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The Island of Knights and Knaves

On the fictional island of Knights and Knaves, every inhabitant is either a knight or a knave. Knights are honest and virtuous, and always tell the truth. Knaves are base and shameful, and always lie.
A stranger comes to the island and encounters three inhabitants, referred to as A, B and C. The visitor asks A whether he' s a knight or a knave. Inhabitant A mumbles an answer the stranger cannot understand. B then says: "A said that he is a knave" while C says: "Don' t believe B, he is lying!"

It is not possible to determine A' s type from this conversation, but it is possible to tell what type B and C are.

A is a knight
B is a Knave
C is a Knight

OK I asked my friend Jerry (he is good at this stuff) he said the there are two possibilities.

1.
A = Knight
B = Knight
C = Knave

2.
A = Knave
B = Knave
C = Knight

I could have figured that out myself

true
false
true



because:
if B told truth..the first one would be a knave..so he wouldn't admit it.. and this means the B one lied...so the last one said the turth

do i make sense?

A his answer can not be heard, does that mean he is lying or he's just speaking softly... Personally I think the first, so that would mean

A. Knave
B. Knave
C. Knight

If C is telling the truth then B lied and A claimed to be a knight. But this doesn't show wether or not he IS a knight as a knave would lie and say he was a knight, and a knight would truthfully say he was a knight.

A = ?
B = Knave
C = Knight


If C is lying then B would br telling the truth about. . . a knave really claiming to be a knave? But wouldn't the knave lie about it? And if A was a knave he would have claimed to be a knight. But B would have said that the a claimed to be a knight. But he didn't. A either way would have claimed to be a knight. So B has to be lying. So B has to be a knave so C was telling the truth.


1. ?
knave
knight

Originally posted by Fishy
A his answer can not be heard, does that mean he is lying or he's just speaking softly... Personally I think the first, so that would mean

A. Knave
B. Knave
C. Knight If A was a knight he would have claimed to be a knight and B would have lied about the claim.
If A was a knave he would have claimed to be a knight and B would have lied about the claim.

I don't like puzzles....

Originally posted by Creshosk
If C is telling the truth then B lied and A claimed to be a knight. But this doesn't show wether or not he IS a knight as a knave would lie and say he was a knight, and a knight would truthfully say he was a knight.

A = ?
B = Knave
C = Knight



Yeah you are right. If:
B said "A is a knave"
C said "B is lying"

If C tells the truth, and B lies one can conclude from what C said that B is a knave, and from B that "A is a knave" is a lie, so A must be a knight.
So in this case:

A.Knight
B.Knave
C.Knight



B said "A is a knave"
C said "B is lying"

If C is lying then B said the truth(he is a knight not a knave). If B said the truth he is a knight, and the sentence "A is a knave" is true. So:

A. Knave
B. Knight
C. Knave

But logic is evil... so... be careful.

Should I shed light on the Island of Knights and Knaves or do you want to rack your brain some more?

Wait... I still have hope

Does it have something to do with the word "he?"

The visitor asks A whether he' s a knight or a knave.

Gender is no object.

Originally posted by Storm
Gender is no object.

But as the real object of the question?....OH, forget it...I hate logic puzzels...

no tips

It all has to do with "A said that"

It's like the door puzzle. "what did the other person say."

A's Claim in this case and what B thinks of it.

A said that he was a knight.
B sais that A said that he was a knave.
C says B is lying about what A claimed.

A had to have claimed he was a knight, after all if A was a knight, it'd be the truth. If he was a knave it'd be a lie.

Now B had to have lied about A's claim. Since a knight wouldn't claim to be a knave, and a knave would not admit he was a knave.

And of course C Was telling the truth about B lying.

Observation: A knave will never call himself a Knave for he then is telling the truth.


Answer: No inhabitant can say that he is a knave. Therefore B's statement must be untrue, so he is a knave, and C's statement must be true, so he is a knight.

God, I hate these puzzles....

Originally posted by debbiejo
God, I hate these puzzles....
You have already said that. Are you going to just repeat your self over and over again?
You have already said that. Are you going to just repeat your self over and over again?
You have already said that. Are you going to just repeat your self over and over again?
You have already said that. Are you going to just repeat your self over and over again?
You have already said that. Are you going to just repeat your self over and over again?
You have already said that. Are you going to just repeat your self over and over again?

But I doooooooooo hate them....A LOT!!!!!!......logic PUZZLES...I'm too right brained for this....I need visuals....many of them....hands on visuals.

debbie cut it out, we got it! no need to derail this thread.

Congratulations to Atlantis001, Creshosk and WindDancer.


Einstein' s Puzzle

There are exactly 5 houses on the street, in a line running from left to right. Each house is a different colour, and each has exactly one owner.

The 5 owners each drink a certain drink, each smoke a certain brand of cigarette, and each have a certain pet.
No owner drinks the same drink as any other.
No owner smokes the same brand of cigarettes as any other.
No owner has the same pet as any other.
The following statements are true:
1. The British man lives in the red house.
2. The Swedish man has a dog for a pet.
3. The Danish man drinks tea.
4. The green house is just to the left of the white house.
5. The owner of the green house drinks coffee.
6. The person that smokes Pall Mall has a bird.
7. The owner of the yellow house smokes Dunhill.
8. The person that lives in the middle house drinks milk.
9. The Norwegian lives in the first house (ie. the one on the far left).
10. The person that smokes Blend, lives next to the one that has a cat.
11. The person that has a horse lives next to the one that smokes Dunhill.
12. The one that smokes Bluemaster drinks beer.
13. The German smokes Prince.
14. The Norwegian lives next to a blue house.
15. The person that smokes Blend has a neighbor who drinks water.
Who has the fish?

Originally posted by Storm
Congratulations to Atlantis001, Creshosk and WindDancer.


Einstein' s Puzzle

There are exactly 5 houses on the street, in a line running from left to right. Each house is a different colour, and each has exactly one owner.

The 5 owners each drink a certain drink, each smoke a certain brand of cigarette, and each have a certain pet.
No owner drinks the same drink as any other.
No owner smokes the same brand of cigarettes as any other.
No owner has the same pet as any other.
The following statements are true:
1. The British man lives in the red house.
2. The Swedish man has a dog for a pet.
3. The Danish man drinks tea.
4. The green house is just to the left of the white house.
5. The owner of the green house drinks coffee.
6. The person that smokes Pall Mall has a bird.
7. The owner of the yellow house smokes Dun-hill.
8. The person that lives in the middle house drinks milk.
9. The Norwegian lives in the first house (ie. the one on the far left).
10. The person that smokes Blend, lives next to the one that has a cat.
11. The person that has a horse lives next to the one that smokes Dun-hill.
12. The one that smokes Bluemaster drinks beer.
13. The German smokes Prince.
14. The Norwegian lives next to a blue house.
15. The person that smokes Blend has a neighbor who drinks water.
Who has the fish? I love these logic puzzles.

Nationality1Norwegian11Dane1111Brit111111German111
1Swede
Color1111111Yellow11111Blue1111Red1111111Green1111
1White
Drink1111111Water111111Tea11111Milk111111Coffee111
1Beer
Pet111111111Cats1111111Horses11Birds11111Fish11111
Dogs
Cigar111111Dunhill11111Blends11Pall Mall1Prince1111Blue Master

The German has the fish.
http://pc59te.dte.uma.es/cdb/series/marvel/bitmaps/nightcrawler.jpg

Nightcrawlers are good at catching fish I guess. . .

So no one else is going to try?

I was told to stop talking...OH...how hard.... ...I have to listen to my elders...

The German has the fish.

Congratulations to Creshosk and Adam_PoE.

Now put your heads together for this crossword.

Horizontal

2. Theory of knowledge.
5. Buddhist unconditioned state of release from suffering.
6. Stoics said we should submit to this in order to have peace of mind.
8. Heidegger' s term for being in the world.
10. Greek god who represented light and reason, according to Nietzsche.
12. Ockham' s ________ cut pretty well.
14. Greek word for city.
15. Theory that all knowledge is based on data that we get through the senses.
16. Kant' s thing-in-itself.
17. Heraclitus' term for the divine voice of reason.
21. According to Hegel, what ideas have to go through in order to arrive at truth.
22. Deductive argument.
25. Branch of Buddhism that stresses immediacy without abstraction.
26. Heidegger' s magnum opus was called Being and _________ .
27. Theory of ultimate reality.
30. Schopenhauer had his will-to-live, Nietzsche had his will-to-power, and William James had his will to ____________.
32. Plato said the philosopher should be a __________, since he knows how a city should be ordered.
33. By the _______, god of the Egyptians, Socrates was fond of saying.
34. Don' t make excuses, just follow Kant' s ________________ imperative.
37. For Kant, ___________________ a priori propositions will give us real knowledge.
39. Theory that there are two separate kinds of substances, such as body and mind.
40. Galileo' s _________________ theory of the heavens got him into trouble with the Catholic Church.
41. Buddhist theory of no-self.

Vertical

1. Everything comes from this, according to Thales.
3. Like Hume, one who thinks we can' t know reality.
4. Leibniz' s windowless _________.
7. One of Aristotle' s four causes.
9. Socrates' defense speech.
11. Units of pleasure for Bentham.
13. View that there is no truth beyond what an individual or society regards as true.
14. What the Cyrenaics considered to be the most important thing.
18. What Marx says workers experience.
19. All things are made of these, according to Democritus.
20. Theory of interpretation for Gadamer and others.
23. I can' t conceive of anything greater, so God exists. This is an ________________ argument for the existence of God.
24. Confucius' Sayings.
26. Study of ends or purposes.
28. According to Kierkegaard, truth is ______________________.
29. Type of intuition that Husserl thought we could have.
31. Word that seems for John Dewey to include almost everything.
35. According to Descartes, we' re born with certain ideas so they must be ________.
36. Thales was said to have fallen into one of these while he was looking at the sky.
38. The female side of things in Taoism.

On a philosophical note, I think paradoxes, especially visuo-spatio ones, arise from a person not seeing the thing for what it is - IOW mindfulness is absent. Meditation should help.

I always used to do the New York Herald Tribune Logic Puzzles, but they became so boring because once I got to know how to go about doing them, I finished the most advanced ones and nothing were left as a challenge. The point is that if you can think logically, you can do them - they should come up with creative puzzles....mmm...

Horizontal

5. Buddhist unconditioned state of release from suffering. NIRVANA

41. Buddhist theory of no-self. ANATMAN

Some answers are on the tip of my tongue though I can' t seem to put my finger on it.

2 across is spelt wrong (epistemology).

36 down should be 'well'.

Across-

8. dasein
10. Apollo
15. empiricism
16. noumenon
17. logos
21. dialectic
22. syllogism
27. metaphysics
30. believe
34. categorical
37. synthetic
39. dualism
40. geocentrical


Down-

3. sceptic
4. monads
7. form
11. hedons
13. relativism
18. alienation
20. hermeneutics
23. ontological
24. proverbs
35. innate

If no one mindeds me adding a puzzle in... I've been thinking about this for a day now... See what you make of it... (copied from another website)

This position was reached in a normal chess game:
BLACK
+---+---+---+---+---+---+---+---+
| B |////| K |/R/| N | ///| | ///|
+---+---+---+---+---+---+---+---+
|/P/ | P | ///| | ///| | ///| |
+---+---+---+---+---+---+---+---+
| |/// | Q |/K/| |/R/| | ///|
+---+---+---+---+---+---+---+---+
|/// | |/// | |/// | |/// | |
+---+---+---+---+---+---+---+---+
|/// | |/// | |/// | |/// | |
+---+---+---+---+---+---+---+---+
|/// | |/// | |/// | |/// | |
+---+---+---+---+---+---+---+---+
|/// | |/// | |/// | |/// | |
+---+---+---+---+---+---+---+---+
|/// | |/// | |/// | |/// | |
+---+---+---+---+---+---+---+---+
WHITE
a) Identify the color of each piece.
b) What was the last move?

Edit! ARG! dam it got messed up... Seems to delete the extra spaces...
http://perplexus.info/show.php?pid=3907
Thats the website for the puzzle...

Originally posted by Victor Von Doom
2 across is spelt wrong (epistemology).

36 down should be 'well'.

Across-

8. dasein
10. Apollo
15. empiricism
16. noumenon
17. logos
21. dialectic
22. syllogism
27. metaphysics
30. believe
34. categorical
37. synthetic
39. dualism
40. geocentrical


Down-

3. sceptic
4. monads
7. form
11. hedons
13. relativism
18. alienation
20. hermeneutics
23. ontological
24. proverbs
35. innate

I think 29 down is 'hyletic'.

Has this thread become leprous?

Damn VVD...knows everything.....

Interesting thread so far the only puzzle I succesfully figured out was the first one, oh and how did the german end up with the fish?!?!

But how does this relate to philosophy?

all about mind power... People who would do logical puzzles tend to be the ones who want to think....

None of the 3 in question can say "I am a knave",(a liar can't say he is a liar) so B must have been lying. This means that B is a knave and C is a knight

Four prisoners are arrested for a crime, but the jail is full and the jailer has nowhere to put them. He eventually comes up with the solution of giving them a puzzle so if they succeed they can go free but if they fail they are executed.

The jailer puts three of the men sitting in a line. The fourth man is put behind a screen (or in a separate room). He gives all four men party hats. The jailer explains that there are two red and two blue hats. The prisoners can see the hats in front of them but not on themselves or behind. The fourth man behind the screen can' t see or be seen by any other prisoner. No communication between the men is allowed.

If any prisoner can figure out and say (out loud) to the jailer what colour hat they have on their head all four prisoners go free. The puzzle is to find how the prisoners can escape.

If B and A are wearing the same colour hat, C can call out immediately that he must be wearing a different colour.

If C doesn't call out after a few seconds, it must be because B and A have different colours. Therefore, B, who can see A's colour, knows he is wearing the other colour and calls that out.

Well done to the both of you.

Once upon a time a farmer went to market and purchased a fox, a goose, and a bag of beans. On his way home, the farmer came to the bank of a river and hired a boat. But in crossing the river by boat, the farmer could carry only himself and a single one of his purchases: the fox, the goose, or the bag of beans.

If left alone, the fox would eat the goose, and the goose would eat the beans.

The farmer' s challenge was to carry himself and his purchases to the far bank of the river, leaving each purchase intact. How did he do it?

He takes the goose first, as the fox will not eat the beans?

Originally posted by Storm
Well done to the both of you.

Once upon a time a farmer went to market and purchased a fox, a goose, and a bag of beans. On his way home, the farmer came to the bank of a river and hired a boat. But in crossing the river by boat, the farmer could carry only himself and a single one of his purchases: the fox, the goose, or the bag of beans.

If left alone, the fox would eat the goose, and the goose would eat the beans.

The farmer' s challenge was to carry himself and his purchases to the far bank of the river, leaving each purchase intact. How did he do it?
I'll assume the farmer is in side A and he needs to get to side B.
The farmer takes the goose to side B, he then goes back to side A picks up the bag of beans goes to side B once more again, leaves the beans but takes the goose back to side A. He leaves the goose in side A but takes the fox to side B. At last he goes back to side A picks up the goose and finally crosses the damn river for good.

Its a sack of corn not beans. Well thats how I know it.

First he takes the Bird,

He Goes back for the fox

He leaves the Fox and takes the Goose back with him

He leaves the Goose and goes with the corn and leaves the corn and the Fox together.

He returns with the Goose

He takes the goose, then the beans, the he go back with the goose, and then he bring the fox, and finally he takes the goose again.

Never noted... there are two ways to do that. You take the goose first, then you can either choose to take the beans, or the fox just before you take the goose back.

He should get his wife to carry one of them.

(most people in the UK should get that one)

lol is that from the office.

He carries the fox across and makes the goose swim beside him (on a leash). He leaves the fox alone on the opposite bank and returns with the beans.
Or
He takes the goose across, goes back for the fox, takes it across, then takes the goose back. He then takes the beans to the fox and goes back for the goose.

BTW for the first puzzle alot of people were assuming that A said anything about his status at all.

Zod (possibly now saldy missed) was correct.

Originally posted by WrathfulDwarf
Observation: A knave will never call himself a Knave for he then is telling the truth.


Answer: No inhabitant can say that he is a knave. Therefore B's statement must be untrue, so he is a knave, and C's statement must be true, so he is a knight.


grrr i was hoping id get to say it!!! lol

The fox, goose and bag of beans puzzle was correctly solved by all of you.

Burning rope

There are two lengths of rope. Each one can burn in exactly one hour. They are not necessarily of the same length or width as each other. They also are not of uniform width (may be wider in middle than on the end), thus burning half of the rope is not necessarily 1/2 hour.

By burning the ropes, how do you measure exactly 45 minutes worth of time?

Originally posted by Storm
The fox, goose and bag of beans puzzle was correctly solved by all of you.

Burning rope

There are two lengths of rope. Each one can burn in exactly one hour. They are not necessarily of the same length or width as each other. They also are not of uniform width (may be wider in middle than on the end), thus burning half of the rope is not necessarily 1/2 hour.

By burning the ropes, how do you measure exactly 45 minutes worth of time?

The real problem is, when you are done how do you tell time?

Light both ends of one rope, and one end of the other.
When both ends of one meet it has been half an hour, immediately light the unlit end of the second rope.
When the two ends meet it has been half of a half hour, 15 minutes.

It has thus been 45 minutes.

at t=0, light both ends of one rope (rope A) and one end of the other (rope B).

at t=30, the double lit rope A will completely burn up, the single lit rope Bwill be half burned. at this point, you light the other end of the single lit rope B (making it double lit)

at t=45, rope B will be completely burnt up

Originally posted by Storm
The fox, goose and bag of beans puzzle was correctly solved by all of you.

Burning rope

There are two lengths of rope. Each one can burn in exactly one hour. They are not necessarily of the same length or width as each other. They also are not of uniform width (may be wider in middle than on the end), thus burning half of the rope is not necessarily 1/2 hour.

By burning the ropes, how do you measure exactly 45 minutes worth of time?

If you light both ends of one rope, it will burn in exactly a 1/2 hour. Thus, burn one rope from both ends and the other rope from only one end. Once the one rope (which is burning from both ends) finally burns out (and you know a 1/2 hour has elapsed), you also know that the other rope (which is buring from only one end) has exactly 1/2 hour left to burn. Since you only want 45 minutes, light the second end of the rope. This remaining piece will burn in 15 minutes. Thus, totaling 45 minutes.

but I guess I'm a little late...

Originally posted by AOR
but I guess I'm a little late...
Thats ok, it'll be a party.

Here is one paradox :

Is the sentence "This sentence is false" true or false ???

Its niether because it does not pose a question

Originally posted by Alliance
Thats ok, it'll be a party.

w00t cheers mate beer

Originally posted by Atlantis001
Here is one paradox :

Is the sentence "This sentence is false" true or false ???

It's both ermm

You need that drink.

Originally posted by Alliance
You need that drink.

Would you care to see my reasoning?

Sure, but I can see reason in both options and therfore your point is techically correct. But something cannot be entirely true and false at the same time.

Regret, Alliance and AOR you all correctly solved the previous puzzle.

No brainteaser now.

Socrates: who leaves behind him a written manuscript ... on the supposition that such writing will provide something reliable and permanent, must be exceedingly simple minded... the strange thing about writing that makes it truly analogous to painting. The painter' s products stand before us as though they were alive, but if you question them, they maintain the most majestic silence. It is the same with written words; they seem to talk to you as though they were intelligent, but if you ask them anything about what they say, from a desire to be instructed, they go on saying the same thing forever. And once a thing is put into writing, the composition... drifts all over the place... And when it is ill treated and unfairly abused it always needs its parent to come to its help, being unable to defend or help itself... But now tell me, is there another sort of discourse that is the brother to the written speech, but of unquestioned legitimacy? ...

Speech!

Correct. The living speech.


Zebra Puzzle
1. There are five houses.
2. The Englishman lives in the red house.
3. The Spaniard owns the dog.
4. Coffee is drunk in the green house.
5. The Ukrainian drinks tea.
6. The green house is immediately to the right of the ivory house.
7. The Old Gold smoker owns snails.
8. Kools are smoked in the yellow house.
9. Milk is drunk in the middle house.
10. The Norwegian lives in the first house.
11. The man who smokes Chesterfields lives in the house next to the man with the fox.
12. Kools are smoked in the house next to the house where the horse is kept.
13. The Lucky Strike smoker drinks orange juice.
14. The Japanese smokes Parliaments.
15. The Norwegian lives next to the blue house.Now, who drinks water? Who owns the zebra?

In the interest of clarity, it must be added that each of the five houses is painted a different color, and their inhabitants are of different national extractions, own different pets, drink different beverages and smoke different brands of American cigarettes. One other thing: in statement 6, right means your right.

Originally posted by Storm
Now, who drinks water?

The Norwegian man.




Originally posted by Storm
Who owns the zebra?

The Japanese man.

Originally posted by Adam_PoE
The Norwegian man.

The Japanese man.

I concur....

Which method did you follow to derive the solution?

There was one part where I had to guess between two places, I chose correctly.

Anyway, it took me a good 10 minutes...

Originally posted by Storm
Which method did you follow to derive the solution?

Deduction.

Originally posted by Storm
Which method did you follow to derive the solution?

I drew it out....drawingouttion? shrug

Here is another one...

Three switches are in the "off" position outside a windowless room with each being connected to one of three light bulbs inside the room. How can you determine which switch is connected to which bulb if you may enter the room only once?

Here is another...

It's night and the electricity is gone in your room. You need a pair of identical socks from your drawer. You have 20 red, 30 green, 50 blue pairs of socks and every sock is identical except its color. Since it is dark, you can't see the colors of the socks. So you pick randomly some socks. At least how many socks should you pick so that you are sure that you picked at least one identical pair (identical pair means a pair of socks with the same color).

The majority of people can't answer this question correctly.

Originally posted by Hydrono
Here is another one...

Switch one light on; turn it off and turn another on and leave it on. Go into the room and feel the off-bulbs. The warm one is connected to the first switch, the on-bulb is connected to the second switch and the third heatless bulb is connected to the third unused switch.

Originally posted by AOR
Switch one light on; turn it off and turn another on and leave it on. Go into the room and feel the off-bulbs. The warm one is connected to the first switch, the on-bulb is connected to the second switch and the third heatless bulb is connected to the third unused switch.

Correct!

Originally posted by Hydrono
Here is another...


The majority of people can't answer this question correctly.
Four. I find it hard to believe most people can't answer it correctly.

The Hardest Logic Puzzle Ever

Three gods A, B, and C are called, in some 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.

Clarifications:It could be that some god gets asked more than one question (and hence that some god is not asked any question at all).
What the second question is, and to which god it is put, may depend on the answer to the first question. (And of course similarly for the third question.)
Whether Random speaks truly or not should be thought of as depending on the flip of a coin hidden in his brain: if the coin comes down heads, he speaks truly; if tails, falsely.
Random will answer 'da' or 'ja' when asked any yes-no question.

Originally posted by Storm
The Hardest Logic Puzzle Ever

Three gods A, B, and C are called, in some 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.

Clarifications:It could be that some god gets asked more than one question (and hence that some god is not asked any question at all).
What the second question is, and to which god it is put, may depend on the answer to the first question. (And of course similarly for the third question.)
Whether Random speaks truly or not should be thought of as depending on the flip of a coin hidden in his brain: if the coin comes down heads, he speaks truly; if tails, falsely.
Random will answer 'da' or 'ja' when asked any yes-no question.

Wow

How do they react to answers they can't know, for example, how would the liar and the truthteller answer "Would God A say he always tells the truth if I ask him" if that was the God that randomly chose?

Originally posted by Storm
The Hardest Logic Puzzle Ever

Three gods A, B, and C are called, in some 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.

Clarifications:It could be that some god gets asked more than one question (and hence that some god is not asked any question at all).
What the second question is, and to which god it is put, may depend on the answer to the first question. (And of course similarly for the third question.)
Whether Random speaks truly or not should be thought of as depending on the flip of a coin hidden in his brain: if the coin comes down heads, he speaks truly; if tails, falsely.
Random will answer 'da' or 'ja' when asked any yes-no question.

This question isn't even possible to find an answer to. 12 possibilities and only 3 bits of information....wow.

Your puzzle can be solved by asking self-referential questions after one with a known answer.



The second question would be “Was your previous answer correct?



Then you have a lot of information.

The truth teller will give identical answers.

The liars would alternate.

The other’s are unpredictable.



If you get two sets of identical responses you have identified the liar, because his alternated.

If you get two alternating responses, you have identified the truth teller and know which response means true.

If the one with the unpredictable responses happens to answer truthfully three times, he will be indistinguishable from the truth teller. Similarly, if he lies three times his answers will be identical to those of the liar. So, his answers are useless, unless they show a pattern incompatible with those that the other two can present, for example TTT and FTF, to simple questions about previous answers. Are there any restrictions on the one with the random answers that prevent him from mimicking the answers of one of the other two players? If not, I give up.


(posting for a friend)

ja and da are not the only possible answers...if you ask the truth god "Are you going to answer this question with the word that means no in your language?" then he cannot answer truthfully and so he cannot answer

Originally posted by jaden101
ja and da are not the only possible answers...if you ask the truth god "Are you going to answer this question with the word that means no in your language?" then he cannot answer truthfully and so he cannot answer That would be additional information we need before solving.

Originally posted by Bardock42
That would be additional information we need before solving.

its actually part of one of the solution...to which to my knowlege there is 2

http://www.uweb.ucsb.edu/~rabern/SSHardPuzzle.pdf

Originally posted by jaden101
its actually part of one of the solution...to which to my knowlege there is 2

http://www.uweb.ucsb.edu/~rabern/SSHardPuzzle.pdf It's only a solution if that is what happens if ask the truth god "Are you going to answer this question with the word that means no in your language?", if in that case the truth God would answer randomly you would have no information. So, that needs to be included in the question.

I hate questions that refer to other questions because all they are is a way of escaping the spirit of the three question formula (and I don't mean because it creates a fourth question, because that is only semi-true, but really because it escapes the point of the issue. It's the sort of answer that just makes the originator change the puzzle).

Originally posted by Ushgarak
I hate questions that refer to other questions because all they are is a way of escaping the spirit of the three question formula (and I don't mean because it creates a fourth question, because that is only semi-true, but really because it escapes the point of the issue. It's the sort of answer that just makes the originator change the puzzle). What do you mean?

I'm referring to the given solutions provided above, which involve asking a question that refers to another question (that you know the answer to) which sidesteps the point of the issue.

Originally posted by Ushgarak
I'm referring to the given solutions provided above, which involve asking a question that refers to another question (that you know the answer to) which sidesteps the point of the issue. Is there a way to solve it without either knowing the answer or asking something paradoxical?

By the parameters of the puzzle, yes.

This is because, as mentioned, if you ask any god "If I asked you would you say 'ja'?" automatically gets you a truthful answer (assuming the Gods know the answer, that is). This is because the true god would answer the question about the queastion truthfully, saying he would say 'ja' or 'da', therefore meaning if you asked him the actual question he would say 'ja' or'da' respectively. If the question is asked of the false God, he would switch his response around (saying 'ja' where the true god say 'da' and vice versa), but then he is lying about what his lie would be, so if you asked him the question above his response is still actually the truthful answer. And as the random God impersonates either true or false, whatever he says to that question would give you the correct answer to the subsidiary question as well, so long as you add a "in your current mental state" rider onto your question.

Not only are they giving the truthful answers, but without even knowing which of 'ja' or 'da' means 'yes' and 'no', we can even discern the truth of the answer by asking such a self-referential question (this is why you specifically ask 'would you say 'ja'?' instead of 'would you say 'yes'?'.). No matter which God you ask, if the God replied 'ja' the answer to the subsidiary question is yes, and if he says 'da' the answer is no, even though we still don't know what ja and da mean.

So, to summarise, ask any God "In your current mental state, if I asked you would you say 'ja'?" gets you the correct answer to the , so long as the God can answer it. Now you have a truthful answer it's only a short hop to unravelling the whole puzzle.

It is this 'bouncing a question off of a question' technique that basically shortcuts the entire riddle, because it turns all three Gods into True Gods, which I doubt was intended.

So now you can force a truthful yes/no answer out of any God it's easy. You just ask, say, the first God if he is random (phrasing the question as above). if he says 'ja' then he is, if he says 'da' he is not. And so on; you;ll easily solve it in three questions.

Some of the above may look complex but the logic involved is actually extremely straightforward and those who specialise in this sort of area would solve it in a minute or so. It really was not intended and destroys the idea of it being the 'hardest puzzle'. You are MEANT to ask a series of questions that tive you meaningful information even with all the ignorance inherent to the scenario, not abuse the asking of questions to force all three Gods to tell you the truth.

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So to answer your question... yes, it is possible, easily, it's just abusive.

Is it possible to answer it without being abusive? if, say, we put in a rule saying you are not allowed to ask them questions about questions? Yes... but it's very fiddly and frankly not much fun unless you are into logic and maths and so on.

I prefer something like the Monty Hall paradox.

Guess the Philosopher

See if you can guess the philosopher from the description by his lover below:

"I felt uplifted and flattered that this remarkable man should carry me up with him into worlds of thought that I had not dreamt of. And if only he had been just different in his person, I should probably have been entirely carried off my feet and have flown with him through worlds of thought and sense. But, to my shame, however much I was thrilled with the beauty and transcendence of his thoughts, I could hardly bear the lack of physical attraction, the lack of charm and gentleness and sympathy."

Emerson

Originally posted by Fire
I could have figured that out myself

It seens to be a very confusing question to me.

Originally posted by Storm
Guess the Philosopher

See if you can guess the philosopher from the description by his lover below:

"I felt uplifted and flattered that this remarkable man should carry me up with him into worlds of thought that I had not dreamt of. And if only he had been just different in his person, I should probably have been entirely carried off my feet and have flown with him through worlds of thought and sense. But, to my shame, however much I was thrilled with the beauty and transcendence of his thoughts, I could hardly bear the lack of physical attraction, the lack of charm and gentleness and sympathy."

Could you perhaps solve the God "ja" and "da" question for us?

Originally posted by Bardock42
That's badly stated. That could be anywhere. You'd have to at least say that there's one window on each wall.

The answer you are looking for is white.


I heard the riddle a bit different though.

"A hunter leaves his cabin and walks ten miles South and ten miles East, there he encounters a bear and shots it. Then he walks ten miles North back home. What color is the bear?

Where would the windows be then, in the floor?
I thought it was obvious

His point was that the windows might all have been on the south wall of any old house. Easier to say all the walls faced south.

Originally posted by Storm
The Hardest Logic Puzzle Ever

Three gods A, B, and C are called, in some 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.

Clarifications:It could be that some god gets asked more than one question (and hence that some god is not asked any question at all).
What the second question is, and to which god it is put, may depend on the answer to the first question. (And of course similarly for the third question.)
Whether Random speaks truly or not should be thought of as depending on the flip of a coin hidden in his brain: if the coin comes down heads, he speaks truly; if tails, falsely.
Random will answer 'da' or 'ja' when asked any yes-no question.
Boolos states that the "first move is to find a god that you can be certain is not Random, and hence is either True or False". There are many different questions that will achieve this result. One strategy is to use complicated logical connectives in your questions (either biconditionals or some equivalent construction).

Boolos' question was:
Does 'da' mean yes if and only if you are True if and only if B is Random?Equivalently:Are an odd number of the following statements true: you are False, 'da' means yes, B is Random?It was observed by Roberts (2001) -- and independently by Rabern and Rabern (2008) -- that the puzzle's solution can be simplified by using certain counterfactuals. The key to this solution is that, for any yes/no question Q, asking either True or False the question
If I asked you Q, would you say 'ja'? results in the answer 'ja' if the truthful answer to Q is yes, and the answer 'da' if the truthful answer to Q is no (Rabern and Rabern (2008) call this result the embedded question lemma). The reason it works can be seen by looking at the eight possible cases.Assume that 'ja' means yes and 'da' means no. (i) True is asked and responds with 'ja'. Since he is telling the truth the truthful answer to Q is 'ja', which means yes.

(ii) True is asked and responds with 'da'. Since he is telling the truth the truthful answer to Q is 'da', which means no.

(iii) False is asked and responds with 'ja'. Since he is lying it follows that if you asked him Q he would instead answer 'da'. He would be lying, so the truthful answer to Q is 'ja', which means yes.

(iv) False is asked and responds with 'da'. Since he is lying it follows that if you asked him Q he would in fact answer 'ja'. He would be lying, so the truthful answer to Q is 'da', which means no.
Assume 'ja' means no and 'da' means yes. (v) True is asked and responds with 'ja'. Since he is telling the truth the truthful answer to Q is 'da', which means yes.

(vi) True is asked and responds with 'da'. Since he is telling the truth the truthful answer to Q is 'ja', which means no.

(vii) False is asked and responds with 'ja'. Since he is lying it follows that if you asked him Q he would in fact answer 'ja'. He would be lying, so the truthful answer to Q is 'da', which means yes.

(viii) False is asked and responds with 'da'. Since he is lying it follows that if you asked him Q he would instead answer 'da'. He would be lying, so the truthful answer to Q is 'ja', which means no.


Using this fact, one may proceed as follows.
Ask god B, "If I asked you 'Is A Random?', would you say 'ja'?". If B answers 'ja', then either B is Random (and is answering randomly), or B is not Random and the answer indicates that A is indeed Random. Either way, C is not Random. If B answers 'da', then either B is Random (and is answering randomly), or B is not Random and the answer indicates that A is not Random. Either way, A is not Random.Go to the god who was identified as not being Random by the previous question (either A or C), and ask him: "If I asked you 'Are you True?', would you say 'ja'?". Since he is not Random, an answer of 'ja' indicates that he is True and an answer of 'da' indicates that he is False. Ask the same god the question: "If I asked you 'Is B Random?', would you say 'ja'?". If the answer is 'ja' then B is Random; if the answer is 'da' then the god you have not yet spoken to is Random. The remaining god can be identified by elimination.

The bear doesn't necessarily have to be white.

How many chucks could a woodchuck chuck if a woodchuck could chuck wood?

Originally posted by The MISTER
How many chucks could a woodchuck chuck if a woodchuck could chuck wood?

None. Because a woodchuck chucks wood but does not chuck chucks.