73 thoughts on “The Nation Has Problems, Vol. 1”

1. I have a clarifying question on #1, but I'm not sure if it reveals too much about my thought process so I've spoiler'd it just to be on the safe side.

   Spoiler: Cool, I can put anything I want here	SelectShow
   Are we supposed to assume anything in the box is stolen if not padlocked, or just the crown?

   1. I don't think that's revealing too much. You should assume that anything inside the box can be stolen if not locked up. The box itself is safe, any padlocks attached to it are safe, and anything inside a padlocked box are safe.

      I can see what your idea was! It's a good idea, but not exactly what I'm looking for. 🙂

2. Spoiler: Check the Recent LTEs	SelectShow
   This isn't spoiled!

   Some may have already noticed this, but I made this change early yesterday. I considered completely redacting the text but opted instead for using "SPOILER" to indicate it was used.

   1. Nice.

      I'm off to go teach some math! I'll be back later this afternoon.

3. Of course, I probably don't need to convince you too much, you're already here because you love statistics.

   You, and most others here, registered before I implemented it, but now anyone registering has to solve a simple math problem. I figured it might help bias the site to consist of math people.

   1. That's one way of making sure Gardy never becomes a WGOMer.

      1. Or Jack Morris.

   2. Like a Canadian sweepstakes!

   3. That might be the coolest thing I've ever heard of. Good job!

   4. can you let us know what it is?

      1. There's a reason why I implemented it after I registered.

         1. Explain Hilbert's 24th problem in 140 characters or less?

4. Alice is an awfully un-trusting lass.

5. This is my answer. Pretty sure I've got it here.

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   Bob sends Alice the padlock to which he already owns the key, and Alice uses that padlock to send the crown.

   1. Spoiler	SelectShow
      Cept if Bob doesn't want the padlock stolen, it needs to be fastened to the box, which means Alice won't have box access to open it and put the crown in.

      1. Okay, or this:

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         It's a combination lock. Alice sends the padlocked box, then calls Bob and gives him the combination.

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            That's where I wanted to go with it with my question below. Time to see just how much of a hard-ass Greekhouse is. :winky-smiley-face-thing:

         2. Spooky, you are doing a great job thinking outside of the box! (Literally in this case)

            Still, the point is not to try and circumvent the rules. These are padlocks, not combination locks. Alice can only open her own locks and Bob can only open his locks. If Alice somehow got Bob the key to one of her padlocks, then Bob could certainly use it, but she'd have to get it to him somehow without it getting stolen. Of course, if she could get Bob something important without it getting stolen, then you would have already solved the problem. 😉

      2. Right, that's what I was trying to get at in my first post.

   2. I think I have it, too. Also, Wikipedia is truly awesome. If you doubt it, check out my answer and take the link. It's like it reads your mind!

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      Alice sends the box padlocked with the crown inside using her one and only lock. She includes instructions on the outside (or via email, or in a letter in code...) telling Bob to put his lock on the box and send it back, marked with a secret, previously agreed upon phrase (so as to thwart a "Man in the Middle" attack, possibly by Mallory. When Alice gets the box back, she removes her lock (confident that the remaining lock is indeed Bob's). She then sends the box back to Bob and Bob unlocks it.

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         In my experience with lockable boxes, there's only enough room for one lock. Otherwise, I like this much. It's got the elegance I was looking for.

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            I was thinking of something like this nice painting, but that might be breaking the rules.

6. Are we to assume that these padlocks involve keys, or no?

   1. Ooh, combination locks! Greekhouse said no numbers, though 😉

      1. At least it isn't fractions.

         1. I love fractions. Nerd alert!!1/3!!1/4!!

7. Oh good lord, this is going to get messy: My only assumption is that Alice's locks all use the same keys.

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   Alice puts a lock (with a key in it)in the box, then locks the box, sends it to Bob. Bob puts his lock on the box, sends it back. Alice takes her lock off the box,(it still has Bob's lock on it and her lock inside), sends it back to Bob. Bob opens the box, now has a lock and key of Alice's- puts the lock on the box, sends it back. Alice takes off her lock, puts the Mauer sideburn crown in the box, locks it and sends it to Bob. Bob unlocks Alice's lock, opens the box and wears his new prize possession to the party deck for the next Twins game.

   1. I was working on something like that until I considered my second solution above involving combination locks. This answer is way more fun, if much less efficient on the part of Alice and Bob.

      1. That's why it's a logic problem, I guess. Convoluted and inefficient!

   2. Spoiler	SelectShow
      Durrr, I didn't even think that one person could own more than one lock. Of course, due to the cost of shipping she might as well just pawn the damn thing and wire the money to Bob.

      1. My wife looks at me like I'm an idiot when I laugh at something as hard as I just did at that.

         1. I'll be here

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            all night

   3. Ah, that is the think I didn't consider. I knew it was going to be like a river crossing problem, I just couldn't set it up correctly.

      1. Yeah, that's the problem that came to mind for me as well. Now I just have to wait for the good doctor to give me the yea or nay on my assumption about the locks being keyed alike. I guess it could go like this instead so it wouldn't matter-

         Spoiler

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         Alice puts a lock (unlocked)in the box, then locks the box, sends it to Bob. Bob puts his lock on the box, sends it back. Alice takes her lock off the box,(it still has Bob's lock on it and her lock inside), sends it back to Bob. Bob opens the box, now has a lock and key of Alice's- puts Alice's lock on the box, puts one of his locks in the box (unlocked) sends it back. Alice takes off her lock, puts the Mauer sideburn crown in the box, locks it with Bob's lock and sends it to Bob. Bob unlocks it, opens the box and puts it on to go play his PS3.

         1. Spoiler	SelectShow
            That's correct! But there's even a more efficient way to do it!

            1. Spoiler	SelectShow
               Bob puts an unlocked lock in the box, locks the box with another lock, and sends to Alice. Alice locks it and sends it to Bob. Bob unlocks his lock and sends it back. Alice unlocks hers, puts the crown in, locks it with Bob's lock that was inside, and sends it back. Bob unlocks and rocks the crown at Target Field.

8. Just to clarify, I don't hate math -- I love math -- I just prefer other people doing the math for me. Thus, I'm a programmer and not so much an analyst. That said, to my mind digital logic and algorithmic thinking are an entirely different thing from "math".

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   Do we assume the padlock itself would not be stolen? Bob couldn't just mail his padlock to Alice, and she puts it on the box containing the treasure to be returned?

   1. I took an elective logic course in college- loved it. I also was forced to take physics and calculus for my major (Biology- why do I need calc for Biology?)- and struggled mightily with both. I just don't find math "fun" once I go past trig.

      1. Yeah, the calc requirement for ComSci was excessive, I thought. Not that some isn't important, but I found it's pretty cool how the brain is able to block out painful memories.

         Digital logic was a blast, although when Mrs. Runner asks me if I want corn on the cob or green bean almondine as a side dish, she doesn't want to hear me answer, "yes."

         1. The stuff on infinite series is actually quite important for a number of CS requirements. Still, something like a discrete mathematics course is more important.

            1. Something more concrete would be useful to many.

               1. Yeah, I think a course more tailored to the degree would be helpful, much like mathematics for dummies business majors with precision down to only two decimals.

               2. Grew up on this. Good stuff.

                  Discrete Math by Sartaj Sahni. UMD teacher was Luker.

      2. Mmmm... I loved calculus.

         1. Well why don't you marry it! /P.W. Herman

   2. Assume that everything that's not locked up (other than the box itself) will be stolen. The pertains to locks, keys, valuables and anything else Alice or Bob might decide to put in the box. Padlocks themselves cannot be stolen once they're locked to the box, but will be stolen if they're in an unlocked box.

      1. building on the prior work:

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         Alice sends a locked box with the crown in it to Bob. Bob puts his lock on the box and returns it. Alice removes her lock and returns the box. Bob removes his lock and rocks the crown in a parade around the block.

         1. That's my thought, as well, though with additional text because I can't type concisely.

            1. ah, I missed yours, Rob. and you probably did yours without the hints from prior competitors!

               (truth be told, I was slowly working my way toward the solution, but probably would have had a more laborious one first without reading sean's)

               1. no biggie. As nice as these spoiler tags are, it really makes keeping track of everyone's posts a bit more of a task.

9. Row Three:

   Spoiler	SelectShow
   Xs pegs, Os are spaces. _____ XXXXX OOXXX Play one: OOXOO XXOXX OOOXX Play two: OOXOO OOXXX OOOXX Play three: OOXOO OOOOO OOOXX OOOXX Play four: OOXOO OOOXO OOOOX OOOOX Play five: OOXOO OOOXX OOOOO OOOOO Play six: OOXOO OOXOO OOOOO OOOOO Play seven: OOXOO OOOOO OOOOO OOOOO OOOOO

   1. Row Four:

      Spoiler

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      Xs = pegs, Os = spaces Essentially I set out to get SBG's setup for level three, just beginning one step higher. ------- XXXXXXX XXXXXOO XXXXXXO OOXXOOO First 5 moves get 5 pegs to row 1. XXXXXOO ------- OOOOOXX OOOOOOO XXXXXXO OOXXOOO Next moves are two sets of the same moves for the bottom two rows moves 6&7 XXXXXOO ------- OOOOOXX OOXXOOO XXOOXXO OOOOOOO moves 7&8 XXXXXOO ------- OOOOOXX OOXXOOO OOXXOOO OOOOOOO moves 9&10 XXXXXOO ------- OOXXOXX OOOOOOO OOOOOOO OOOOOOO move 11 gives us SBG's arrangement to move up three levels, except that we are now starting from level 1, so it should attain level 4 after applying the set of 7 moves outlined in SBG's solution. XXXXXOO ------- OOXXXOO OOOOOOO OOOOOOO OOOOOOO moves 12-18 (see SBG above) OOXOOOO OOOOOOO OOOOOOO OOOOOOO ------- OOOOOOO OOOOOOO OOOOOOO OOOOOOO Not really seeing any generality that would lead to a proof of a limit here, but I'll keep thinking.

      1. Spoiler	SelectShow
         Heh. That's fewer pegs than I thought possible. Something seems messed up though, since you remove 19 pegs in only 18 moves! Otherwise, it seems right to me.

         1. Spoiler	SelectShow
            Something seems messed up though, since you remove 19 pegs in only 18 moves! That is weird. Let me look at this... Ah-ha! I labelled two separate moves as move 7.

      2. In regard to figuring out how far up you can go, there's only one proof I've ever seen, and it's extremely clever. The guy who proved it is very famous, so don't feel bad if you can't get it and definitely don't lose sleep over it. 🙂

   2. Spoiler

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      That's correct, and it is done using the fewest possible number of pegs. There are basically two different solutions using that number of pegs (what mathematicians would call non-isomorphic solutions). For instance, another solution which is essentially identical to the one SBG gave is to reverse the order of the pegs on the bottom row. That, of course, is essentially the same solution. There is one other solution that is not just a reflection or shift of this one, but as you would expect, it still looks pretty similar.

10. That's quite the vid, Greek. I might have to look up a few more of those.

    1. Yeah, she's quite the talker. I got to see her give a talk on making hyperbolic planes with balloons while I was in New Orleans, too. I think that vid is also up on here site somewhere.

11. I haven't read anyone else's work, so forgive me if these have already been presented:

    Spoiler: AMR thinks aloud about it

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    If a padlock (without the key) were sent in an unlocked box, would that be stolen? As it is a lock without a key, it is not valuable. Then, Alice sends Bob her unlocked box and padlock, with instructions for Bob to put his lock in the box, lock it with her lock, and send it back. Then she could put the gift in the box with Bob's lock and send it to him. I'm guessing this falls apart, because then Alice could just ask Bob to send her his unlocked lock without the box. And the unlocked box will be valuable, too.

    Spoiler: AMR's alternate solution

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    CER has a little lock-box for money. In this box is a coin-slot. I've been worried that she would drop her key in the slot and require destruction of the box to get out anything that was in it. Which has inspired this solution: 1. Alice alters her box enough to allow something to enter but not to exit. Say through a slit, just big enough for a key to be put in it. Maybe with a huge magnet also in the box that would grab the key to make removing it impossible without unlocking the box. 2. Alice locks this altered box (with the magnet inside, if necessary) and sends it to Bob with instructions to make a copy of his key (out of something magnetic) and to put this key in her box and to also send his locked box to her. (From experience, he should test out the key copy to make sure it was copied to sufficient accuracy.) 3. When she receives both boxes, she unlocks her box, gets his key, unlocks his box, and puts the treasure inside. Then she sends it to him.

    I'm unsatisfied with either of these solutions. I wanted something more elegant.

    1. I got yer elegance right here:

       Spoiler	SelectShow
       Alice sends the crown in a locked box Bob pulls out his Glock and blows the lock off, opens the box and wears the crown to meet the cops at his door.

       1. But a thief could do the same thing!

12. I just wandered in here looking for "tweets by Alison Brie". Am I in the right place?

    1. I have no idea who she is, but I have to question her career strategy, given her role in this gem.

       1. Given that she's a regular in Community and a recurring character in Mad Men, it would seem she's recovered.

          Still...wow.

          1. This one looks worse.

             1. A guy in a horror film, playing a Devil-type character, named "Kane Hodder?" I'm dubious.

                1. Wow, I had no idea how bad some of her stuff had been prior to her TV acting. I'll give her a pass though, cause you know, she's Alison Brie.

                   1. The beauty of IMDb is that most actors come from hilariously humble beginnings, and now we get to know about them.

                      1. Just think, once you get famous we'll get to look back and laugh at all the filthy porn movies you were in!

                         1. When I go on talk shows, I'll have to say "Please don't ask me about my first 346 films."

                            1. And counting!

                            2. You just took the backdoor to success!

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