The Logic Puzzle Answers, Work Thus Far on the HLPE

Or: Belated and Underwhelming, the Failings of One Particular Puzzler.

This one's late, and these answers should have been here yesterday. But, as Sunday-Wednesday is my work week, and I do the whole school in the mornings thing, that didn't happen. So here are your answers, and then if I can find my digital camera by the end of writing this post, I'll take a picture of my scribbly work at solving HLPE (I still do not have an answer).

First off, how about I just know out the one in the footnote to last time. The answer is fairly well known, for which we might blame Bowie and Henson. You ask either guard if, say, the other guard would tel you that the road to your left will lead you to paradise. Then choose whichever road the guard indicates that the other guard would tell you doesn't lead to paradise. Or watch this.

Gnomes Buried to Their Gnecks

All right, for this one, lets start right away and clear up a strategic question. A good way to figure out the answer is by asking "What would make this puzzle easy?" and then moving from there if we find anything helpful at that point. Again we have:

Now hand-drawn!
(And yeah, I always make A smoke a cigarette for some reason.)

I've labeled these A-D from left to right, and have a terrible hand drawn picture of the situation. I like it better this way, more character, and it's how I usually tell it. Now, a few things would make it easy like the wall not being there or them being told there was only one black hat, and that hat being on B or C. But instead how about the only difference is that B and C are wearing the same color hat, like so:

Again, terrible drawing. 

Ok, so if things were different like so, D would know immediately what his hat color is and shout it out setting them all free. Since that is not the case, C will know that not having heard that, he must be wearing a different hat color than B. That simple.

Blue, Brown, and Green

Here's my favorite one. It's hard but it's damn satisfying. This one requires yet another counterfactual like above, but then the critical move is abstraction from the simple case to the much more complex one. It's also most rigorously shown with mathematical induction, but I'll sketch that after demonstrating the answer.

First, imagine the counterfactual: It would be simple if only she said this to a group, and only one member of which had blue eyes. The blue-eyed islander would look around and not see anybody else on the island that had blue eyes. He'd figure it must be him. Now here's the crucial step to get the solution, and it seems so simple in retrospect: What if there were two people? Why, they would look around, see one other person and realize that this could be the only person with blue eyes. After the ferry man came and went though, these blue-eyed islanders would of course see their other blue-eyed island mates not having left. They would realize that this person must have seen someone else, but since they only saw one other person with blue eyes, it must be them, and indeed on the second night, these two blue-eyed people would leave. The case of three runs exactly the same way, and they leave the third night. This is iterable indefinitely. Thus all and only blue-eyed people would leave on the 100th night. Everyone else will never leave the island.

A quick sketch of the answer by Mathematical Induction: So we've already done the case of 1, that a single blue-eyed person will leave on night 1. Lets assume n blue-eyed people will leave on night n. Now we show that if n+1 people were on the island, they cannot leave on night n because they will see n people but they know that those people would leave on night n if there are n people. Excluding other people, they know there must not be n people, but that there can be at most one more person with blue eyes, them. And so it follows from the n case that the n+1 case. Q.E.D.

Don't Get Stuck with Random

...And a segue into the HLPE which will be posted with solution and commentary next week.

I'm going to be fairly lazy with this response, since it is hard to come up with and I can't easily reduce it to a simple case like I have done with the others. First we have to notice though, that essential to the strategy this one uses is to cut out as a possibility the unreliable person you are asking. If we never pick the person we question we don't have to worry about asking random and not being able to decide if the person who answered us was random. Whatever answer she gives, we won't be picking her this way. So the best question to ask if random isn't who we're talking to is (lets imagine we're gesturing to one and then the other, and if that seems like cheating, imagine phrasing the question another way): Is that sister older than that sister? Then, to guarantee you pick only the eldest or youngest, pick whichever sister she indicates is younger based on her answer.

If you're talking to the eldest, who only tells you the truth, she'll indicate random is older and marrying the younger of these two puts you with the youngest. If you're asking the youngest, she'll lie and indicate the middle (random) girl is older, and so marrying the one she indicates to be younger gets you the eldest.

Relation to the Hardest Logic Puzzle Ever:

So we might use this and reformulate the HLPE. We might reduce it to asking a similar question and either determining all but the answer on the second question where we could rule out who we're asking as random, and then just determine our one last bit of information. The ja and da thing is making this difficult though. You can't waste any of these questions, so the idea is to ask about as many things as possible with one question. I've been assuming answers and drawing trees based around possible questions like "Is it true that Not Both ja is yes and C is more likely to tell me the truth than A?" said to B... It's yielded no results, so another thing is, and I'll accept help: If you can get an answer in 5 questions or less for this problem, I want your sequence of questions.

An upcoming post, I think, will be a post about craft beer and style put next to traditional. Not in a value based way, but maybe just determining qualities for them.

A couple of (under-appreciated) places for Mexican cuisine in Pilsen

Or: The Pilsen guide to chilaquiles, part one

So, one thing I enjoy a whole hell of a lot is chilaquiles. Luckily my apartment might be in the most densely chilaquiles-populated portion of the city. I used to joke that I'd some day write the Pilsen guide to chilaquiles because of the volume I consume.


Joke no more, this shall be the first of a series of posts about chilaquiles and pleces to get them, especially in Pilsen. I'll also suggest one other restaurant that I just never see anyone in, but makes delicious food in my neighborhood.


Pilsen, for those of you not from Chicago, or those who have yet to the particular neighborhood, is a nice little community in the southwest side of Chicago. It has a lively population of Mexican immigrants who hold festivals, and have block parties, and have contributed several lovely Murals to the neighborhood. I'll post on that sometime, too. The murals really are awesome.


La Casa Del Pueblo Taqueria


On to the chilaquiles. The first place I think that I should talk about has long been among my favorite spots. The menu is incredibly authentic at this place; several dishes at Casa are top notch. They also have things at least from time to time that I rarely see. Extremely reasonable pricing.

This place has a really nice feel to it and the morning rush is mostly Spanish-speaking, the staff is mostly bilingual, but "Chilaquiles" is the same in English and Spanish anyhow. 


The walls have posters of art by Diego Rivera and Frida Kahlo, as well as posters showing different sorts of garlic and chiles or tomatoes. 


Their horchata is also not to be missed, and either that or coffee are fantastic next to their wonderful Chilaquiles.


It's hard to judge what makes a good plate of chilaquiles. The dish has very few essential qualities. They generally come as chilaquiles rojos o verdes, that is to say with a red chile sauce or a green tomatillo salsa. Almost always they have eggs, though those are either scrambled or over easy, and sometimes off to the side or else mixed in. They always have either fried stale tortillas or tortilla chips mixed in. They range from mild to very spicy. Like judging a beer, it's important to meet each on its own grounds in a sense.

The chilaquiles at Casa succeed very well at their aims, I think, or at least what I read them to be. Rick Bayless visited a bunch of restaurants in Pilsen a few years back. I know next to nil about famous chefs or if the taste of this one is to be taken into account, but he did describe La Casa Del Pueblo's Taqueria as having more of a home cooked taste. It's not greasy fast food, or fancy gourmet cooking. People go to take large portions to family gatherings.


I prefer the Chilaquiles at Casa in the red tomato chile sauce, which is very mild but also extremely flavorful. Scrambled eggs are mixed in and indistinguishable from the rest of the dish. The totopos (fried tortillas or chips) are crispy and salty. This is a meatless version, which is the case for about half of them in the neighborhood, with a bunch also being made with cecina. It's good if you want flavor, and not spice, and something pleasing at no extreme. Delicious enough that I need to slow myself down every time.


Part 2: DeCOLORES galeria y sabores


Another small restaurant, this time on the very eastern side of Pilsen, at Halsted near 17th street. This place is fairly new, not more than two years I believe, and keeps with the artistic tradition of the neighborhood, and has a small gallery of local art. When I went, oil paintings of mugshots on wood blocks were being displayed.

Taquitos de Papa

Also artistic is the food presentation. Just one such instance shown to the left from their appetizer menu: the delectable taquitos de papa. This is among the places that looks like it was done with more flair, and more attention. It feels fancier, but the service is really chill and nice. In the end, it comes down to being thoroughly artistic. The julienned vegetables and such topping the dish to the left, laid carefully then topped with a nice portion of (I think) queso cotija. 


The dish itself was also delicious, and filling with the potato stuffed, fried taquitos. My entrée (Camarones Diabolicos, whole shrimp cooked with lime and habanero) was flavorful and had a nice heat to it. The mole (Morgan ordered Enchiladas Mole) was creamy and nutty, with a rich peanut base. You'll spend more here, but I can't for the life of me understand the ridiculously mixed reviews on yelp. This feels lie a place worth supporting.

The Hardest Logic Puzzle Ever

Or: The Prince from Turandot, Bilbo Baggins, Sarah Williams (from the movie Labyrinth), and the Dread Pirate Roberts are all very glad they weren't being questioned by Raymond Smullyan.


Today's post is about logic puzzles. Many people do not like them, and if you are reading this and you are such a person and are reading this, don't worry. I will soon have an upcoming post about beer, or art, or chilaquiles. Something more colorful. Something less sterile. Just wait. And hell, maybe I'll even be able to breathe some life into logic puzzles if you don't find them naturally interesting the way I do.


I was recently on a wikipedia article and saw a link to something called "The Hardest Logic Puzzle Ever". I'm not sure why I've never been told about this. I love puzzles. I love logic puzzles especially. I found the death last year of Martin Gardner to be a very sad thing. I tell people logic puzzles at parties (as you can imagine, I am the life of the party).


Boy is this one a doozy. At least I think so. Admittedly, I don't yet know the answer.


I'll start by just stating the problem. This statement of it was I believe Smullyan's own, original statement. It's taken from above wikipedia page

Three gods A, B, and C are called, in no particular order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer all questions in their own language, in which the words for yes and no are da and ja, in some order. You do not know which word means which.

This may already look familiar to you. Especially if you've seen the movie Labyrinth. It's got David Bowie in it if you haven't, so maybe that'll make you want to see it, then it will look familiar. These seem to be known generally as "knight and knave" problems, problems where knights tell the truth and knaves lie, all of which have their roots in Smullyan. Even the one in Labyrinth, for which they say Smullyan was an inspiration directly. *


Raymond Smullyan is a logician and writer. He supposedly has a fantastic guide to Gödel's incompleteness theorem accessible to anyone fairly well versed in first-order logic that's on my reading list. He also apparently writes about piano, taoism, recreation mathematics, and magic. Seems like an interesting fella.


I have a particular love of logic puzzles that I may explore further in a post next week. I give out three generally, in order of least to most difficult, and give people a week to get them. On the Hardest Logic Puzzle Ever (after: HLPE) I am giving myself two weeks. I will post the answer then. Today I'm posting my three favorites, though. In a week I'll post more about logic puzzles in general, and the answers to those three. Plus I'll post any work I have on HLPE. The next week, I'll post the solution or solutions to HLPE and about it. (I know George Boolos wrote about the puzzle.)


Here are your puzzles:
1) Gnomes buried to their Gnecks


Of course Gnomes have Gnecks. Here's a hat-color problem.

I did not make this picture. Anyhow, here's the deal: These gnomes wake up buried to their gnecks. They are told that two of them are in blue hats, two in red hats. They're told if any one of them can guess his own hat color, then they all go free. Get it wrong? Death for all of them. They also know where each of the other gnomes are, and which way they are each facing (basically they know who can be seen by whom).  Whic, by the way, the one on the far right can see the two in front of him, the guy directly ahead of him can see the one in front of him. Obviously, no one can see past the wall. So these gnomes are totally logical and are pretty quick, so which gnome if any figures out his hat color?


2) Blue, Brown, Green eyes.


This is a similar sort to the last problem. It's been covered by the writer of XKCD. His write up gets around most of the bad questions I hear about it. To save space, I'm just linking to his. Here it is: http://xkcd.com/blue_eyes.html


Note, this is one of my favorites of all time. I find it fun, and I find it very rewarding.


3) Don't Get Stuck with Random


This feels like a slightly tamer version of HLPE and its solution might give us a clue, where its solution fails on HLPE, we may clearly see the obstacles presented by HLPE. It's a sort of Knights and Knaves problem. It's pretty difficult. Here we go. 


You enter a kingdom and are told you are to marry one of the three daughters of the king. The eldest always tells the truth. The middle daughter will randomly tell you the truth or lie to you.  The youngest will only ever lie to you. Despite being at different ages, it's impossible to tell which one is which. The king isn't telling you who's who. You don't get a full interview. You get to ask one yes/no question to any one daughter (but remember, you won't know which it is you will be talking to). Your goal is clear: you want a question that will lead you to safely select either the eldest or youngest, but not to select the middle daughter.


Well, there you are. My three favorite puzzles, and the puzzle I plan to struggle with. If you have an interest in this, watch for my post next week, when I'll reveal answers and further explore concepts. If you don't, I'll have more not-about-logic-puzzle posts soon.




*This one is fairly easy. You're at a fork in the road. One road leads to paradise, the other to certain death. There are two identical guards, you know one's a knight and the other a knave. Ask a single question to choose the correct road. That is, the one not to certain death. 

A Preview Showing of Chris Sullivan's "Consuming Spirits"

....Or: Maiming the helpless and child-rearing.

This past Thursday I went to the Gene Siskel Film Center with a friend. We'd seen that there was an animated film that looked very interesting playing there, a drama called "Consuming Spirits" by artist Chris Sullivan, and thought we'd go see it. Neither of us expected the crowd we walked into there.

It probably is not a very surprising statement for me to say it's the most crowded I had seen it. As it turns out this was a special event, and I've never been to a special event there. Tickets were sold out, and this was its only showing. I was glad we had bought these tickets well ahead of time.  Turned out the movie has yet to be released, and a short discussion with the animator and artist who made this.

There are a few features of this film that make it stand out, and I think it's worth pointing them out. I will confine my comments considerably towards the messages I feel were presented, its humor, and its formal features. Should the movie be released in a year or two, this will not spoil experience of the plot, which is remarkable enough in its culminating moments that there is most certainly something to spoil.

1. The animation is both richly detailed and informed by the feel of the story and setting.

What you see next to the text here is rendered in color. Paper cutouts are the characters, and some of their surroundings, such as the microphone, left. The Chicago Reader called the animation technically proficient but rarely pretty, and particularly that the characters look grotesque, mirroring their personalities. This is just one place where the outer world in the film resembles the inner lives of the characters. Those paper cut outs also allow for wonderful detail on the characters, and the rough, painted small town surrounding them. It seems very original at every step. He also does not confine himself to this one style of animation. Pencil and paper animation shows up especially in the recollection of Earl Gray, the horticulturalist and radio host shown above. Animation with 3-d models on an uneasy felt ground lend to the small town feeling, which we can assume is somewhere around Pittsburgh, and seem playful with the children toys around it.


2. Subtle humor shines throughout, and livens the tone of a sometimes excessively dark movie.


In the discussion after the film, Chris Sullivan himself referred to the film as seeming mean-spirited, but little was said about all of the bad jokes, puns, and occasional academic gaffs that elicited many giggles from the audience. To show how pervasive these are, you need look no further than the title, which in the first quarter of the movie loses its flat and dark meaning of "the spirits which consume us/the characters/the town" and points to the double meaning "consuming distilled alcoholic beverages" which the town does at an Irish-themed bar called 'Juice of the Barley'. At one point a man eats a package of donut holes called 'Diabolical's Glory Holes'. A man thinks he's renting a porn called 'Titty Cut Follies'.


It's not just gags, either. The humor is also gained a la Coen Brothers when the small town folk and their small town quirks are portrayed. I wouldn't describe this portrayal as mean in any way, either. It actually seems a bit loving (if amused) and never shows superiority over them.


3. The dark, cynical message of the movie feels painful enough to also feel true.


I saved the best for last here. This is a very dark movie, and it is a drama. It may even be a tragedy. But it's as much a tragedy for the sad events that progress through the movie as it is for the sad events which just keep happening, and maybe to just about everyone. The characters are twisted and troubled. Their last names are Blue, Violet, and Gray, and these characters seem sad and self-centered, bruised, and distanced. The radio hosts banal answers on gardening, fertilizer, and pests drone on until they become (I think) an inner monologue showing a troubled soul. The heroine shows strength and occasionally dignity, but is far from blameless. If the movie has villains, they are accepted for some of their worst acts and condemned for their least harmful. The sick and senile mother is simultaneously cruelly taunting and self-sacrificing, leaving us no easy answers on any of our characters.


But then the movie reflects on itself, and maybe gets to what it meant to say, when over the radio narration used as a trope throughout we hear an extended metaphor for children and their highly imperfect parents. It reminds me somewhat of this poem by Philip Larkin (which is where this blog gets its maybe-temporary name). The metaphor goes that when children are helpless, we hurt them so that they may never truly stand up straight, they'll have a harder time liberating themselves. Then when they do, through their harm, we get to claim ownership as a cause. This is much more heartbreaking in the words of the film's heroine, Genny Violet.




So, well done to Chris Sullivan of SAIC. His work happens to be moving, even if it is mean-spirited.

Obligatory Explanatory Post

I've had far too many blogs that don't go anywhere. As so many other blagosphere novices, I'm trying to make this not one of those this time.


I'm intending to accomplish this in the very lazy way of not giving the things any sort of theme at all. For the most part, I intend to be brief (something I've done less than wonderfully at in the past). To name a few things, I intend to write about the best places to get chilaquiles around me, movies and plays I see, attitudes towards beer (or coffee or tea), reasoning, stuff I read, gender, and whatever the hell else comes up. 


I aim to do this at least four times per week. Here goes nothin'.


Also. The name and address are likely temporary. I had no idea what to call this.