage than 80%?  e.g.: it would only display:  /dev/ASDF   3801088     670648  83% 41759   32% /usr How can I manually install a package on MiKTeX (Windows) I'm new to LaTeX, investigating using it for some work projects.  I'm using MiKTeX on Windows.  My employer's locked-down network blocks the application's automatic installation function.  I can take my laptop home and successfully install from there, but if I need a package in the middle of the day I'm stuck.  I am able to access the CTAN website and download the package files (.dtx or .ins?), but I don't know what do do with them.  How can I do a manual package installation? If $S$ is a nonempty subset of group $G$, then $S^{|G|}$ is a subgroup of $G$. Let $G$ be a group with $|G| = n$ and let $ \emptyset \ne S \subseteq G$.   I want to show that $S^n$ is a subgroup of $G$ where by $S^n$ I mean the set $\lbrace s_1\cdots s_n \; | \; s_i \in S\rbrace$. How to set Windows bootloader as default bootloader? I have a Win 7/11.10 dual boot system with Grub 2 as the default bootloader. However, I want to make Windows bootloader the default bootloader (grub 'dos' like interface scrares the hell out of my sister) so when I start the PC I will have the following boot options: 1. Windows 7 2. Ubuntu  NB: A process to reverse this operation so Grub can be the default bootloader again will also be appreciated How check if a picklist value is available or not for a specified record type ( through SOQL)? Thanks in advance How would one throw an unwilling creature? My bugbear barbarian, who can lift about double the weight of a wolf, wanted to throw the wolf at a second wolf. How would we go about doing that given existing rules options? Projection on the hyperplane $H: \sum x_i=0$ How do I find out the number, type, resolution &amp; refresh rate of additional monitors I can attach to my MacBook or MacBook Pro?  This is an attempt at a canonical QA, as per the Meta QA -   to try prevent the myriad "same but different" questions we get on every possible combination of computers, cable &amp; monitors There are perfectly good resources out there that Ask Different should not have to duplicate the efforts of. $a _{1} = \frac{1}{2}, a _{2} = 1, a _{n}= \frac{1}{2} a_{n-1} + \sqrt{a _{n-2} }$  Show by the induction that it's $\le 4$ and also by the induction that $a_{n+1}-a_n \ge 0$  If it comes to first I don't know what to do and if it comes to second I tried many different ways but I couldn't prove it. It's my understanding that a z-score can only be calculated and accurately used for data sets that are normally distributed.  Since "perfect" normal distribution almost never occurs in real-world data (where "perfect" normal distribution is defined as 1. The mean, median, and mode all equal the same number, 2. the distribution is perfectly symmetrical between all standard deviations on both sides of the mean, and 3. the distribution is asymptotic), how "close" can the distribution be to perfectly normal for the z-score to still be a valid statistical measure?  If the answer is it has to be a perfectly normal distribution, then my question is why is the z-score so important since it would seldom be a valid measure on real-world data? GR. Einstein's 1911 Paper: On the Influence of Gravitation on the Propagation of Light Show $\sum\limits_{n=0}^{\infty}{2n \choose n}x^n=(1-4x)^{-1/2}$ How do you prove that $\sum\limits_{n=0}^{\infty}{2n \choose n}x^n=(1-4x)^{-1/2}$? I tried to identify the sum as a binomial series, but the $4$ and the $-1/2$ puzzle me. (This series arises in studying the first passage time of a simple random walk.) How can all labels of a given type of node be restyled in Tikz?  Imagine that there are nodes of different styles, and that only the nodes of style X should have red labels. Is this possible without having to change all labels one by one of nodes of style X?