How Can You Solve the 4 Doors to Hell Riddle?

[Numbnut247]

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?

 

[daveb]

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.

 

[JamesU]

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?"

 

[turbo]

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.

 

[Numbnut247]

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.

 

[JamesU]

what if he was a demon from hell?

 

[Mattara]

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.

That is the wrong answer. It isn't states in the question that he entered via a door. So as a result, that is the wrong answer.

 

[Numbnut247]

That is the wrong answer. It isn't states in the question that he entered via a door. So as a result, that is the wrong answer.

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?

I wrote a person ENTERS a room, meaning that he used something that would cut through a wall to get into the room. If I'm not mistaken, that is what a door is. I did not say the person is in a room, or the person sees 5 doors. I specifically said that the person ENTERED. If he did not enter the room using a door, how could he have entered the room? It is called an indirect assumption.

 

[DaveC426913]

A person is dropped into a room with 5 doors...

 

[Lyuokdea]

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.[/color]

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

 

[JamesU]

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[/color]

 

[davee123]

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 open-ended, 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

 

[NateTG]

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.

Actually, you'd only need 3 questions, not 5, and, as a consequence, only 3 stones. For example:
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.

 

[davee123]

Actually, you'd only need 3 questions, not 5, and, as a consequence, only 3 stones. For example:
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.

Ahh, true! So we need what? Between 17-32 doors and 5 stones?

DaveE

 

[RandallB]

Ahh, true! So we need what? Between 17-32 doors and 5 stones?

Max 16 Doors w/ 5 stones

 

[NateTG]

Max 16 Doors w/ 5 stones

There are 5 yes or no answers - so 2^5=32 max doors. (You won't know which stones tell the truth or lie, but you don't care.)

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.

 

[davee123]

Max 16 Doors w/ 5 stones

I did an example with 18, and was able to draw a search tree that only took 5 questions-- hence I assume that 17-32 require 5 questions (makes sense since 2^5 = 32).

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

 

[NateTG]

I did an example with 18, and was able to draw a search tree that only took 5 questions-- hence I assume that 17-32 require 5 questions (makes sense since 2^5 = 32).

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.

To make (2) add an extra question you must require that we know whether red or blue means true. Otherwise you can use questions like 'if red means true and ... or if blue means true and.. ".

 

[RandallB]

Those stipulations seem to force you to use all 5 questions, or, at least I think they do.

5 questions would require 6 rocks.

 

[NateTG]

5 questions would require 6 rocks.

If you can ask each rock one question, and there are 5 rocks, how do you come up with anything other than 5 questions?

 

[Mk]

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?

So he uses five doors to enter the room, meaning all five doors are used to get back out, which means he must have came from hell. Or does the door he came through have four doors behind it?

If I were faced with the question using my head to figure out how to stay out of hell, I would not be asking 5 rocks for help. Do you take me for some sort of idiot?

Maybe I should force the five stones to open each door so: worst-case scenario, four rocks go to hell.

I would definitely take the stones with me which ever door I opened. Five all-knowing rocks—the great advances in society from these rocks and I. We would be written of in the textbooks!

 

[RandallB]

So he uses five doors to enter the room,

The OP didn’t say he entered though any door, just that he entered the room.
Assume he came though an opening (no door), guarded from his exiting till the opening is bricked up. The point is to solve the riddle.

If you can ask each rock one question, and there are 5 rocks, how do you come up with anything other than 5 questions?

You cannot ask a question useful to picking a door without asking about the next rock that has yet to answer because you don’t know if it’s telling the truth or not.
Unless you have a question that would reveal which one's are true without losing the chance to gain info about the doors at the same time.

 

[NateTG]

You cannot ask a question useful to picking a door without asking about the next rock that has yet to answer because you don’t know if it’s telling the truth or not.
Unless you have a question that would reveal which one's are true without losing the chance to gain info about the doors at the same time.

If the rocks are alternating truth teller/liar, then you can, for example, simply ask:
Would the (previous/next) rock say that door a, b or c is the good exit?

(As in my post above.)
Since one of the two rocks is a liar, and other is a truth teller, the net result is a lie. You can't tell which of the two rocks was the liar, but you don't care.

 

[RandallB]

If the rocks are alternating truth teller/liar, then you can, for example, simply ask:
Would the (previous/next) rock say that door a, b or c is the good exit?

(As in my post above.)
Since one of the two rocks is a liar, and other is a truth teller, the net result is a lie. You can't tell which of the two rocks was the liar, but you don't care.

Excactly that's why you need a next (6th) rock. A previous rock that's already givin its one answer wouldn't apply.

 

[RandallB]

If the rocks are alternating truth teller/liar, then you can, for example, simply ask:
Would the (previous/next) rock say that door a, b or c is the good exit?

(As in my post above.)
Since one of the two rocks is a liar, and other is a truth teller, the net result is a lie. You can't tell which of the two rocks was the liar, but you don't care.

Excactly that's why you need a next (6th) rock to get to five questions. A previous rock that's already givin its one answer wouldn't apply.

 

[davee123]

Excactly that's why you need a next (6th) rock to get to five questions. A previous rock that's already givin its one answer wouldn't apply.

Why not? Simply adjust your last question to: "What would the previous rock have said if I had instead asked ..."

But regardless, according to the stipulations given to require 5 questions and 5 rocks, you still need to learn which rocks are truth tellers and which are liars. Plus, you don't even need to involve another rock in your final question:

1) Are you a truth telling rock? (if red, then red = yes,
if blue, then blue = yes)
2) If I asked you later whether you were a truth telling
rock, what would you say? (A lying rock would say "no",
a truth telling rock says yes)
3) Is the correct door one of A, B, C?
   Y => 4) Is the correct door one of A or B?
        Y => 5) Is the correct door A?
             Y => choose door A
            N => choose door B
        N => choose door C
   N => 4) Is the correct door D?
        Y => choose door D
        N => choose door E

Obviously adjust the Y/N according to the answer received in #2.

DaveE

 

[NateTG]

Ok, let's try it this way:

There are 5 rocks, and we know they're alternating truth tellers and liars, and we can ask each rock one questio, and there are 32 doors:

Ask rock 1:
Would rock 2 tell me that the favorable exit is among doors 1 through 16?

Ask rock 2:
Would rock 3 tell me that the favorable exit is among doors 1 through 8 , or among doors 17 through 24?

Ask rock 3:
Would rock 4 tell me that the favorable exit is among doors 1 through 4, 9 through 12, 17 through 20, or 25 through 28?

Ask rock 4:
Would rock 5 tell me that the favorable exit is one of the doors in 1,2,5,6,9,10,13,14,17,18,21,22,25,26,29,30?

Ask rock 5:
If I had asked rock 4, "does the favorable exit have an even number" would rock7. 4 have said yes?

Start with 1.
If rock 1 answered yes add 16
If rock 2 answered yes add 8
If rock 3 answered yes add 4
If rock 4 answered yes add 2
If rock 5 answered yes add 1
The result is the number of the door that is the favorable exit.

 

[RandallB]

Why not? Simply adjust your last question to: "What would the previous rock have said if I had instead asked ..."

But regardless, according to the stipulations given to require 5 questions and 5 rocks, you still need to learn which rocks are truth tellers and which are liars. Plus, you don't even need to involve another rock in your final question:

1) Are you a truth telling rock? (if red, then red = yes,
if blue, then blue = yes)
2) If I asked you later whether you were a truth telling
rock, what would you say? (A lying rock would say "no",
a truth telling rock says yes)
3) Is the correct door one of A, B, C?
   Y => 4) Is the correct door one of A or B?
        Y => 5) Is the correct door A?
             Y => choose door A
            N => choose door B
        N => choose door C
   N => 4) Is the correct door D?
        Y => choose door D
        N => choose door E

Obviously adjust the Y/N according to the answer received in #2.

DaveE

Now you've used up two questions without getting any information about the doors. With only 3 questions remaining how are you going to decide between more than 16 doors?

 

[RandallB]

Ok, let's try it this way:
Ask rock 1: ... ... ...
...The result is the number of the door that is the favorable exit.

Rock 5's answer = I don't know if #4 would be T or F to a different question, I only know that I will give the alternate T / F based rock 4's being T / F with the answer already given. If you ask about the next rock that I know will alternate from me I would know.
As it is I cannot give a Y or N reply to this question. I shall remain blank but your question still counts.

 

[davee123]

Now you've used up two questions without getting any information about the doors. With only 3 questions remaining how are you going to decide between more than 16 doors?

Sorry, I should have been more specific. In the above, I was not enacting the stipulation that there were more than 5 doors. It was an effort to change the problem as little as possible, while requiring a more singlular solution. One could either make the stipulations above, OR stipulate that there were instead 17-32 doors.

Rock 5's answer = I don't know if #4 would be T or F to a different question, I only know that I will give the alternate T / F based rock 4's being T / F with the answer already given. If you ask about the next rock that I know will alternate from me I would know.
As it is I cannot give a Y or N reply to this question. I shall remain blank but your question still counts.

The rocks are all-knowing rocks. The only questions they can't answer would have to be paradoxical in nature. Hence, you can't ask things like "Will I find the right door?" because you could then proceed to prove the rock wrong. However, you could instantly invent some new language in your head, where "foo" meant 1 and "blip" meant 2, and ask the rock whether foo+foo=blip, and it would respond accordingly. What you could NOT do would be to ask if it was GOING to be true, since you could then change the values of foo and blip.

If you *really* want to get overly persnickity, you can restate the exact situation as a complete hypothetical to each rock every time within your question, and still get the correct answer.

DaveE