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Logic Problem Help
Mrninjaman
Registered User new member
Registered User new member
Ok I have a Extra credit prob for my math class, Its essentially just a logic problem that I swear i've seen before but i can't figure it out so I figured I'd reach out to the friendly interweb. So anyways here goes
Essentially it goes like this, You have 3 people who just left a room, 1 always lies (say bob), 1 always tells the truth (jim) and 1 will do either (and edgar). You get to ask two questions to find out if the room they just left is for staff or students. Both questions will go to the same person but you have know way of knowing which person you are asking the questions of.
Like i said I swear i've seen this question before i just can't for the life of me remember it. My prof gave us a hint, she said in the 1st question we need to verify that the person we are talking to isn't edgar, the person who will lie or tell the truth. and then with the second question get our answer.
So any idea's or input would be awesome, and if anyone wants to see the actual text for the problem let me know.
Tia
Essentially it goes like this, You have 3 people who just left a room, 1 always lies (say bob), 1 always tells the truth (jim) and 1 will do either (and edgar). You get to ask two questions to find out if the room they just left is for staff or students. Both questions will go to the same person but you have know way of knowing which person you are asking the questions of.
Like i said I swear i've seen this question before i just can't for the life of me remember it. My prof gave us a hint, she said in the 1st question we need to verify that the person we are talking to isn't edgar, the person who will lie or tell the truth. and then with the second question get our answer.
So any idea's or input would be awesome, and if anyone wants to see the actual text for the problem let me know.
Tia
Mrninjaman on
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Once you have just the Truth teller and the Liar, you simply ask one of them (either one) what the other one will tell you if you ask whether the room is for staff or for students.
Let's pretend the room is for staff:
The liar will tell you that the truth teller will tell you it is for students (which is a lie)
The truth teller would tell you that the liar will tell you it is for students (which is the truth)
Therefore the room must be for staff.
still trying to work out the first bit with the 'either' guy though
So The whole process..........
1) Ask the group:
Are you the person that can both lie and tell the truth.
The truth teller will say no
The liar will say yes
and the Either person can say one or the other
Therefore you know for sure that the person that gives an opposite response to the other two is either the truth teller or the liar.
2) (Let's pretend the truthful answer is Staff)
Then you ask the person who is by themself , "If I asked you if the room was for staff, would you say yes or no?"
The liar (who knows he would say no) says he would say yes
The Truth teller says he would say yes
So if the person says yes, it is for staff. If he says no, it is for students.
That is, if we assume the room is the staff room then the Truth says yes, the Lie says no, and Edgar says either, but we don't care about that because it will match one of the other guys. So if we eliminate the odd response we have someone who is either lieing or someone who is telling the truth and the other person is obviously the flip flopper.
Or something. It seems like I've seen this problem as boolean logic before.
Well that's what I said when I wrote:
"1) Ask the group:
Are you the person that can both lie and tell the truth.
The truth teller will say no
The liar will say yes
and the Either person can say one or the other
Therefore you know for sure that the person that gives an opposite response to the other two is either the truth teller or the liar."
However as Wazilla has pointed out, the OP wrote "Both questions will go to the same person" which, as Wazilla pointed out, makes it a lot more difficult.
I don't see how you can post the two questions to the same person considering that one of them can say either lie or truth.
I'd ask Tia to clarify if you do in fact have to say both questions to just one person or not.
1. The second question can vary based on the answer to the first.
2. That Edgar's responses are not purely random, and that instead, he has a 50% chance of answering a question truthfully, and a 50% chance of lying. For example, if I asked Edgar what 2+2 equaled, he would have a 50% chance of saying 4, and a 50% chance of saying anything else, not an equal chance of saying anything.
Solution:
Are an odd number of the following statements true for you personally?
X: You're Jim.
Y: You're Edgar.
Z: You're Edgar and, on this question, you're lying.
For Bob (Always tells the truth) none of the statements are true. Because zero is not an odd number, he will tell the truth and answer "No."
For Jim (Always lies) only statement X is true. Because one is an odd number, he will lie and thus answer "No."
For an Edgar who randomly tells the truth (on this question) only statement Y is true. Because one is an odd number, he will tell the truth and answer "Yes."
For an Edgar who is lying (on this question) statements Y and Z are true. Because two is an even number, he will lie and answer "Yes."
Thus after question one we know if we are talking to Edgar or not.
If we are NOT talking to Edgar (First question gave a response of "No.")
If only Jim and Bob were playing this game, and I asked the one of the two who you are not, whether the room was for staff or students, what would he say?
If the room is actually for staff:
Bob would be honest and say Jim would lie and answer "Students."
Jim would lie and say Bob would lie and answer "Students."
If the room is actually for students:
Bob would be honest and say that Jim would lie and answer "Staff."
Jim would lie and say Bob would lie and answer "Staff."
Either way, you know the room is the opposite of the answer to the second question.
Conversely, if we ARE talking to Edgar (First question gave a response of "Yes.")
Are an odd number of the following statements true for you personally?
X: 2+2=4
Y: The room is for staff.
Z: You're Edgar and, on this question, you're lying.
If the room is for staff:
If Edgar randomly tells the truth (on this question) then statements X and Y are true, so he will answer "No."
If he randomly lies, then statements X, Y, and Z are true, so he will answer "No."
If the room is for students:
If he randomly tells the truth, then statement X is true, so he will say "Yes."
If he randomly lies, then statements X and Z are true, so he will answer "Yes."
Either way, an answer of "No." on the second question means the room is for staff and an answer of "Yes." means the room is for students.
This is a similar problem to Smullyan's The Hardest Logic Puzzle Ever which is where some of you might remember it from.
Nice work!
By George I think he's got it.
Hey Tia, Well I based my theory on the premise that you can ask the whole group the same first question.
Actually if it is the case that you can only ask 1 person both questions, I believe that Varcayn's process is the correct one.
Well, if he sometimes lies, then he might lie about the even/odd replies, right? I mean, there's no way that you can "force" him to answer one way or the other.
Obviously if he's being truthful he has to say yes because "I an Edgar" is the only one that applies.
However if he's lying, since "I am Edgar" and "I am Edgar and, on this question, I'm Lying" are both true and the truth is that 2 out of 3 statements is true (an even number), he has to lie and says Yes.
He doesn't have the option of lying about that because I don't ask him. I asked if an odd number of statements were true or not, that is all he can lie about.
If he was some sort of super-rational entity capable of anticipating my questions, and could randomly lie about whatever he wanted, then the entire problem changes. However, we assume that the liar can only lie about the question that is directly posed to him. Meaning that for a question with only two possible responses, the only option the liar has is the option that an honest person would not pick.