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# All Gnytte Long

Great puzzle. Thanks!

posted by mrgrimm at 9:47 AM on January 13, 2010

Well, yes, but it's basically called "logic." More specifically, though, for this problem, all you need is Propositional Logic, in which everything is either True or False.

That entire problem can be modeled with a set of propositions, such as "Artoo is a Mnaivv on Day 1" or "Lexx had sex with Oliver on Night 4." Every such proposition is either true or false. There are many ways to model a given problem with such propositions.

Once you have your propositions (again, all statements of fact that are either True or False), you can describe relationships between them based on the interviews in the problem. For example, in the first interview, Artoo says "Etrusco is not infected." Therefore, if Artoo is a Gnytte on that day, then Etrusco isn't infected, but on the other hand if Artoo is a Mnaivv, Etrusco

The entire problem can be encoded like that into simple logical statements about whatever propositions you've created. In the end, you'll essentially have one big long logic formula. (Believe it or not, it's pretty much the same thing as a Sudoku puzzle.) At that point, you can proceed to solve it in two ways, broadly:

1) Guess-and-check. See what happens if you try to set AM1 to be True. That may imply two other statements that conflict. Backtrack and try something else. This can be done very methodically.

2) Resolution. There are codified ways in which logic statements can be combined to form new logic statements. By applying these rules methodically, you can take pieces of the logic formula you have and

This will take you a while. Luckily, we have solvers, programs that are well-engineered and highly efficient at solving exactly this type of problem. The most efficient actually combine both methods 1 and 2. You will spend far more time encoding the problem into a correct model than the solver will take to find a solution.

posted by whatnotever at 12:43 PM on January 13, 2010 [6 favorites]

The disease is not sexually transmitted, which suggests that you should assume they cannot get infected in the course of the 5 days.

posted by davejay at 1:41 PM on January 13, 2010

Hmm. Okay.

I'm thinking not any easier: I can't imagine any way to solve the puzzle short of writing a computer program (or perhaps a fairly complicated Excel spreadsheet). The weird words for truthteller and liar don't really make much of a difference.

posted by UrineSoakedRube at 1:58 PM on January 13, 2010

It's not as hard as it looks initially—I solved it in about 8 hours more or less by hand, and that involved a lot of backtracking to find mistakes I had made, and inefficient solving methods. Probably would have taken less than half that if I hadn't made any mistakes along the way. When I say "more or less by hand," I did use Excel to track information, but didn't use any Excel functions. The only advantages Excel had over pencil-and-paper were a) making it easy to do lots of sequential ctrl-Zs when trying to backtrack to where I made a mistake, and b) color-coding some cells when I made a "guess" so I could differentiate between what I knew for sure and what was based on my guess, and undoing

Thanks, Wolfdog! That was a lot of fun.

posted by DevilsAdvocate at 11:34 PM on January 14, 2010

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# All Gnytte Long

January 13, 2010 9:16 AM Subscribe

The Sexaholics of Truthteller Planet - yes, it's one of those rotten logic problems, one of many that can be found at Tanya Khovanova’s Math Guide to the MIT Mystery Hunt.

The rooster has sex with all of them.

posted by Joe Beese at 9:23 AM on January 13, 2010 [1 favorite]

posted by Joe Beese at 9:23 AM on January 13, 2010 [1 favorite]

That's perverse!

posted by Saxon Kane at 9:39 AM on January 13, 2010

posted by Saxon Kane at 9:39 AM on January 13, 2010

*Surveillance Night 4: Security cameras have been vandalized...*

Great puzzle. Thanks!

posted by mrgrimm at 9:47 AM on January 13, 2010

FANTASTIC. Love these puzzles, will love driving myself crazy with this one.

posted by bearwife at 9:48 AM on January 13, 2010

posted by bearwife at 9:48 AM on January 13, 2010

This year's hunt starts at noon on Friday. If you are into puzzling, are in the Boston area and have a weekend to kill, that gives you two days to find a team. You won't be sorry you did.

posted by Lazlo Hollyfeld at 10:03 AM on January 13, 2010

posted by Lazlo Hollyfeld at 10:03 AM on January 13, 2010

THE MAN IN THE RED HOUSE OWNS THE ZEBRA!!!

what? shit.

posted by GuyZero at 11:01 AM on January 13, 2010

what? shit.

posted by GuyZero at 11:01 AM on January 13, 2010

Is there a good way to draw out and solve logical relationships similar to algebra, where you draw out and solve numerical relationships? I imagine that enough people have thought about logic over the millenia that someone has to have come up with something. This puzzle's large enough that doing it haphazardly by intuition is probably not gonna work...

posted by Zalzidrax at 11:04 AM on January 13, 2010

posted by Zalzidrax at 11:04 AM on January 13, 2010

Oh man I am so excited for Mystery Hunt. The saddest thing last year was when I went to sleep and missed the Dr. Who meta puzzle. No sleep this year!

posted by shaun uh at 11:06 AM on January 13, 2010

posted by shaun uh at 11:06 AM on January 13, 2010

Zalzidrax, the closest thing I know to a system of notation for logical relationships is boolean algebra. (in this case, set notation might also be important.)

Wikipedia has good introductions to both.

posted by Fraxas at 11:08 AM on January 13, 2010

Wikipedia has good introductions to both.

posted by Fraxas at 11:08 AM on January 13, 2010

Actually, boolean algebra and set notation are somewhat limited subfields of what is in general called "formal" or "symbolic" logic, which fits Zalzidrax's description. Try this AskMe thread for example. Unfortunately I haven't been able to find any good online introductions yet, but memail me if you're curious.

posted by 7segment at 12:30 PM on January 13, 2010

posted by 7segment at 12:30 PM on January 13, 2010

*Is there a good way to draw out and solve logical relationships similar to algebra, where you draw out and solve numerical relationships?*

Well, yes, but it's basically called "logic." More specifically, though, for this problem, all you need is Propositional Logic, in which everything is either True or False.

That entire problem can be modeled with a set of propositions, such as "Artoo is a Mnaivv on Day 1" or "Lexx had sex with Oliver on Night 4." Every such proposition is either true or false. There are many ways to model a given problem with such propositions.

Once you have your propositions (again, all statements of fact that are either True or False), you can describe relationships between them based on the interviews in the problem. For example, in the first interview, Artoo says "Etrusco is not infected." Therefore, if Artoo is a Gnytte on that day, then Etrusco isn't infected, but on the other hand if Artoo is a Mnaivv, Etrusco

*is*infected. Given propositions "AM1" meaning "Artoo is a Mnaivv on day 1" and "EI1" meaning "Etrusco is infected on day 1," this can be written in propositional calculus as "AM1 implies EI1" and "not AM1 implies not EI1."

The entire problem can be encoded like that into simple logical statements about whatever propositions you've created. In the end, you'll essentially have one big long logic formula. (Believe it or not, it's pretty much the same thing as a Sudoku puzzle.) At that point, you can proceed to solve it in two ways, broadly:

1) Guess-and-check. See what happens if you try to set AM1 to be True. That may imply two other statements that conflict. Backtrack and try something else. This can be done very methodically.

2) Resolution. There are codified ways in which logic statements can be combined to form new logic statements. By applying these rules methodically, you can take pieces of the logic formula you have and

*derive*new statements. Eventually, you will be able to derive statements like "AM1 is true," thus proving that Artoo is a Mnaivv on day 1.

This will take you a while. Luckily, we have solvers, programs that are well-engineered and highly efficient at solving exactly this type of problem. The most efficient actually combine both methods 1 and 2. You will spend far more time encoding the problem into a correct model than the solver will take to find a solution.

posted by whatnotever at 12:43 PM on January 13, 2010 [6 favorites]

One question: can inhabitants get infected in the course of the 5 days, or do uninfected inhabitants remain uninfected? There didn't seem to be any guidance on this (and this would make the puzzle that much harder).

posted by UrineSoakedRube at 1:17 PM on January 13, 2010

posted by UrineSoakedRube at 1:17 PM on January 13, 2010

The real question is, "how much easier would the puzzle be to parse if not for the awkward fake words?"

posted by explosion at 1:21 PM on January 13, 2010 [1 favorite]

posted by explosion at 1:21 PM on January 13, 2010 [1 favorite]

*One question: can inhabitants get infected in the course of the 5 days, or do uninfected inhabitants remain uninfected? There didn't seem to be any guidance on this (and this would make the puzzle that much harder).*

The disease is not sexually transmitted, which suggests that you should assume they cannot get infected in the course of the 5 days.

posted by davejay at 1:41 PM on January 13, 2010

*The disease is not sexually transmitted, which suggests that you should assume they cannot get infected in the course of the 5 days.*

Hmm. Okay.

*The real question is, "how much easier would the puzzle be to parse if not for the awkward fake words?"*

I'm thinking not any easier: I can't imagine any way to solve the puzzle short of writing a computer program (or perhaps a fairly complicated Excel spreadsheet). The weird words for truthteller and liar don't really make much of a difference.

posted by UrineSoakedRube at 1:58 PM on January 13, 2010

Hey! This was one of the puzzles I helped to solve in last year's Mystery Hunt! I was working on it with another guy, and we kept distracting people unintentionally by talking about all the different ways these aliens could be having sex with each other. I think we used graph paper to plot out the possibilities.

I also enjoyed The Combatant's Guide to Zyzzlvaria. Each clue is similar to, but not the same as, a passage from the Hitchhiker's Guide to the Galaxy. Each corresponding answer is one letter away from the thing the original passage describes. So, the answer to "Mostly Sith" ("Mostly Harmless") is "Darth" ("Earth"). There's another passage which is clearly talking about the Restaurant at the End of the Universe (Milliways) but mentions 86.4 seconds, so the solution is "Millidays". You have to do something with all the letter differences to get the end solution, but one of my teammates solved that part.

Really looking forward to this year's hunt.

posted by A dead Quaker at 2:16 PM on January 13, 2010

I also enjoyed The Combatant's Guide to Zyzzlvaria. Each clue is similar to, but not the same as, a passage from the Hitchhiker's Guide to the Galaxy. Each corresponding answer is one letter away from the thing the original passage describes. So, the answer to "Mostly Sith" ("Mostly Harmless") is "Darth" ("Earth"). There's another passage which is clearly talking about the Restaurant at the End of the Universe (Milliways) but mentions 86.4 seconds, so the solution is "Millidays". You have to do something with all the letter differences to get the end solution, but one of my teammates solved that part.

Really looking forward to this year's hunt.

posted by A dead Quaker at 2:16 PM on January 13, 2010

This is the first Mystery Hunt I'm going to miss in almost 15 years, and I'm bummed. My sense is that crazy-ass logic puzzles (I'm looking at you, Dan Katz and your god-damned duck conundrae) have increased in both frequency and difficulty over the years. The biggest shift in the Hunt is still the birth of Google -- some of the early Mystery Hunts can now be done by a single person in a few hours. Because there's not really such a thing as "trivia" anymore (or, at least, you have to go really, really out of your way to find something not recorded in some crazy wiki somewhere), a lot of the replacement difficulty has come from (a) increasing the sheer number of puzzles and (b) inventing puzzles that are onerous to even brute-force.

(Go Mayhem!)

posted by range at 4:48 PM on January 13, 2010

(Go Mayhem!)

posted by range at 4:48 PM on January 13, 2010

That index of puzzles is the start of a crazy scheme of mine that I haven't actually gotten off the ground yet. Good to see someone else is out there not just cataloging puzzles, but posting all the delicious information. Someday, I'd like to see a really good set of collective puzzling information, not just one team's internal resources.

(go sages!)

posted by lorimt at 10:30 PM on January 13, 2010

(go sages!)

posted by lorimt at 10:30 PM on January 13, 2010

I remember movement last year to develop a FOSS solution to Puzzle Hunting. Something that glued puzzle management, solving and collating into one shiny package. A puzzle concordance would be a great addition to that!

(go codex!)

posted by persona at 4:09 PM on January 14, 2010

(go codex!)

posted by persona at 4:09 PM on January 14, 2010

*I can't imagine any way to solve the puzzle short of writing a computer program (or perhaps a fairly complicated Excel spreadsheet).*

It's not as hard as it looks initially—I solved it in about 8 hours more or less by hand, and that involved a lot of backtracking to find mistakes I had made, and inefficient solving methods. Probably would have taken less than half that if I hadn't made any mistakes along the way. When I say "more or less by hand," I did use Excel to track information, but didn't use any Excel functions. The only advantages Excel had over pencil-and-paper were a) making it easy to do lots of sequential ctrl-Zs when trying to backtrack to where I made a mistake, and b) color-coding some cells when I made a "guess" so I could differentiate between what I knew for sure and what was based on my guess, and undoing

*those*when my guess led to a contradiction. But it turns out guessing wasn't even necessary (some of the "inefficient solving methods" I mentioned before), which I found out when I was going over parts of the solution a second time when I had backtracked well beyond the mistake I was trying to find. It would definitely be possible to solve this one with pencil and paper only.

Thanks, Wolfdog! That was a lot of fun.

posted by DevilsAdvocate at 11:34 PM on January 14, 2010

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And sex used to be so simple...

posted by Theta States at 9:21 AM on January 13, 2010