# Difficult Riddle!

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### #1 Iraq11

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Posted 27 October 2006 - 05:50 PM

A Muslim M enters a room with 5 doors. One of the doors will lead him to his brothers and sisters in Islam and the other 4 will lead him to enemies of Islam.

In the middle of the room, there are 5 people lined up in a single line, numbered 1 to 5. These people are either hypocrites (liers) or truthful (trustworthy), but a person have to tell the truth if the person before it lies and vice versa. For example, if person 1 is a lier, person 2 is truthful.

The Muslim M does not know anything else about the 5 persons. Also, he cannot ask a direct question to find out if a stone is lying or not. For example, he cannot go up to person 1 and ask if 1 + 1 is equal to 2.

The Muslim M can ask only up to one question per person and M cannot go backwards in the questionings. For example, if M asks person 4, he cannot ask person 3, 2, or 1.

How does M lead himself to safety (with his brothers and sisters)?

### #2 BelinQuest

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Posted 28 October 2006 - 06:14 AM

Does he know how many are liers and how many are truthful?

### #3 Iraq11

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Posted 29 October 2006 - 04:00 PM

Does he know how many are liers and how many are truthful?

What he knows is :
- Either: 3 are liers and 2 are truthful
- or: 2 are liers and 3 are truthful

### #4 BelinQuest

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Posted 29 October 2006 - 04:25 PM

What he knows is :
- Either: 3 are liers and 2 are truthful
- or: 2 are liers and 3 are truthful

I think I know the answer, would you like me to say or is it better to wait and see if others guess?

### #5 Iraq11

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Posted 30 October 2006 - 09:31 AM

I think I know the answer, would you like me to say or is it better to wait and see if others guess?

I think it's better that you wait a bit to see if other members try to get the answer...

### #6 aminata

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Posted 31 October 2006 - 02:10 PM

Stand in the first position and be truthful

I really dont know what the answer is. I wait for some else to answer

### #7 freedslave

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Posted 03 November 2006 - 01:25 PM

What he knows is :
- Either: 3 are liers and 2 are truthful
- or: 2 are liers and 3 are truthful

ok i thought i knew the answer, but i'm not so sure now...

hmmm....

Edited by freedslave, 03 November 2006 - 01:49 PM.

### #8 freedslave

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Posted 03 November 2006 - 01:51 PM

bro Iraq11...can this be solved by logic, or is there another way?

### #9 storm

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Posted 03 November 2006 - 07:55 PM

i thought i knew this, but with the choice of 2 doors and 2 people but i can't figure it out with this one.

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Posted 03 November 2006 - 10:06 PM

What would the other person answer if I asked: "Are you a liar?"

If the first answers: No then that means the first person is truthful.
If the first answers: Yes then that means the first person is liar.

Then you can ask the next people which door is the safe one...

### #11 Iraq11

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Posted 04 November 2006 - 10:51 PM

bro Iraq11...can this be solved by logic, or is there another way?

It can be solved by logic and intelligence, brother. There is no "trick" behind it.

What would the other person answer if I asked: "Are you a liar?"

If the first answers: No then that means the first person is truthful.
If the first answers: Yes then that means the first person is liar.

Then you can ask the next people which door is the safe one...

Although it is not the solution I know, this seems to be a good start, LibertÃ©. Could you please detail your answer, and remember that you can ask at most 4 questions!

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Posted 04 November 2006 - 11:07 PM

Well in with my method I will either know that the first person is a liar or a truthful person. So if he is a liar I just have to ask the next one along which door is safe, and if he i truthful I ask the person after next which door is safe.

Isn't that it?

Edited by LibertÃ©, 04 November 2006 - 11:08 PM.

### #13 Iraq11

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Posted 05 November 2006 - 01:11 AM

Well in with my method I will either know that the first person is a liar or a truthful person. So if he is a liar I just have to ask the next one along which door is safe, and if he i truthful I ask the person after next which door is safe.

Isn't that it?

But the five persons can only say "Yes" or "No" (maybe I forgot to mention it in the riddle's description, sorry). So if person1 is a liar then you ask person2 (a truthful in this case) "which door is safe", what will be his answer: 'Yes' or 'No'? Same applies if person1 is truthful...
An answer with 'Yes' or 'No' is not compatible with a question beginning with 'which'.

Nice try LibertÃ©, but it doesn't solve the riddle!

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Posted 05 November 2006 - 03:04 AM

But the five persons can only say "Yes" or "No" (maybe I forgot to mention it in the riddle's description, sorry). So if person1 is a liar then you ask person2 (a truthful in this case) "which door is safe", what will be his answer: 'Yes' or 'No'? Same applies if person1 is truthful...
An answer with 'Yes' or 'No' is not compatible with a question beginning with 'which'.

Nice try LibertÃ©, but it doesn't solve the riddle!

I don't think you made it a condition that the questions had to be answered with a Yes or No, but I should have guessed!

So...

Since we now know which person is truthful or a liar (by establishing which of the 2 the first person was).

We can ask the second person (P2) if door 1 (D1) is the one we want.
If the first person is truthful, then this person must be a liar so if he says YES then we know it isn't. If he says NO then we know it is and the problem is solved.
If the first person is a liar, then this person must be truthful so if he says NO then we know it isn't. If he says YES then we know it is and the problem is solved.

We can do the same to the remaining three people, each time either finding the correct door or eliminating one. So by the last person we have either found the door, or elimated 4 of them.

Problem solved?

Edited by LibertÃ©, 05 November 2006 - 03:05 AM.

### #15 llogical

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Posted 05 November 2006 - 09:32 AM

Salaams
the order can either be
t,f,t,f
or
f,t,f,t
either the lies will be insynch or they won't be in synch
ex. people may say:
door 1, door,3, door1, door 4
so obviously door 1 is it.

IF they are in synch like
door1,door2,door1,door2
then
then just ask the last person if door 3 is it.
if the person answers yes then he is lieing bcaz it has to be either
door1 or door 2.
If the person says no, then he is not lieing thus the
person before him must be lieng...
so if the person before him said door2, the answer will be door 1
?

Edited by llogical, 05 November 2006 - 09:33 AM.

### #16 Iraq11

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Posted 05 November 2006 - 11:50 AM

Salaams
the order can either be
t,f,t,f
or
f,t,f,t
either the lies will be insynch or they won't be in synch
ex. people may say:
door 1, door,3, door1, door 4
so obviously door 1 is it.

IF they are in synch like
door1,door2,door1,door2
then
then just ask the last person if door 3 is it.
if the person answers yes then he is lieing bcaz it has to be either
door1 or door 2.
If the person says no, then he is not lieing thus the
person before him must be lieng...
so if the person before him said door2, the answer will be door 1
?

Thank you llogical for your logical answer. But, as I said to LibertÃ©, the 5 persons can only say "Yes" or "No". Can you please modify your answer so that it takes this condition into consideration?

I don't think you made it a condition that the questions had to be answered with a Yes or No, but I should have guessed!

So...

Since we now know which person is truthful or a liar (by establishing which of the 2 the first person was).

We can ask the second person (P2) if door 1 (D1) is the one we want.
If the first person is truthful, then this person must be a liar so if he says YES then we know it isn't. If he says NO then we know it is and the problem is solved.
If the first person is a liar, then this person must be truthful so if he says NO then we know it isn't. If he says YES then we know it is and the problem is solved.

We can do the same to the remaining three people, each time either finding the correct door or eliminating one. So by the last person we have either found the door, or elimated 4 of them.

Problem solved?

You are very close to the solution, LibertÃ©. However, you didn't solve the problem, you know why?
Let's count how many questions you need to ask (in a worst case scenario) using your method:

Since we now know which person is truthful or a liar (by establishing which of the 2 the first person was).

This was one.

We can ask the second person (P2) if door 1 (D1) is the one we want.

That was question number two.

If the first person is truthful, then this person must be a liar so if he says YES then we know it isn't. If he says NO then we know it is and the problem is solved.
If the first person is a liar, then this person must be truthful so if he says NO then we know it isn't. If he says YES then we know it is and the problem is solved.

Since the two cases are symetrical, let's suppose p1 is truthful and therefore p2 is liar.
Remember, LibertÃ©, that you have asked 2 questions and therefore you have at most 2 other remaining questions.

We can do the same to the remaining three people, each time either finding the correct door or eliminating one. So by the last person we have either found the door, or elimated 4 of them.

You have only 2 remaining questions:
Question nÂ°3: you ask p3 (truthful, using my supposition) if d2 leads to Islam. If he says "Yes" you win, else you go to next step.
Question nÂ°4: you ask p4 (liar) if d3 leads to Islam. If he answers "No" you win. If he says "Yes", you will know for sure that either d4 or d5 lead to Islam, but there is no "next step" because you have consumed your 4 questions...
So which one, d4 or d5? You can't know...

Problem solved?

Not yet!!

### #17 freedslave

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Posted 05 November 2006 - 01:56 PM

Wow this is becoming complicated...
Brother Iraq11, just to clarify...if there are 5 persons how come we only get to ask 4 questions?

### #18 hkrespect

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Posted 05 November 2006 - 03:00 PM

Wow this is becoming complicated...
Brother Iraq11, just to clarify...if there are 5 persons how come we only get to ask 4 questions?

The Muslim M can ask only up to one question per person

### #19 llogical

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Posted 05 November 2006 - 03:28 PM

Salaams

Thank you llogical for your logical answer. But, as I said to LibertÃ©, the 5 persons can only say "Yes" or "No". Can you please modify your answer so that it takes this condition into consideration?

coolbeans
first off, I'm assuming that we are not allowed to actually check the doors? bcaz that would make it too easy.
Now b4 I try to put my answer in boolean format, there are totall of 5 doors including the
one that M enters from?
Because If so then we have totall of 4 doors to choose from
and the format can only be
TFTF or FTFT
But if there are 6 doors then it has to be
tftft or ftftf
lemme know which condition applies b4 I go further?
Peace

### #20 Haqqul_Yaqeen

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Posted 05 November 2006 - 04:27 PM

Looking at LibertÃ©'s question "Are you a liar?" how would you know that the person is telling the truth if he answers NO? I understand that if he answers YES, then he's definitely a liar, because he could be lying about the fact that he's a liar....But if he answers NO, then can't he be lying?

I'm confused...