
#1
Apr106, 03:34 PM

P: 26

A person enters a room with 5 doors. One of the doors will lead him to safety and the other 4 will lead him to hell where he will die. In the middle of the room, there are 5 stones lined up in a single file, numbered 1 to 5. These stones will either lie or tell the truth, but the stones have to tell the truth if the stone before it lies and vice versa. For example, if stone 1 lies, stone 2 has to tell the truth. The person does not know anything else about the stones. Also, he cannot ask a direct question to find out if a stone is lying or not. For example, he cannot go up to stone 1 and ask if 1 + 1 is equal to 2. How does he lead himself to safety?




#2
Apr106, 04:21 PM

P: 927

What kind of question can he ask, if not a direct one? You mean one to which he doesn't already know the answer? I've never heard of asking an indirect question.




#3
Apr106, 04:27 PM

PF Gold
P: 745

Any type of question:
Ask stone 1: "is door #1 the door to safety?" Ask stone 2: "Would stone #3 saw that door 1 goes to safety?"(if its answer matches #1, it's true" ask stone 3 or 4(whichever is the truth): "what doorleads to safety?" 



#4
Apr106, 04:29 PM

PF Gold
P: 7,367

4 doors to hell riddle
To solve this, just set up a grid with the numbers of the stones on one axis and the numbers of the doors on the other. Ask each stone if the door with the corresponding number will lead to safety and put a Y or N in the grid. The deviation from a strict YNYNYN pattern is the correct door, and it does not matter whether the stone in queation is a liar or is truthful.




#5
Apr106, 05:00 PM

P: 26

Actually the answer is the person should ignore the stones and merely exit the room with the door he used to get to the room.




#7
Apr206, 07:53 AM

P: 398





#8
Apr206, 11:21 AM

P: 26





#10
Apr206, 01:08 PM

P: 198

Ask stone number 1: "If, after asking you this question, I were to ask number 2 if door number 1 is the right door, what would he tell me?" Assumably the stones know the system because they have to know whether they should lie or tell the truth. So the question should generate a "Yes." for every door that is not the right door, and a "No" for the door that is the right door, as there will be one lie told regardless of whether the patern is LTLTL or TLTLT. By going through asking this question for every stone he can find the right door. Or he could just chill in the room, I mean, if he has a 4/5 chance of going to hell, then sitting in a room with 5 stones isn't such a bad fate. ~Lyuokdea 



#11
Apr206, 04:19 PM

PF Gold
P: 745

Ask stone 1: "would stone #2 give me the same answers as you?"
Depending on if it's yes or no, you ask the 4 other stones about 4 of the doors, and if they all end up meaning that the doors don't lead to safety, go out the remaining door 



#12
Apr306, 11:51 AM

P: 657

Ask Stone #1: If I asked stone #3 if it were a liar or a truth telling stone, what would it say?
If stone 1 answers "truth teller", then ask stone 1, 3, or 5 which door is the correct exit. If stone 1 answers "liar" then ask 2 or 4 which door is the correct exit. Actually, in retrospect, that's a great question to ask in liar/truth teller problems "If I asked you later whether you were a liar, what would you say?" A liar, who, when asked, would REALLY reply "no" would *have* to lie about what he would say, thus telling you flat out that he would later say he was a liar! And conversely, a truth teller would tell you that he was a truth teller. Bam! But back to the problem in question. I have to admit this is rather openended, making this riddle very easy. You don't need 5 stones at all, as evidenced in my particular solution. Actually, for that matter, it doesn't say how many questions should be asked, or even that questions SHOULD be asked. It just asks "How does he lead himself to safety?" Clearly, the way to lead himself to safety is to NOT walk through one of the wrong doors. Whether or not he actually walks through the CORRECT door isn't necessarily relevant to the problem, it's just implied. As is the whole "what question(s) should he ask?" A better problem might be had by stipulating: 1) He can only ask each stone one question 2) Each question must be yes/no It's still possible, but now you need all 5 stones for the sake of the rule mechanics (although you don't need all 5 questions), and you need 4/5 questions. DaveE 



#13
Apr306, 12:53 PM

Sci Advisor
HW Helper
P: 2,538

You ask the first rock, would the second rock answer yes if I asked whether one of the first two doors was the door out? Since one of the first two rocks must be a liar (by the t/f alternation rule). I know that if the answer is no, then the door out is one of the last three, otherwise, it's one of the first two. Clearly it's possible to proceed with a binary search from there. 



#14
Apr406, 09:40 AM

P: 657

DaveE 



#15
Apr406, 01:25 PM

P: 1,545





#16
Apr406, 02:10 PM

Sci Advisor
HW Helper
P: 2,538

If the stones are individually randomly truth tellers or liars, rather than the alternating pattern that is given in the original question, then you'd need an extra question. 



#17
Apr406, 02:11 PM

P: 657

Maybe we can make the problem require 5 rocks if we stipulate: 1) Must distinguish by the end which rock is which 2) Rocks can only answer with red or blue, one is "true" one is "false", we don't know which is which initially 3) Can only ask each rock 1 question Those stipulations seem to force you to use all 5 questions, or, at least I think they do. DaveE 



#18
Apr406, 02:24 PM

Sci Advisor
HW Helper
P: 2,538




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