A $60\times 60$ square $S$ is divided into $2\times 5$ rectangles. Prove that no matter how this is done there is a way to divide $S$ into $1\times 3$ rectangles so that each of the above $2\times 5$  rectangles contains one of the $1\times 3$ rectangles. A bashy idea (which I cannot actually complete) is to show that we can always remove one-by-one connected figures of $30$ squares, composed of three $2\times 5$ rectangles, so that the resulting figure remains connected; and then check that each such figure of $30$ squares can be tiled with a $1\times 3$ rectangles. Any idea of something smarter? (Or if not, at least a fast way to complete the details of the above strategy?) Any help appreciated!
A $60\times 60$ board is partitioned into rectangles of size $2\times 5$ (or $5\times 2$). Is it true that there always exist another partition into rectangles of size $1\times 3$ (or $3\times 1$) such that any $2\times 5$ (or $5\times 2$) rectangle contains a $1\times 3$ (or $3\times 1)$ rectangle?  For the "simple" partition into $2\times 5$ rectangles, this is certainly true: use the simple partition into $1\times 3$ rectangle.  Another way to partition is to first partition the $60\times 60$ board into $12\times 10$ boards, and then for each such board, put two $2\times 5$ at the top and ten $5\times 2$ below. It is not hard to tile each such $12\times 10$ board with $1\times 3$ (or $3\times 1)$ rectangles so that each $2\times 5$ (or $5\times 2$) contains a $1\times 3$ (or $3\times 1)$ rectangle.  (I'm assuming that an $m\times n$ rectangle has $m$ rows and $n$ columns.)
How resilient is Ubuntu to repeated "power-off" shutdowns? My company is considering the use of Ubuntu as an OS for use on a hardware device.     It would be installed on compact flash drive - apparently this is not standard flash drive but a specific type of memory that is supposed to "cope" with immediate power shutdown (I am not sure how this is achieved but they are supposedly a "high end" card).    The units that would be run using Ubuntu are the type of units that will not be gracefully shutdown - the power cable would be removed and that is that.     Can anybody give me some advice on the potential problems that can occur? Is Ubuntu a good system that can deal with this kind of power outage and reboot successfully on next startup?     I realise that nothing is unbreakable, but is it a commonly used OS for an embedded setup? Is it asking for trouble to use Ubuntu in this kind of environment? How can I convert a string to boolean in JavaScript? What is the benefit of review a scientific paper as a referee? I've seen many boads with weird zig-zag shaped tracks just like the one below. Why are they designed like that? Voting on Meta sites generally express agreement and disagreement with a proposal, unlike on the Q&amp;A sites where they indicate useful/good vs. non-useful/bad content.  It seems to me that a down-vote on Meta Stack Exchange should not carry a -1 rep penalty, which only discourages down-voting. With this discouragement, questions on Meta SE will be biased towards agreement, since for every up-voter, there may be several in disagreement who don't want to lose the rep for down-voting.  Can the penalty for down-voting on Meta SE be removed? I know that the movies were written to be a stand alone universe on their own, but what key elements were missing in the movies that were vital in the books that viewers are missing out on? Yes, I'm really sure I want to delete that post Attempting to delete questions on the mobile site on iOS causes two notification messages asking me to confirm the deletion, which it shouldn't do.  I haven't really looked into it, but it may just be that the handlers from full.js and mobile.js are both being triggered, as there seems to be the flash of the error dialog indicating something went wrong on the supposed second AJAX request when the response from the first triggers a page reload.  You can see this happening by following the method calls; the mobile view first calls   StackExchange.question.init() -&gt; StackExchange.question.fullInit()   -&gt; StackExchange.vote.init()     -&gt; u()    ...where u() sets a delegated click handler on  $("div.post-menu *[id^='delete-post-'], table.flagged-posts *[id^='delete-post-']")   ...that calls .preventDefault() on the event, but doesn't block other handlers from firing.  It then later calls StackExchange.mobile.init(), which in turn calls the method J() that sets up a similar handler directly on $(".delete-post").  Since both handlers get triggered, there's two confirmation dialogs, and two attempts to delete the post. The extra handler in mobile.js seems unnecessary, so just removing it would appear to be the easy fix to the problem. Animating eye texture in a head mesh I'm trying to animate a mesh with different eye textures but it's not working.     This is a texture made by me to animate but I still couldn't figure out how to do it. I've seen tutorials on the internet but they don't work to me. How do I change the GRUB boot order? I have been using the Copy Attributes add-on to copy some properties from active object to selected objects. This add-on is not enabled by default and must be explicitly enabled. But its a very useful workflow enhancing tool.    There is a limitation though. Not all properties can be copied and even those that can be copied are copied in groups (Its hard-coded in to the add-on).  My question is if there is a built-in feature or any another other way to copy any property from the active object to the selected objects? Mavericks unusually high RAM usage I thought Mavericks was suppose to utilize RAM memory better, thus run smoother.  Running ML on Mac mini 2012, with 16GB RAM...always running smoothly even with over a dozen apps running.  Now, after installing Mavericks, my Mac is SLOW, eating up RAM like crazy! Looking over usage, of the 16GB of installed memory...on average it uses 10-14 GB RAM when barely running a few apps!!!   There is this kernel_task that is always running with over 1GB of RAM and most apps are not taking that much RAM, so what is using up all my RAM?! File cache? It shows very high in that new description, with about 1/3 of my total RAM Is there any way I can use  partitions on Windows&nbsp;7?  I have tried to install , but it doesn't seems to run on Windows&nbsp;7. In Pillow Problems and a Tangled Tale Lewis Carroll presents the following problem:     A bag contains a counter, known to be either white or black. A white counter is put in, the bag is shaken, and a counter is drawn out, which proves to be white. What is now the chance of drawing a white counter?   One can easily reason that in the end, the bag must be in one of three states:   Black remains, new white taken New white remains, original white taken Original white remains, new white taken   In two of those states, a white counter remains to be drawn. Therefore, the chance is 2/3.  How can one arrive to this answer using Bayes' theorem? I am attempting to write a filter using something like sed or awk to do the following:   If a given pattern does not exist in the input, copy the entire input to the output If the pattern exists in the input, copy only the lines after the first occurrence to the output   This happens to be for a "git clean" filter, but that's probably not important. The important aspect is this needs to be implemented as a filter, because the input is provided on stdin.  I know how to use sed to delete lines up to a pattern, eg. 1,/pattern/d but that deletes the entire input if /pattern/ is not matched anywhere.  I can imagine writing a whole shell script that creates a temporary file, does a grep -q or something, and then decides how to process the input. I'd prefer to do this without messing around creating a temporary file, if possible. This needs to be efficient because git might call it frequently. I'm runing 15.04 on a dell xps 13 bluetooth recognises devices when i  try to add them but won't let me connect to them Here is the results from my terminal.  ~ $ uname -a; lspci -nnk | grep -iA2 net; lsusb; dmesg | grep -i bluetooth; dmesg | grep -i firmware; lsmod | grep bluetooth  Linux aaron-XPS-13 3.19.0-15-generic #15-Ubuntu SMP Thu Apr 16 23:32:37 UTC 2015 x86_64 x86_64 x86_64 GNU/Linux 02:00.0 Network controller [0280]: Broadcom Corporation BCM4352 802.11ac Wireless Network Adapter [14e4:43b1] (rev 03)     Subsystem: Dell Device [1028:0019]     Kernel driver in use: wl Bus 003 Device 002: ID 8087:8001 Intel Corp.  Bus 003 Device 001: ID 1d6b:0002 Linux Foundation 2.0 root hub Bus 002 Device 001: ID 1d6b:0003 Linux Foundation 3.0 root hub Bus 001 Device 003: ID 0bda:5682 Realtek Semiconductor Corp.  Bus 001 Device 002: ID 0a5c:216f Broadcom Corp.  Bus 001 Device 001: ID 1d6b:0002 Linux Foundation 2.0 root hub [    8.164048] Bluetooth: Core ver 2.20 [    8.164065] Bluetooth: HCI device and connection manager initialized [    8.164069] Bluetooth: HCI socket layer initialized [    8.164073] Bluetooth: L2CAP socket layer initialized [    8.164079] Bluetooth: SCO socket layer initialized [    8.353160] bluetooth hci0: Direct firmware load for brcm/BCM20702A0-0a5c-216f.hcd failed with error -2 [    8.353166] Bluetooth: hci0: BCM: patch brcm/BCM20702A0-0a5c-216f.hcd not found [   20.289452] Bluetooth: BNEP (Ethernet Emulation) ver 1.3 [   20.289455] Bluetooth: BNEP filters: protocol multicast [   20.289459] Bluetooth: BNEP socket layer initialized [   20.310897] Bluetooth: RFCOMM TTY layer initialized [   20.310907] Bluetooth: RFCOMM socket layer initialized [   20.310912] Bluetooth: RFCOMM ver 1.11 [  886.399085] Bluetooth: hci0 urb ffff8800d8c15e40 failed to resubmit (2) [  895.471190] Bluetooth: hci0: BCM: patching hci_ver=06 hci_rev=1000 lmp_ver=06 lmp_subver=220e [  896.113983] Bluetooth: hci0: BCM: firmware hci_ver=06 hci_rev=1624 lmp_ver=06 lmp_subver=220e [    8.353160] bluetooth hci0: Direct firmware load for brcm/BCM20702A0-0a5c-216f.hcd failed with error -2 [  896.113983] Bluetooth: hci0: BCM: firmware hci_ver=06 hci_rev=1624 lmp_ver=06 lmp_subver=220e bluetooth             491520  22 bnep,btusb,rfcomm ~ $ Why does the question's closed status disappear when clicking to load a new edit? 2.8 mesh select mode hotkey changed The hotkey for mesh select mode (vertex, edge, face) while in edit mode Ctrl + Tab has been reassigned in 2.8. Is there another hotkey assigned for this? I have a box that I have extruded to the shape I want. Then I placed a cylinder so that it intersects the box. After that I deleted the bottom faces of both the cylinder and box.  Now what I want to do is delete the portion of the cylinder that is inside the box and join the nodes so that it is one object. I have already joined the meshes so I can select points/edges/faces from either shape. It seems like the easiest way would be to just put nodes where the edges of the cylinder and box intersect and then delete the parts I don't care about. I can't find a good way to do that though.  What's the best way to accomplish what I'm trying to do? Is it true that smell is lost flavor? This is a maxim that I hear frequently, especially as a defense of cooking methods that don't produce a lot of aroma: if the aroma is in the air, it means it's left the food.  As an example, some people complain about the lack of aroma produced in sous vide cooking, to which the sous vide advocates retort that this is evidence that more flavor is in the food.  Likewise, I recently saw , where he went for a low-and-slow approach that produces little aroma: here, too, he claimed the flavor-retention defense to its lack of appeal. "Don't be disappointed, but my roasting technique doesn't flood your kitchen with good Sunday roast smells. This is a good thing, because smells are lost flavor" he said, while "SMELL = LOST FLAVOR" popped up on the screen.    I suppose it stands to reason, and that's the appeal of this explanation, but is it the truth? Does smelling a food necessarily imply that the final product will be less flavorful, and is it strictly because the aroma is escaping? Bash copy all files that don't match the given extensions When I import pictures from my camera in Shotwell, it also imports the video clips. This is somewhat annoying, as I would like to store my videos in another folder. I've tried to write a bash command to do this, but have not had success.  I need a command that meets the following requirements:   Locate all files in a directory structure that do not have an extension of .jpg, .png, .gif, or .xcf (case insensitive). Move all of these files into a target directory, regardless of whether the file names or directory paths contain spaces or special characters.   Any help would be appreciated!  EDIT: I'm using the default shell in Ubuntu, meaning that some commands are aliased, etc.  EDIT 2: I've attempted this myself (not the copy part, just the listing of files part). I turned on extglob and ran the following command:  $ ls -R /path | awk '   /:$/&amp;&amp;f{s=$0;f=0}   /:$/&amp;&amp;!f{sub(/:$/,"");s=$0;f=1;next}   NF&amp;&amp;f{ print s"/"$0 }'   This lists everything. I tried using grep on the end of it, but haven't the foggiest idea of how to get it to not match a pattern I give it. The extglob switch didn't help much with grep, even though it does help with other commands.