There's a classic logic puzzle in which a person must take a fork in the road, one of which is safe, but the other is a deadly trap. Two men guard the fork, one of which always lies, but the other always tells the truth. The person gets to ask one question in order to determine which path is the safe one.
Mathematician Raymond Smullyan has added another dimension to this puzzle. See if you can figure it out:
Link via Marginal Revolution | Raymond Smullyan
UPDATE 3/18/10: Here's the solution.
Mathematician Raymond Smullyan has added another dimension to this puzzle. See if you can figure it out:
There are three guardians, A, B and C. Their names are Knight, Knave and Chaos. Knight always speaks truly, Knave always lies. Chaos tossed a coin this morning to decide whether today he would behave like Knight or like Knave.
Your task is simple: ask three yes-no questions, each of a single guardian, and determine which is Knight, which is Knave, and which is Chaos. There is, alas, a complication: the guardians understand English but will answer in the local language, in which “Da” means yes and “Ja” means no. Or possibly “Ja” means yes and “Da” means no – you cannot remember.
Link via Marginal Revolution | Raymond Smullyan
UPDATE 3/18/10: Here's the solution.
If you ask all three guardians "How would chaos answer the question 'is chaos telling the truth today?' ", then you will always get Y, Y, N. N will be the Knave. And this will also tell you which of Ja/Da is yes.
If only you had one more question to ask the Knave which of the other two was Chaos...
Of course you might get lucky and hit an N in the first two Guardians you question; but that's not a solution.
Only one
So, the first question is "Are you a liar." All three will answer no to that, so you know what the word for "no" is. Second question, "Will person number 2 tell me that person number 3 is a liar?" If the answer is yes then chaos is a truth teller, if the answer is no then chaos is a liar. The next question is "will person number 2 tell me that person number 3 wants me to go this way?" If chaos is a truth teller then yes means that's the bad way, no means it's the good way. If chaos is a liar then yes is good, no is bad.
WHAT... is your quest?
WHAT... is the air speed velocity of an unladen swallow?
http://www.giantitp.com/comics/oots0327.html
if you ask "does ja (or da, doesn't matter which one) mean no?", and the person answers with the same word, then they're lying, so you'd be able to tell who the knight or the knave is by seeing which one is the "odd one out"
here's why:
If ja meant no, and the person answered with ja, then they'd be lying, because they'd either be:
A) saying "yes", which, if you think about it, would contradict itself, or
B) saying "no", which also would contradict itself (by saying "no", they're confirming the question, while at the same time negating it)
either way the person is lying. There will be two "knaves" or two "knights" when you ask the question to all three. Whoever is left out is the true knight or knave.
Ja=yes Knight Knave Chaos (truthful)
Are you Chaos? da ja ja
Does Ja = yes? ja da ja
Does Da = No? ja da ja
Ja=yes Knight Knave Chaos (lies)
Are you Chaos? da ja da
Does Ja = yes? ja da da
Does Da = No? ja da da
Ja=No Knight Knave Chaos (truthful)
Are you Chaos? ja da da
Does Ja = yes? ja da ja
Does Da = No? ja da ja
Ja=No Knight Knave Chaos (lies)
Are you Chaos? ja da ja
Does Ja = yes? ja da da
Does Da = No? ja da da
So if one answers the same for all 3 questions while the other two answer different for 1 & 2 then the one that answered all the same is chaos and Ja is yes, then you know who knight and Knave are.
If two answer the same for all three then the one that didn't is Chaos and Ja is no and the one that agreed with Chaos on question 2 is Knight.
Anybody see anything wrong in the logic?
If two answer the same for all three then the one that didn't is Chaos and Ja is no and the one that said Ja with Chaos on question 2 is Knight.
*********
This took forever to write out the logic in words.
What about knowing what's yes and what's no? And where do you get the part about asking as many questions as you like?
I'm sure the riddle involves the tossing of the coin somehow.
LOL, yes, exactly yes. Excellent.
What fourth path? The path you just came down to reach where they are.
Has anyone actually found a solution?
If A answers “ja”, he’s Chaos. Then ask Guardian B, “If I asked you, “Are you Knight?”, would you say “ja”?”. The answer is “ja” if B is Knight, and either way the problem is now solved.
If A answers “da”, he’s either Knight or Knave. So ask him instead, “If I asked you, “Are you Knight?”, would you say “ja”?” If the answer is “ja” he’s Knight; otherwise he is Knave.
So, now, ask him “If I asked you, “Is guardian B Chaos”, would you say “ja”?” If he answers “ja”, B is Chaos, and C is the opposite of A. If he answers “da” then C is Chaos and B is the opposite of A.