Math Puzzle

This cool puzzle (and solution) comes from my friend Mike.

Alice secretly picks two different real numbers by an unknown process and puts them in two (abstract) envelopes.  Bob chooses one of the two envelopes randomly (with a fair coin toss), and shows you the number in that envelope.  You must now guess whether the number in the other, closed envelope is larger or smaller than the one you’ve seen.

Is there a strategy which gives you a better than 50% chance of guessing correctly, no matter what procedure Alice used to pick her numbers?

I initially thought there wasn’t, or that the problem was paradoxically defined, but it turns out that it’s perfectly valid and the answer is “Yes.”  See my first comment for an example of one such winning strategy.

This puzzle is similar to, but not the same as, the two envelopes paradox.  For more time-devouring reading, see Wikipedia’s List of Paradoxes.

Android Bug Reports, Songs, Rovers

The following is a partial list of bugs in Android (or associated software) which have impacted my actual life in some way.  Some may have been fixed since I last encountered them.

  • When navigation is muted, but you hit volume down just to be safe, it unmutes and starts blaring, waking other passengers on the bus.
  • Sometimes the GPS stops getting locks on satellites until the phone is rebooted.  (This may be related to the GPSStatus app, installed to avoid this kind of thing.)  To be fair, satellites are very small and far away, so you can hardly blame it for having trouble.
  • You can say “Call <contact name>”, and contact names+addresses show up in the navigation search with “navigate to” options, but you can’t say “Navgiate to <contact name>” like you can with all other major actions.  This means you have to type their full address to find out which exit to take from the traffic circle, and it’s really hard to type while holding the wheel steadily to the left like that.
  • Sometimes, when arranging home screen icons, you feel sad and you’re not sure why.
  • If you follow Google’s guidelines and have your own Jabber DNS records set up in a particular way on your Google Apps server, it screws up Google Talk’s ability to authenticate, which in turn (for some bizarre reason) causes all app downloads to hang midway through.  This is rare enough that the error messages are not Googleable.  But don’t worry, it’s easy to figure out as long as you’ve read all of the source code to Android and to Google’s servers, which is good practice when you get any product.
  • Sometimes the home screen icons all disappear.  The only thing which fixes this is a restart, going through five menus to kill the “Home screen” process, or crying quietly for hours until the icons start to feel sorry for you and come back.
  • Occasionally, when swiping the lock sideways to unlock the phone, the lock button images are rotated by 90 degrees.  This is probably connected to your Jabber server somehow.
  • Sometimes an Android user will think they hear someone say their name, but they’re not sure, so they say ‘Yes?’, but then it turns out it was something else.
  • Maps Navigation doesn’t cache your route, so if you drive through an area with bad cell coverage, it may silently stop notifying you of upcoming turns, and you won’t realize anything’s wrong until you discover you’ve taken NH Route 2 all the way to the White Mountains, which are very cold.
  • Latitude doesn’t update well on either end.  Often times, it will tell you someone was in a particular place “5 minutes ago”, and then 10 minutes later — after multiple restarts — it will still say it got that last update from them “5 minutes ago” even if they’re actively using Maps, so you have no idea whether they’ve left.  This can continue for hours as you slowly run out of air in the closet.
  • The phone occasionally locks on full brightness and turns off the keyboard backlight, which is fixed by un-checking and then re-checking the “automatic brightness” checkbox, also about five menus deep, which is hard to see when you’re squinting because the screen is so bright.  Fortunately, it never gets very dark where I live in Boston.  Unfortunately, it’s extremely dark at night in the White Mountains.
  • Navigation instructions silence things like podcasts players, but don’t pause them.  Thus, to hear that missing sentence or two, you have to switch over to the podcast app and hit ‘back’ several times, then swerve your car to avoid the stupid stop sign that shouldn’t be in the middle of the sidewalk to begin with.
  • Google Voice doesn’t do push notifications, so you often get voicemails quite some time after the caller leaves them, sometimes after you’ve already called them back.  This can make you call your doctor back again and have a really confusing conversation where you accidentally get a second prescription. Which you can then get filled and sell on the street. Come to think of it, this bug might be a feature.
  • If you stop for gas, sometimes navigation suspends, but doesn’t resume when you start driving again (or just disappears without notifying you), so you miss the upcoming turn and think you’re already on I-95, and by the time you discover your mistake and turn around you’ve lost enough time that you totally get to the conference too late to catch Richard Stallman doing his acapella Bad Romance cover which is the whole reason you paid the entry fee in the first place.
  • If you have several Google accounts, there’s no way to select which one to use for Google Checkout purchases.  It just picks whichever one it notices first, even if it’s one from an old Google account tied to your mom’s credit card, so now she might know that you bought the app to turn the phone into a vibrator.  (The app doesn’t really work since the vibrate motor is too weak, but the reviews by people who don’t understand its purpose are hilarious.)
  • If you have a secondary account that it’s decided to use for Checkout, and you want to delete it so the phone will use your primary one, you can’t.  Why?  Because that account is used for an essential service and so can’t be deleted.  As far as I can guess, that service is Google Checkout.  This bug report is dedicated to Joseph Heller.
  • Google Chrome in OS X follows the Apple guidelines concerning the green “+” button, and has it make the window no bigger than it deems necessary to fit the current page’s contents.  This annoys a lot of people. Since there are no OS X Chrome extensions, the best workaround seems to be registering maximizechrome.com and putting a giant <div> there.  Whenever you need to maximize, you load that page before hitting the green button.  (This bug is not, technically, related to Android in any way.)
  • There’s a Fantastic Contraption app on iPhone, but not Android. This is probably a feature rather than a bug, since it means Android users can spend time on things other than playing Fantastic Contraption.

These issues aside, I’m really happy with my Droid.  The screen is incredible, it’s much faster and easier to use than the G1, and I wouldn’t trade away the physical keyboard and persistent SSH for anything.


I just about fell out of my chair when I saw this.  Thank you to everyone who appeared in it, and to Olga and Elaine for doing whatever black magic they did to get them all together. <3. (Side note: I met Neil Gaiman once, back when I was in college, when his book tour came near my town. At the signing afterward, I talked awkwardly to him for what seemed like several minutes while he signed stuff for our group. Later, my friends pointed out that I was speaking too quietly for him to hear—or, in fact, to notice that I was standing there at all. I’ve been quietly embarrassed about that ever since and this video makes me feel better.)


If anyone is still sad about my Spirit comic, maybe this person’s rewrite – author unknown, found on a random image page – might provide some comfort.  Also, I got a couple of nice letters from members of the Spirit/Opportunity teams, and it’s very clear how proud they are of these little rovers. Next, Europa!