A hard liar/truthteller type puzzle - Page 9

bravos1 · #81 06-01-2007, 11:10 PM

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 Ok, I'm fairly certain the solution is along the lines of what Luckay was saying. You have to line up everyone on the island and keep asking them about the next person until the pattern emerges. This may require using all 99 (or maybe 100) questions to go fully down the line. I don't know the full pattern though. I know some things, like if 50 people in a row say "knight" the last person targetted has to be a knight. Then you take your knight and use your remaining 50 questions to go back to #1 and ask what he is. Then if you find out #1 is a spy, you burn a question on number #2, but if you find out #1 is a knight, you already know what #2 is cause you asked #1, so each remaining question will reveal 1 spy no matter what. The question is how to find the pattern in the 100 line questions. I suspect it involes the ratio of spy to knight answers. Dunno if I'm gonna finish figuring this out, but I'm pretty sure this is well onto the right track for anyone who wants to finish.

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your gonna get 50 answers of "knight" in a row by chance like never ever!

AlexM · #82 06-01-2007, 11:37 PM

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 Ok, I'm fairly certain the solution is along the lines of what Luckay was saying. You have to line up everyone on the island and keep asking them about the next person until the pattern emerges. This may require using all 99 (or maybe 100) questions to go fully down the line. I don't know the full pattern though. I know some things, like if 50 people in a row say "knight" the last person targetted has to be a knight. Then you take your knight and use your remaining 50 questions to go back to #1 and ask what he is. Then if you find out #1 is a spy, you burn a question on number #2, but if you find out #1 is a knight, you already know what #2 is cause you asked #1, so each remaining question will reveal 1 spy no matter what. The question is how to find the pattern in the 100 line questions. I suspect it involes the ratio of spy to knight answers. Dunno if I'm gonna finish figuring this out, but I'm pretty sure this is well onto the right track for anyone who wants to finish.

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your gonna get 50 answers of "knight" in a row by chance like never ever!

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Doesn't matter. You have to account for every possibility.

bravos1 · #83 06-02-2007, 12:06 AM

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 Ok, I'm fairly certain the solution is along the lines of what Luckay was saying. You have to line up everyone on the island and keep asking them about the next person until the pattern emerges. This may require using all 99 (or maybe 100) questions to go fully down the line. I don't know the full pattern though. I know some things, like if 50 people in a row say "knight" the last person targetted has to be a knight. Then you take your knight and use your remaining 50 questions to go back to #1 and ask what he is. Then if you find out #1 is a spy, you burn a question on number #2, but if you find out #1 is a knight, you already know what #2 is cause you asked #1, so each remaining question will reveal 1 spy no matter what. The question is how to find the pattern in the 100 line questions. I suspect it involes the ratio of spy to knight answers. Dunno if I'm gonna finish figuring this out, but I'm pretty sure this is well onto the right track for anyone who wants to finish.

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your gonna get 50 answers of "knight" in a row by chance like never ever!

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Doesn't matter. You have to account for every possibility.

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The thing is that you'll never come to a conclusion about who is who that way. You'll get a bunch of random answers and won't know if it is a knight telling the truth, a spy lying, or a spy telling the truth.

bravos1 · #84 06-02-2007, 12:16 AM

I know how we can figure out if one random person is a knight or a spy, but if he turns out to be a spy, I run into problems solving the rest.

LuckayLuck · #85 06-02-2007, 12:19 AM

let's work backwards

the last person to be cleared is going to be cleared by a knight saying whether they're a knight or a spy

'holla

Nicholasp27 · #86 06-02-2007, 12:48 AM

u're on the right track...u've figured it out for case 1: person a is a knight...let's do it mathematically, though

it takes n people to get 50 "knight" responses
you then have 150-n questions left
you know the identities of n-50+1 people (n-50 said 'spy' so they are spies and 1 is person a as knight)

so, do u have enough questions left to ask the knight for all the unknown peoples' identities?

u do if:
150-n>=n-50+1
199>=2n

well, n<=99, thus 2n<=198 which is <199

so case 1, person a is a knight, is solved

now do a similiar method for case 2: person a is spy...

Nicholasp27 · #87 06-02-2007, 01:14 AM

ok, i can prove that it is impossible

Nicholasp27 · #88 06-02-2007, 01:22 AM

1) there are only two ways to tell someone's identity: catch them lying or get 50 others to agree to their identity
2) spies can choose to ALWAYS tell the truth
3) due to 2), you cannot formulate a solution that revolves around catching a person lying
4) thus, the only possible solution would involve getting 50 people to agree on someone's identity

counterexample for 4) that proves it cannot be done:

a) ask 50 people about person a and they all say spy
you know know that person is a spy, but are down to 100 questions...all u know about the 50 people is that at least 2 are knights, but that's it

b) repeat a with a 2nd person, with same results; now down to 50 questions and only know 2 identities

c) repeat a with 3rd person, using up the rest of your questions, and even if that person is a knight, doesn't matter, as questions are used up

in fact, even if b is knight, u still have only 50 questions left to ask him/her about 98 people

so 4) does not work

so we have now shown that the 2 ways in 1) do not work

so the only way that there is a solution is if you can prove 1) wrong; that there is another method other than catching someone in a lie or getting 50 people to agree to someone's identity

Nicholasp27 · #89 06-02-2007, 01:24 AM

btw, not that it matters but, if 49 people say someone is a knight, they must be a knight, as even if those 49 were all lying spies, that person being a spy would make there be 50 spies, which is illegal

so only takes 49 agreeing someone is a knight to make them a knight

if 49 say someone is a spy, then that person could be a spy or a knight, so need 50 to say someone is a spy

AlexM · #90 06-02-2007, 02:00 AM

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1) there are only two ways to tell someone's identity: catch them lying or get 50 others to agree to their identity

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False. I already showed one other way.

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4) thus, the only possible solution would involve getting 50 people to agree on someone's identity

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False again. The line strategy is another option.

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so the only way that there is a solution is if you can prove 1) wrong; that there is another method other than catching someone in a lie or getting 50 people to agree to someone's identity

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And I already showed how this might be possible in this thread...