a logic puzzle

You're right. Two questions only permits 2 bits of information, insufficient to select among 6 possibiliites.

I heard this puzzle a year ago,at an information theory seminar, it's possible I misremembered... (I'm never wrong, but occasionally mistaken)

ok, expand the problem: figure out the correct form of the problem!

Like, you may ask 3 questions, one to each person.

Or, you must get a single bit of information, - should I turn left or right to reach the airport? - and allowed 2 questions. No need for identification.

Both of these seem challenging.

No, that would create difficulties, these puzzles are always yes/no

-- Mark T.

Good point! I hadn't thought of that. I think we must assume both knight and knave would give a random answer.

-- Mark

The problem as originally stated did not mention "I don't know" as a legitimate response, but maybe it was ill posed, it may be logically necessary.

I can't recall the solution, but it was the usual form of these knight/knave puzzles; "if I asked you how he would answer blah blah"

-- Mark

It wasn't raining?

I thought you were wrong that one time when you thought for a moment you were wrong, when indeed you were actually right.

Gordon

So don't ask both questions of the same person. (Though it's still not possible if there are only two possible responses.)

It wasn't raining.

I think this is unsolvable even with an arbitrary number of questions (even if you remove the yes/no restriction). As the number of questions increases, you can only increase your level of confidence in identifying the inhabitants but you can never be sure. The reason is that it is always *possible* that even after n questions, the answers of the randomizer exactly match those of one of the other inhabitant making these two indistinguishable.

David

Well I was wrong, it is certainly possible with 4 yes/no questions.

David

This is not applicable, since the puzzle stipulates, "yes/no question".

Hope This Helps! Rich

BEGONE, googloid trash! >:{

You can't use the same bit twice and count it as different information.

Which is completely determined by bit #1.

Alan

SPOILER: : : : : : : : : : SPOILER: : : : : : : : : : SPOILER: : : : : : : : : :

It wasn't raining, merely windy. ;-)

("Then why did they have the umbrella?" I hear you cry. Probably because without it there wouldn't have been a puzzle. Maybe it was for shade from that merciless California sunshine, or maybe it was a field test of a new umbrella frame design. Who could know?) ;-)

Cheers! Rich

Rich Grise wrote: ) On Wed, 25 Mar 2009 05:17:18 -0700, Derek Holt wrote: )> On 24 Mar, 19:36, Willem wrote: )>> Mark-T wrote: )>>

)>> ) they answer any question yes or no, 50-50. )> )> OK, if we allow the "I don't know/cannot answer" response, ) ) BZZZZT!! ) ) Disallowed in the problem spec.

BZZZZT!!

Nope. The line you quoted is only for the randomizer.

The line for the knights and knaves are: "They will answer any yes/no question" (And the knight always tells the truth and the knave always lies)

So a knight or knave is perfectly allowed to answer "I don't know" or "I can't answer that" or something similar.

However, thinking on this, the knave is _not_ allowed to answer "I don't know" to a yes/no question that he does not know the answer to. But he can't answer 'yes' or 'no' either, because that's not a lie (a lie is an intentional mistruth)

So, any yes/no question that you know the three people do not know the answer to will do.

Knight answers: "I don't know." Knave answers: "I know but I'm not telling." Randomizer answers 'yes' or 'no'.

SaSW, Willem

Michael Koch wrote: ) Hi, ) )> It's impossible. There are 6 possible combinations and you only get 4 )> "bits" of info. ) ) Don't we have 3 bits of information? ) The answer to the first question is bit number 1. ) Then you can decide whom you ask the next question. This decision can ) depend on the first answer. You can ask the same guy again, or you can ) ask one of the other guys. This information is bit number 2. ) The answer to the second question is bit number 3.

Bit number 2 depends on bit number 1, so it's not actually a separate bit. Or, to put it differently: The only things you count as bits are the bits of information you receive.

SaSW, Willem

Mark-T wrote: ) On Mar 24 ,Derek Holt wrote: )> Suppose you ask one of them "If I asked the randomizer 'Is 2+2=4?" )> what would she say?" Then the knight can only answer "I don't know". )> But it is difficult to predict how the knave would respond. ) ) Good point! I hadn't thought of that. ) I think we must assume both knight and knave ) would give a random answer.

Why must we assume that ? The rules do not state that the knight or the knave are limited to answering 'yes' or 'no'. It only sais that they will answer any yes/no question.

(And the randomizer will answer yes or no to *any* question)

SaSW, Willem

Because they successfully controlled the umbrella?

Funny how many people assume it was raining when in fact it was a sun umbrella!

Sun umbrella... That California sun can be brutal. Or as Mark Twain said "The coldest winter I ever spent was summer in San Francisco"!

It's possible with 3 yes/no questions.

Call a person consistent if he isn't the randomizer.

First question, ask A "Is it true that either B a knight, C is a knave, or both?"

Answer is yes: A is the randomizer: B & C are both consistent. A is the knight: C is the knave (consistent). A is the knave: C is the knight (conistent).

Answer is no: A is the randomizer: B & C are both consistent. A is the knight: B is the knave (consistent). A is the knave: B is the knight (consistent).

Second question, ask the consistent person "Do you exist?". Third question, ask the consistent person "Is A the randomizer?".