# 4 doors to hell riddle

1. Apr 1, 2006

### 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?

2. Apr 1, 2006

### 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.

3. Apr 1, 2006

### 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?"

4. Apr 1, 2006

### 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.

5. Apr 1, 2006

### 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.

6. Apr 1, 2006

### JamesU

what if he was a demon from hell?

7. Apr 2, 2006

### Mattara

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.

8. Apr 2, 2006

### Numbnut247

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.

Last edited: Apr 2, 2006
9. Apr 2, 2006

### DaveC426913

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

10. Apr 2, 2006

### 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.

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. Apr 2, 2006

### 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

12. Apr 3, 2006

### 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

13. Apr 3, 2006

### NateTG

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.

14. Apr 4, 2006

### davee123

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

DaveE

15. Apr 4, 2006

### RandallB

Max 16 Doors w/ 5 stones

16. Apr 4, 2006

### NateTG

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.

17. Apr 4, 2006

### davee123

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

18. Apr 4, 2006

### NateTG

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.. ".

19. Apr 4, 2006

### RandallB

5 questions would require 6 rocks.

20. Apr 4, 2006

### NateTG

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