Housing shortage in Monopoly
What happens when you need to tear-down a hotel but no houses are in the bank in Monopoly?
How to determine a matching color code from a physical sample? I need to make a restaurant menu design that matches restaurant wallpapers. For some reason my client cannot get color codes used in wallpaper, but he provided me with a sample. (see below)    How can I get the correct color codes from the wallpaper? (someone mentioned that there are scanners for this purpose, but I could not find any information regarding that)  Let me know if this question should be in another site. The security guard problem Why is the Mann–Whitney U test significant when the medians are equal? I've received a results from a Mann-Whitney rank test that I don't understand.  The median of the 2 populations is identical (6.9). The uppper and lower quantiles of each population are:   6.64 &amp; 7.2 6.60 &amp; 7.1   The p-value resulting from the test comparing these populations is 0.007. How can these populations be significantly different? Is it due to the spread about the median? A boxplot comparing the 2 shows that the second one has far more outliers than the first. Thanks for any suggestions. How can I verify a Google authentication access token?  I need to somehow query Google and ask: Is [given access token] valid for the [example@example.com] Google account?  Short version: It's clear how an access token supplied through the  can be used to then request data from a range of Google services. It is not clear how to check if a given access token is valid for a given Google account. I'd like to know how.  Long version: I'm developing an API that uses token-based authentication. A token will be returned upon provision of a valid username+password or upon provision of a third-party token from any one of N verifiable services.  One of the third-party services will be Google, allowing a user to authenticate against my service using their Google account. This will later be extended to include Yahoo accounts, trusted OpenID providers and so on.  Schematic example of Google-based access:    The 'API' entity is under my full control. The 'public interface' entity is any web- or desktop-based app. Some public interfaces are under my control, others will not be and others still I may never even know about.  Therefore I cannot trust the token supplied to the API in step 3. This will be supplied along with the corresponding Google account email address.  I need to somehow query Google and ask: Is this access token valid for example@example.com?  In this case, example@example.com is the Google account unique identifier - the email address someone uses to log in to their Google account. This cannot be assumed to be a Gmail address - someone can have a Google account without having a Gmail account.  The Google documentation clearly states how, with an access token, data can be retrieved from a number of Google services. Nothing seems to state how you can check if a given access token is valid in the first place.  Update The token is valid for N Google services. I can't try a token against a Google service as means of verifying it as I won't know which subset of all Google's services a given user actually uses.  Furthermore, I'll never be using the Google authentication access token to access any Google services, merely as a means of verifying a supposed Google user actually is who they say they are. If there is another way of doing this I'm happy to try. UK PLAB Visa Refusal due to unexplained bank deposits I had applied for a PLAB (Doctors) Visa for the UK to appear in PLAB test. I got refused on the basis of two recent large deposits in the bank statement I provided (my mothers). In reality, these are my own savings which I had deposited in her account to make it more strong. The only objection I got was that I must provide evidence for the source of these deposits. Other than this, I have previously travelled to the UK and USA as well as other parts of the world and my travel history is fine. Can someone please advise on how to proceed and re-apply? Does a logistic regression maximizing likelihood necessarily also maximize AUC over linear models? Once in a while you wish to address a comment to someone in particular, so you type @ and then you pause ... because the username is  or .  Short of using copy-paste to get their username right (which is even more cumbersome on a mobile device), is there another way around this? In a few cases I've noticed that the system will attempt to "promote" a comment to a reply, but I'm not sure if that's very reliable.  Should user names at least start with a normal letter?  Update  The auto-complete feature seems to normalize Zalgo'ish usernames, so typing the letter L will trigger the suggestions as expected; this is of course knowing that the name actually spells "lawrence", which may not always be obvious.  Knowing the way of the symbol ninja would surely help to type Ω using only the elbows as well, but not everyone is blessed with the same keyboard layout.  Suggestion  It would be nice to have a reply feature like this:        When ↳ reply is clicked, it will automatically populate the comment box with @username pre-filled in.   Additional notes  To clarify, I'm not suggesting to put the "reply" on all comments, as proposed , because in most cases the owner of a post is already notified of a new comment; this would strictly be to effect cross-commenter communication. Open a direct file on the hard drive from Firefox (file:///) I have a small PHP system I created for myself. This system contains a few .doc and .docx file documents. I want to be able to open them directly from the browser without downloading them.  I created a link: &lt;a href="file:///c:/mysite/myfile.docx"&gt;myfile&lt;/a&gt;. But Firefox does not open the link. href="http://localhost/myfile.docx" works fine - it offers me to download the file.  Any ideas on how I can do it? Do I need to change something in the Firefox options or security settings? Why is the gap between the translation and the last line of the gloss so wide in my interlinear gloss? C# Compiler should give warning but doesn't? Captured variable in a loop in C# Identification of particles and anti-particles The identification of an electron as a particle and the positron as an antiparticle is a matter of convention. We see lots of electrons around us so they become the normal particle and the rare and unusual positrons become the .  My question is, when you have made the choice of the electron and positron as particle and anti-particle does this automatically identify every other particle (every other fermion?) as normal or anti?  For example the proton is a particle, or rather the quarks inside are. By considering the interactions of an electron with a quark inside a proton can we find something, e.g. a conserved quantity, that naturally identifies that quark as a particle rather than an antiparticle? Or do we also just have to extend our convention so say that a proton is a particle rather than an antiparticle? To complete the family I guess the same question would apply to the neutrinos. I'm training a neural network for regression. The input vector consists of $140$ entries.   For each feature vector entry, I calculate both min and max over the training set. The difference max-min of some entries are smaller than 1e-5. I understand I can normalize such feature entries by say MinMaxScalar. However, if the difference max-min is this small, can I discard such entries since they seem to be so insensitive? I know that if you create a custom object, with an Auto-number Name field with a format, e.g. MYC-{0000} you will be able to create records from MYC-0000 to MYC-9999.  The moment you create 10,000 records Salesforce happily extends the range and you can then create MYC-10000 to MYC-99999.  My question is, what is the limit to this - for obvious reasons its a difficult one to test. I know instances that have exceeded 999,999 e.g. MYC-1000000 but am interested to know how far this extends to.  EDIT: When the field has a data type of Text the maximum length is 80. Is it safe to assume that the same is true for Autonumber (though that would be a very big number)? Include the "People Reached" and "Helpful Flags (count)" data in SEDE I have 16GB RAM. Do I need 32GB swap? I read many places that the rule of thumb for swap space is to double the amount of physical RAM. However, 32 GB does seem a LOT. Do I need that much? Do I need it at all with this high amount of physical RAM? How to show that a Banach space $X$ is reflexive if and only if its dual $X'$ is reflexive? What is the command to run System Settings from a terminal? System Settings can be run from the launcher (pinned by default), the Dash, or the power cog. But what command would I enter in a terminal window if I want to run it from there? I'm trying to work out what value resistor to use in a LED circuit. The equation I'd use to do this is:  $$ R = \frac{V_{cc} - V_f}{I_f} $$  Seems logical, and makes complete sense. The answers to the question  confirm this too.  I have the following LEDs:   \$ V_f = 3.3V \$ \$ I_{f_{typ}} = 20mA \$   Using a 5V power supply:   \$ V_{cc} = 5V \$   Plugging these into the above equation gives:  $$ \begin{eqnarray} R &amp; = &amp; \frac{V_{cc} - V_f}{I_f} \\   &amp; = &amp; \frac{5V - 3.3V}{20mA} \\   &amp; = &amp; 85\Omega \end{eqnarray} $$  All good so far.  However, if I use the calculator at , that gives me 100&Omega;. If I use the ElectroDroid app on my phone, that gives me 85&Omega;.  So, I assume that the linear1 calculator is using a different method of calculating this resistor value; is there some better way of doing this? I am trying to recreate a penne pasta. I am creating a cylinder removing the two end faces and then I solidify the mesh.  However I do not know how to extrude (or cut away) the two ends to make them pointy like in the picture of the penne below. I have tried to use bisect and mirror, but without successful results.  Any idea?