Of Knights and Knaves

March 15, 2005 7:12 AM

There is an island where all the inhabitants are either knights or knaves. Knights always tell the truth, and knaves always lie [PDF]. Can you tell which is which?
posted by skoosh (18 comments total)

Previously covered in the Blue: Puzzles by Raymond Smullyan (whose sadly out-of-print What Is The Name of This Book? first turned me on to the wonderful world of knights and knaves), and Lateral Thinking Puzzles.
posted by skoosh at 7:26 AM on March 15, 2005

isn't this pretty much that scene from the movie labyrinth with the two doorkeepers? it really gets the mind going, but where are the answers?!?! the rest of the site is pretty interesting as well - lots of good exercises. i'm always up for a good logic puzzle (as long as the answers are there). thanks!
posted by venus in furs at 7:32 AM on March 15, 2005

"You meet nine inhabitants: Mel, Bart, Sue, Betty, Rex, Zeke, Sally, Zoey and Homer."

Ow, my brain. This is good.
posted by Plutor at 7:37 AM on March 15, 2005

Also featuring the list that no Mefi member should be without. ;)
posted by GeekAnimator at 7:39 AM on March 15, 2005

Ouch. I think that I worked out the first one, but it's gone steadily downhill form thereon in.

I'm going to stick to blowing bubbles and drooling...
posted by Chunder at 7:42 AM on March 15, 2005

Anyone know whether this kind of thing can be represented diagrammatically?
Just looked at puzzle 382 (the one Plutor references) and quickly ran away... but it looks like it begs some kind of pictorial representation.
posted by Chunder at 7:47 AM on March 15, 2005

There! Are! Four! Lights!
posted by fandango_matt at 8:00 AM on March 15, 2005

There! Are! Four! Lights!
Ahhh... GeekCred.
posted by raedyn at 8:15 AM on March 15, 2005

Arturo Perez-Reverte uses a form of this riddle in his book The Nautical Chart. I've never been satisfied with the solution given in the book.
posted by goatdog at 8:18 AM on March 15, 2005

A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie.

You meet two inhabitants: Zoey and Mel. Zoey tells you that Mel is a knave. Mel says, `Neither Zoey nor I are knaves.'

Can you determine who is a knight and who is a knave?

Zoey can't be a liar. If Zoey were lying, then Mel is actually a knight and telling the truth. If Mel is telling the truth that there are no liars, a contradiction would arise since we stated that Zoey is a liar.

Since Zoey's not a liar, he is a knight, and therefore telling the truth, which makes Mel the knave.

Zoey is the knight, Mel is the knave.

A helpful tool is to understand what it means if Mel is lying. Mel says, 'Neither Zoey nor I are knaves.' which translates into not(exist(liar)). So if Mel is lying, the world has not(not(exist(liar))), which becomes exists(liar).
posted by philosophistry at 8:20 AM on March 15, 2005

For puzzle 382, distill all of the statements to what they're really saying.

Mel: Sally=Knight
Bart: Rex=Knave
Sue: Mel=Knave Homer=Knave
Betty: Betty=Knight Sally=Knave
Rex: Betty=Knight Rex=Knight
Zeke: At least one: Sally=Knight Sue=Knight
Sally: Betty=Knight
Zoey: Sue=Knight
Homer: Either Betty=Knave or Zeke=Knave

Assume that:
Mel=Knight

Therefore:
Sally=Knight
Betty=Knight
Rex=Knight
Bart=Knight
Sue=Knave
Zoey=Knave
Homer=Knight

However we must call Zeke a Knave because of Homer's true statement, and yet we know her statement is true, making her a Knight.

Assume that:
Mel=Knave

Therefore:
Sally=Knave
Sue=Knight
Zoey=Knight
Homer=Knight
Zeke=Knight
Rex=Knave
Bart=Knave

The paradox here is that Betty must be a Knave because Sally is a Knave. However, if Betty is a Knave then Sally must be a Knight.
posted by ManicExpressive at 8:24 AM on March 15, 2005

Puzzle 382 abstract and solution in rot13 (WARNING: potentially accurate):


Zry: Fnyyl=Xavtug
Oneg: Erk=Xanir
Fhr: Zry=Xanir ^ Ubzre=Xanir
Orggl: Orggl=Xavtug ^ Fnyyl=Xanir
Erk: Orggl=Xavtug ^ Erk=Xavtug
Mrxr: Fnyyl=Xavtug i Fhr=Xavtug
Fnyyl: Orggl=Xavtug
Mbrl: Fhr=Xavtug
Ubzre: Orggl=Xanir i Mrxr=Xanir

n) Vs Zry=Xavtug:
Fnyyl=Xavtug
Orggl=Xavtug
Fnyyl=Xanir
Orggl=Xanir (n pbagenqvpgvba)

Gurersber:
Zry=Xanir
Fnyyl=Xanir
Orggl=Xanir

o) Vs Oneg=Xanir:
Erk=Xavtug
Orggl=Xavtug (snyfr, frr nobir)

Gurersber:
Oneg=Xavtug
Erk=Xanir

p) Vs Mbrl=Xavtug:
Fhr=Xavtug
Zry=Xanir
Ubzre=Xanir
~(Orggl=Xanir i Mrxr=Xanir)
be
Orggl=Xavtug (snyfr, frr nobir)
Mrxr=Xavtug

Gurersber:
Mbr=Xanir
Fhr=Xanir
~(Zry=Xanir ^ Ubzre=Xanir)
naq
Zry=Xanir
Gurersber:
Ubzre=Xavtug

q) Vs Mrxr=Xavtug:
Fnyyl=Xavtug i Fhr=Xavtug
ohg
Fnyyl=Xanir ^ Fhr=Xanir

Gurersber:
Mrxr=Xanir

Va pbapyhfvba:

Zry=Xanir
Oneg=Xavtug
Fhr=Xanir
Orggl=Xanir
Erk=Xanir
Mrxr=Xanir
Fnyyl=Xanir
Mbrl=Xanir
Ubzre=Xavtug
posted by skoosh at 9:13 AM on March 15, 2005

How funny, I was going to put together a post on Smullyan. Here's a nice link. (PDF)
posted by dances_with_sneetches at 9:20 AM on March 15, 2005

I prefer the solution to this presented in 'The 10th Kingdom' myself.
posted by InnocentBystander at 9:24 AM on March 15, 2005

So What Happened After The Wise Man Discovered He Was Wearing The Red Hat?
A "Where Are They Now?" for characters in brain teasers.
posted by soyjoy at 9:27 AM on March 15, 2005

Addictive. But head-hurting.
posted by slf at 10:39 AM on March 15, 2005

But really, are there answers somewhere to these? It would be nice to know if I'm doing any of these right or am completely off.
posted by Sangermaine at 4:53 PM on March 15, 2005

I'm slightly afraid to try it, lest I be thrown into an oubliette... But it still looks very interesting.
posted by elf_baby at 11:46 PM on March 15, 2005