Traversing Rooms (Difficult!)

Why count steps if you can simply count seconds ?

How many seconds? ;)
1 minute vs 2 minutes? - you'd need 2 "amounts of time" according to my script ;), a longer and a shorter one.
I think counting seconds would be too error-prone and 1 minute as "basis unit" would be too short in my opinion...

And you wouldn't have to count steps at all. You'd just "measure time" in room laps.

BTW, when I said
>n+1 will always take longer to complete than n
I meant that one person's n+1 laps will always take longer to complete than the other person's n...

@ e_tadeu
Just trying to clarify, especially as English is not my native tongue:
>The moment that [x] touches the doorknob of a room, [y] cannot be in that room any more.  
By this you mean that whenever someone  touches the doorknob of a door leading to another room, the other person cannot be in that other room, correct?

There's probably some stunningly simple solution... ;)

@Infinity08
Sorry, I've submitted without refreshing first. I"ll try to answer whan I"m at home, I"m leaving work now...

>> which suggests that exceptional intelligence may not be a guarantee of coming up with compatible strategies.
My thoughts exactly :)
There must be some simpler solution we're overlooking, which suggests that none of us have the same level of intelligence of the two persons in the riddle heh

@mlmcc
Beat me to it!

>They did not communicate with each other during the whole process
Would the following scenario invalidate the above statement?:

If the doorknobs are just decoration (not turnunig) and you can simply push the doors open as jkmyoung said, then of course it would be easy, as there is no rule explicitly prohibiting both individuals being in the same room at the same time, except for the doorknob rulrs.
So the doorknobs have to be functional ones you can (and have to) turn.
When the woman goes into room C, she closes the door but keeps the doorknob turned for a while. The man enters room A, closes the door without yet releasing his doorknob and keeps an eye on the first doorknob. He knows that a few seconds after this ("the woman's") doorknob is released, she will have entered room A and after a while, he will release his doorknob, and swiftly move into room C. And so on, you get the idea...
This doesn't necessarily have to be considered "communicating", does it? It's more like a strategic delay of action ;)

>The man enters room A
Should be "The man enters room B" :/

"The moment that the woman touches the doorknob of a room, the man cannot be in that room any more"

>holding the door knob of the room just left will prevent the next person occupying it.

Do you understand it this way? I don't know...  The *moment she touches* the doorknob of the room she has just left, that room is empty.


BTW, thanks for the Sigma pointer!

Sorry maramom.  But it looks like we would be freed.

A little more logic.

The woman in room B knows she cannot get up until the man does.  Thinking logically she reasons I cannot get up since I don't know if he has gotten up.  Also if I do get up then I must sit after he does.  Therefore since I can't know when he sits I won't know when I can sit.  She also knows the man is intelligent and will realize that though he can get up he won't know if it is safe to enter room B since I might still be here.  Therefore since he will think logically and he won't enter room B but will stay put.  Therefore she will stay put.

Logic fromthe man's point.  I can get up but as soon as I leave this room I had better not go into the room she is in.  Therefore I have to wait until shes gets into room C before I go into room B.  Since I cannot be sure she has left room B I can't safely enter.  I also know she is intelligent and will think logically.  She will realize that she cannot get up because she doesn't know when I get up.  Since he knows she cannot safely get up and will reach a similar conclusion, he decides to stay put.

Since they were able to do the process 10 times it must be simple and not rely on timing or knowledge of when the other person has done something.  The easy solution is to not move.  I see no rules that require them to move only rules that inhibit their movement in some way.

mlmcc

@mlmcc

>> 5-  The woman has to get up from the floor after the man.  
>>10-  The woman may only sit down after the man.  

The woman must determine whether the man has stood or not, as she would be required to get up if he does so. Doing nothing seems to be a logical solution, but the wording of #10 makes me believe that the man must rise in order that the woman may sit down after the man. It is implied that they were both seated at the same time in the beginning of the test.

More on the above:
After reviewing the post again it appears you may be right, mlmcc, as that #10 action, perhaps, isn't required.  Only if she chooses to sit, it must be after the man. If she's already seated, it would be a new action of sitting down that must follow the man's seating. It looks to me like you've got the best solution!

Are we assuming rule 1
1-  They both have 1 hour to traverse the three rooms and return to the room where they started, always walking in the direction A - B - C - A.
is optional then?

No.  That rule simply states they can move around for one hour and if they move room to room the order in which they mustt go.  I don't see anywhere that states they must move.  I also don't see anywhere that states the doors are lettered to indicate where the door goes.

mlmcc

@TName
>By this you mean that whenever someone  touches the doorknob of a door leading to another room, the other person cannot be in that other room, correct?

I think it is, otherwise it would be a very dumb problem, huh? :)

@Masqueraid

>Do you have the answer already or are you looking too? - only asking because the text you've posted contains all the spelling mistakes from the Webpage of English translation of Sigma.

I do not have the answer, and yes, I just copied it because I'm *very* curious to know if there is a simple straight answer! :)

>Are we assuming rule 1 is optional then?

They must follow *all* instructions, so, staying at the room is not a valid option.

The only answer I could found would be something like this, but it is not a very simple one, and, as stated before, there can be *other* clever strategies that would be incompatible. Here it is:

I thought about this solution: they count the time using their own heartbeats. Because they can have different heartbeat frequencies, they must work with ranges, assuming that the minimum heartbeat is 60 beats per minute, and the maximum (at rest) is 180 bpm. Using this range, they both compute a "script" to follow (like the one described by Adam314), with a timing that would minimize the probability of breaking the instructions.

They would begin waiting a little between the actions, and the waitings would become longer as the sum of "errors" get larger (because of the range of the beatings).

These are the extreme situations: the man is at 60 bpm and the woman is at 180 bpm, or the inverse, the man is at 180 bpm and the woman is at 60 bpm. So, the other could be counting the time 3 times faster or 3 times slower than the other.

At first, the man would get up right away. The woman, knowing this, would wait just a little, let's say, 10 beats, and would get up and move directly from B to C. The man, knowing this, would wait a little more, let's say, more 40 beats (to be very sure) and move from A to B.

They would be waiting increasingly more every time, and the total amount of beats would be 58 * 60 = 3480 beats, and at the end they could use the other syncronization point (the lights), so that the man sits when the lights turn on again, and the woman sits some 40 beats after that. This leaves just 6 synchronization points that they must compute using the heartbeats. It would be something like 580 beats at average for each synch point (each one would be waiting the double of this). They could arrange such that at first they would wait very little, and then the waiting would become longer.

What do you think?

I thought about hearbeats at some point and looked up lowest / highest, and when I learned that there are individuals with a pulse of below 30, I lost all hope :)

Just a thought: they don't know anything about the physical condition or the agility of the other, but they know one thing: that the other one is "exceptionally intelligent". Assuming each considers him/herself also "exceptionally intelligent", they can only rely on one similar "speed" - they will probably solve logical problems and calculations in a similar amount of time. They might decide to solve certain problems before every move. Calculate what?

TBH I think using heart rate is making this needlessly complex.  We have to assume that the two people do not meet so there would be no way of knowing that one had a resting heat rate of 50 and the other 100.  I would imagine that both rates would rise given the situation although one may cope with this better than the other and be less affected.

I would suggest simply counting aloud would be more reliable

As each change of room happens the woman can position herself at the door waiting to enter the next room and the man could place himself in the centre of the room (which at 25m square would mean he has at least 12meters to travel before reaching the door) before waiting to proceed.

If they used the first light signal to synchronise the start of counting this allows:

- Sufficient delay to ensure that the woman stands up last
- The woman to move safely from B -> C as she knows it is empty
- The man can safely assume that after five minutes of counting the woman will have moved to C and he can move from A -> B

[I have varied my previous solution here where the woman could continue to count off to (say) 30 minutes and move to A knowing that the man will have entered B.  This would place the woman at the door to B ready for the one minute warning and the man at the door to C]

When the one minute warning light comes on both start counting off seconds.  The man must immediately move to room C.
The woman will know that the man must move immediately the lights come on  so allows a few seconds delay and returns to room B
The man knows that when the light comes on he must move to room C which is empty and the woman is at the door to B waiting for him to close the door to room C behind him.  He also knows he must allow her to enter B and close the door before he enters A so again delays a few seconds (he will already be slower than her - assuming they are equally able to move - as he has one extra room to cover) and then enters A.

I still think the solution I proposed before about the man sitting as soon as he is back into room A and then making his way to the centre allows for any last minute confusions about when the woman should sit. She can otherwise comfortably count off fifty seconds from the last signal and sit which should complete the manouver.

>>6-  The man and woman are not permitted to communicate between each other in any way, or obtain from others any information allowing them to figure out where the other one is.

I was assuming that neither the man or woman knew which room the other one was in at the starting point...therefore, neither would know that C was empty to begin with.

Was this assumption incorrect?

e_tadeu
Are you sure that all steps must be taken? Is there more info on this puzzle elsewhere? As seen throughout this thread, several intelligent answers were given, but all different, which leads me to believe the only way that two highly intelligent beings could perform this task, and think exactly alike, is to outsmart the alien by using the rules as stated. According to the rules, as stated, their were few "requirements". I believe that mlmcc's reasoning is the ONLY way this could have been done each time without flaw.

This puzzle was taken from the Sigma Society qualifying exam.  As such I suspect we won't get to know the answer unless you take the test

http://www.sigmasociety.com/sigma_teste/sigma_teste_eng.asp

mlmcc

mlmcc, that link only seems to work as a Google cache for me.

Thanks, mlmcc, for the link.
I checked the German translation which states:
1- Beide müssen innerhalb von einer Stunde sämtliche Räume durchgangen haben und wieder in ihrem Raum sein, in dem sie die Tour gestartet haben, die Gangrichtung muss grundsätzlich A-B-C-A sein.

müssen: must

maramom

A (partial) translation to English might be nice. Partial as in more than just "must".
From what I understand from the German text it does say they must have traversed all 3 rooms in an hour.

@NicoLaan
translation:
1- Both must travel through all rooms within an hour and end up within the original room where they began the tour. The direction must be (basically) A-B-C-C.
I was merely emphasizing "must", because the English translation didn't clearly state the traversing "must" occur, and semantics can play a role in puzzle solving. mlmcc and I took a similar approach at reviewing the rules. The German translation does not allow for our method of interpretating some of the steps as optional.

It seems that according to the Sigma Society Test instructions(http://www.sigmasociety.com/sigma_teste/sigma_teste_eng.asp),  there may be more than one acceptable answer to this question, and even some "functional" answers that may be partially accepted.

correct A-B-C-C from above post to:
A-B-C-A

Just in case I'm not the only one who can't get maramom's link to work this is the Google cache:
http://tinyurl.com/f6n3s

>> It seems that according to the Sigma Society Test instructions there may be more than one acceptable answer to this question, and even some "functional" answers that may be partially accepted.

That kind of makes the question invalid, as both persons from the riddle won't necessarily come up with the same solution either ... It has to be by pure chance then that they succeeded the first time, and then they probably applied the same techniques the 9 subsequent times, and apparently with an equal amount of luck they could pull it off 9 more times.

What's the Sigma Society anyway ? Another of those recruitment companies like Infosys ? That would explain it :)

What about this:
When the woman enters room C, she closes the door but keeps the doorknob pressed/turned. After entering room B, the man could go to the door B/C and simply (but gently :) push it open without touching the doorknob. Now everything would be very easy.

3-  The moment that the woman touches the doorknob of a room, the man cannot be in that room any more.  
Holding the doorknob would mean the man can't enter B
If there are latches on the doors we don't know about them

Heh, she could keep the door from locking with a piece of tape heh ... but I don't think that's the intended solution :)

"The moment that the woman touches the doorknob of a room, the man cannot be in that room any more"
>Holding the doorknob would mean the man can't enter B

It seems we can't agree on what this sentence is really supposed to mean.
As I stated before, for me "the moment" simply means "the moment". Either that or "from that moment on" (regardless if the doorknob is still being held or not), which wouldn't make sense, as it would keep the man from *ever* entering the room (as she will *have* to touch the doorknob to close the door).
Other opinions on this?

Infinity08, should I understand from your comment that you agree with MASQUERAID on the interpretation of rule 3 (and 4)? (Regardless if it's the intended solution or not).
I'd really like to clarify this (the linguistical/logical aspect). Thanks ;)

It sounds like this would violate rule 6:
6-  The man and woman are not permitted to communicate between each other in any way, or obtain from others any information allowing them to figure out where the other one is.

As holding the door knob would be a type of communication...

I'm using "the moment that..." as a single point in time so that from the point that the doorknob is touched the rule is applied.
Does this help : http://encarta.msn.com/thesaurus_561566001/at_that_moment.html ??

>> Infinity08, should I understand from your comment that you agree with MASQUERAID on the interpretation of rule 3 (and 4)?
Yes, it does say "The moment", and not "Starting from the moment" :

    "The moment that the woman touches the doorknob of a room, the man cannot be in that room any more."

Btw, if we really want to be pedantic, it also says "not any more" in the end, which implies that the man has already been in the room. What if he hasn't been there already, does the rule still count then ? Ie. is this scenario valid ?

1) the woman goes to C, closes the door, but HOLDS the doorknob in her hand
2) the man goes to B after waiting a short while, and closes the door between A and B
3) the woman opens the door again (still holding the doorknob), so they can see each other (carefull not to give each other a sign)
4) once the man has seen her, she closes the door, and goes to room A, closes that door, but again HOLDS the doorknob in her hand
5) the man just waits a while after he has seen the woman close the door, and then goes to room C, closing the door between B and C
6) the woman re-opens the door (still holding the doorknob), so they can see each other (carefull not to give each other a sign)
7) once the man has seen her, she closes the door and returns to her original room B
8) the man waits a while more after he has seen the woman close the door, and then goes to his original room B, closing the door

but I guess that still breaks rule 6 :)

>I'm using "the moment that..." as a single point in time so that from the point that the doorknob is touched the rule is applied.

From the point... until when? If you apply the rule for a duration (as in "From the moment the woman touchest the doorknob...") then we disagree, and I don't see why you post a thesaurus-link explaining "at that moment" as: "just then, then, at that point, at that time, at that point in time, at that juncture, at that moment in time". I know very well what "at that moment" means, but I still don't know why it should be interpreted in this case as the beginning of a period of time.
If you consider "the moment that..." as a single point in time, then the rule is applied at that point, and not from that point on.
Just to make sure there's no misunderstanding:

The woman touches the doorknob at some point in time.
1.The man is not allowed to be in the adjacent room at that very moment.  //This is how I understand the rule
2.Additionally, the man is not allowed to enter the room while she holds the knob.  //This is how I thought that you understand the rule
3.Additionally to 1 and 2, the man may not enter the room after the woman has touched the doorknob.  //This would paralize any movement, I guess.

>Does this help : http://encarta.msn.com/thesaurus_561566001/at_that_moment.html ??      
That doesn't help, as it just confirms (in my opinion) what I said: At the moment she (standing in room C) touches the doorknob of the door B/C, the man is not allowed to be in room B. He isn't there. Room B is empty, as the man is still in room A. He will enter room B *while* she is still holding the doorknob.
As I said, I fail to see an element of duration in any of the synonyms in that link.

>Does this help : http://encarta.msn.com/thesaurus_561566001/at_that_moment.html ??    
That's why I asked.

Just to make my intepretation clear I'm using "FROM the moment" so until she lets go I believe the man is prohibited (by Rule 3) from being in the room on the other side of the door.  This lasts until the state changes i.e. she isn't touching the door knob.  Once she has let go the prohibition vanishes.

Agreed there are other ways to interpret this
- Just the instant that contact is made -[TName]
- The instant contact is made and for the next sixty seconds ("the moment")
- From the instant contact is made until contact is broken - [MASQUERAID]
- From the instant contact is made until the end of the test (which would mean Rule 1 becomes impossible)

Assuming the door knob cannot be used to give any form of signal (Rule 6) is there any advantage in either interpretation?

>> Assuming the door knob cannot be used to give any form of signal (Rule 6) is there any advantage in either interpretation?
Probably not, as I found out writing down my last scenario ...

>Assuming the door knob cannot be used to give any form of signal (Rule 6) is there any advantage in either interpretation?

I don't know, there might be one. Allow me to summarize (and digress a bit... :)

Doorknob solution 1:
After entering a room, person X closes the door but keeps the doorknob pressed for a longer period, to make sure person Y sees when the knob is released. Y behaves the same.
The problem is, this delay in releasing the knob could be interpreted as communicating (even if no one does anything he/she wouldn't have to do anyway).

Doorknob solution 2:
After closing the door B/C, the woman (if she notices that the door can be pressed open in the direction B>C when not blocked by the knob mechanism) keeps the doorknob pressed/turned. The man, after passing door A/B, approaches door B/C without even looking at the knob (he knows that - if the door is "suitable" - the woman hasn't released the doorknob. He knows it simply because he knows she is smart), and tries to press the door open. If it doesn't work, he'll choose the next solution on his mental list, knowing that she will have done the same. But let's asume that it does work. Now they're both in room C. The man closes the second door. The woman opens the door C/A, slips into room A, closes the door without touching the doorknob and then she enters room B, where she will wait until after the second light signal. Then she will sit down.
The man will wait in room C for quite a while (even though 30-40 seconds would be enough). Then he will enter room A and sit down.
*This* holding of the knob can't be considered communication, because no one is informed of anything. The man doesn't even have to pay attention to the knob.
The big problem is that this solution (besides being quite unelegant) only works in one of two cases. A certain door has to open in a certain direction when pressed.

But before we reject the solution for this reason, we should realise that it *does* work in one of two cases.
And, if possible, the solution it is very simple and safe. We can't know if it is possible, but the two people will know, because they are there and they can try.

This makes me think that, if there is no solution which is at the same time the most simple, the most secure and 100% feasible under all unspecified circumstances (and I've begun to doubt that) there is not *one* solution we're looking for, but a list of possible solutions in a certain order. Before they were brought to their initial room, the two had the same amount of information that we have. As soom as they were in the rooms, they knew more details then we will know. And they can start choosing from their mental hierarchy of solutions.

If someone comes up with a solution that only works if the walls of the rooms are bright yellow and if that solution is very simple and safe, then we can't simply reject it. The walls might be yellow, and the man and the woman will know it and act accordingly.

We weren't told to describe what they would do if they just knew what they were told and what we know, but "describe the method they used..."

This part of rule 6 :

>> or obtain from others any information allowing them to figure out where the other one is.

kind of restricts ANYTHING that would allow them to know where the other is at any given time. So neither of the proposed solutions involving the doorknob will be any good, since that's exactly the advantage they have in those solutions : they know where the other is because information was left behind (the door not closed/locked).

This is just a badly formulated riddle. In an actual situation, they would NOT be able to fulfill the task, unless be sheer luck, not by reasoning.

I agree that the task is likely a matter of luck. There is one form of communication that does not appear to be restricted, however, and perhaps the great minds here can play with this:

There are four lamps in each room. If one or more were unscrewed it could create a binary code.. not to show where the other is, but to signal a countdown of some kind.

This allowance depends on the strictness of the translation:
6-  *The man and woman are not permitted to communicate between each other in any way*, or obtain from others any information allowing them to figure out where the other one is.

It depends if this means they can't communicate their location, or just have absolutely no communication. Any thoughts?

I'd say if they can't communicate in any way, that there can be no communication at all ... So, any kind of communication, including the lamps, would be out of the question.

To solve the puzzle, they have to come up with the same strategy, and the same numbers (number of steps, seconds, ...). That seems highly unlikely to me.

>There are four lamps in each room
Two, I think. Not that it would make much difference, I guess...

>>To solve the puzzle, they have to come up with the same strategy, and the same numbers (number of steps, seconds, ...). That seems highly unlikely to me.

I agree, (notice my scepticism from early on)  
http://www.experts-exchange.com/Miscellaneous/Puzzles_Riddles/Q_21966718.html#17400413

I just found it peculiar the way the lamps were described in detail:
.. on each door there are two lamps (one on each side of the door)

and since some clarity is lost in the entire translation,  ... *The man and woman are not permitted to communicate between each other in any way*, or obtain from others any information allowing them to figure out where the other one is. ...may infer the communication of whereabouts is forbidden, not necessarilly all communication.

I don't know exaclty how they'd use it even if it were allowed.

>>Two, I think. Not that it would make much difference, I guess...
Two per door

>Two per door

"on each door there are two lamps (one on each side of the door)

As I understand it, "one on each side of the door" means that each of a door's two lamps is in another room.
Do you understand "each side" as left side and right side?

Great, another one of this riddle's clear-cut, non-ambiguous statements... ;)

>>As I understand it, "one on each side of the door" means that each of a door's two lamps is in another room.
Do you understand "each side" as left side and right side?

No I've looked at this as one on each room's side (i.e.  on the B/C door there's a lamp on the B-side and one on the C-side - so two lamps in each room)!!!

In any event I think we're meant to solve this with a solution that relies on both knowing the other is "exceptionally intelligent".  That doesn't mean they are telepathic but that they will be able to predict each other's behaviour given the information they have, rules and common objective.

It's on this basis that I proposed a solution.

Nope :) As I said before, this is a badly formulated riddle.

>>Can anyone find a fault in this reasoning?

Knowing that the other is "exceptionally intelligent" does not help you conclude their whereabouts, only their *likely* whereabouts.

If the man believes that, because the woman has thought the problem through she will realise she has to move into C as quickly as possible to allow him to move, that doesn't in itself guarantee that is has happened only that it is likely to have happened.  The man does not "know" that the woman is in C only that it is likely she is, he could still open the door to B and find her in there and  then both get to stay with the aliens!

But I think we are all agreed that the semantics of the rules makes it difficult to have a "right" answer. As witnessed by the length of this thread!

It would be great to see the accepted answer from the site - if only to pull it to pieces!!

lol

Yet another method to determine the timing....

I think the only solution to them having the same timing is something like "well, i'm exceptionally intelligent, and this is the method I thought of, so the other person, being exceptionally intelligent, must have come up with the same method"

In reality, I don't think two people being exceptionally intelligent guarantees them coming up with the same method.  

>>It would be great to see the accepted answer from the site - if only to pull it to pieces!!
My thought exactly

>>I am wondering, if the rooms are all sealed, solid and opaque with the only access going to the other rooms - How did these people get in there?
Teleported of course!

>>In reality, I don't think two people being exceptionally intelligent guarantees them coming up with the same method.
They would if there's only 1 method.

>>They would if there's only 1 method.
Well, yes, that is true.  

I suspect the doors are marked in some way otherwise they wouldn't know which door to try since going in the wrong door would be an automatic loss.

mlmcc

>marked in some way

Hinges!
Each door is hinged and will only open one way, the barrel of the hinge is visible only from the room that the door opens into.
If you open a door towards you, you first approach the door to reach the doorknob and then step back as you open the door. This would be in conflict with ‘always walking in the direction A - B - C – A’.

The aliens must have provided for a solution and so the hinges must all be arranged to allow travel in ABCA direction, doors opening away from you, so each room has one door that opens inward and one door opening out.
They now know that: The woman is in room B, The man is in room A, Which of the doors lead to rooms A, B and C.

Lamps on, Man stands up quickly as he knows that the woman will wait a little while.
Woman, knowing that the man has stood up quickly, will wait just a couple of seconds and then stand. She will immediately open the door with no hinge barrel visible and walk into room C.
The man, realizing that she has paused only long enough for him to stand will estimate how long it takes her to move to the next room by miming the pacing and open/close door action. After completing his delaying mime he will quickly enter into room B – he enters fast because she will expect him to.
The woman has to wait for two open/close door periods before changing rooms again. One of these periods she has already used by moving to room C, and the next is a mime.
She knows that he will have moved to room B as quickly as he could and so will expect to find room A empty, she opens the door and enters A closing the door behind her….

The times are roughly the open/close/walk times, estimated by miming the action or actually performing it.

Time      Woman            Man
1      B->C            mime
2      mime            A->B
3      C->A            mime
4      mime            B->C
5      A->B            mime
6      mime            C->A
7      mime            sits
8      sits

This is yet another way to handle the timing.  There is no guarantee that both will come up with the same method of timing - as there have been several presented already.

They do both know that these actions (open door and go through it) have to be performed. Any extra counting and delay could obviously be anything but they are both also aware of that. If they could communicate then anything will do -spit on the wall and wait till it reaches the floor, heartbeats, time till their eyes get used to the changed level of illumination, but they know that the other will choose the only method possible. Opening doors is one action that they both know the other will know and have to do - I can't think of another.

I have been wondering about removing the delay altogether, as soon as the 59 minute light comes on they run around as fast as they can trying not to be caught, but I think a crash would be inevitable and to repeat this 10 times would be too unlikely.
   

lol at your last solution !! :)

opening and going thru a door takes a small amount of time.  So if I wait that amount of time, i'm waiting about 1 second... maybe 2 seconds.  If the other person is just a little slow for some reason, i will catch up before.  So to be careful, I decide to wait just an extra 2 seconds, but now if the other person doesn't do this, they will catch up to me.  This method isn't robust, and I don't think it would be even if the two people had decided this was the method they were going to use, as there isn't enough "buffer" time in case the two people move at different speeds.

>method isn't robust
I agree it's not perfect, but if it's that or be experimented on I think I'd risk it.

The run-around catch-up idea came from picturing myself in a room with two doors, knowing that someone may come through one of them at any moment and I must not be in there when they do - the other person would feel the same and that's why they both run.

I suppose there's no clues in the nationalities of the two people? I don't know enough about them, but there may be some taboo about opening doors, or about the man following the woman?

>I agree it's not perfect, but if it's that or be experimented on I think I'd risk it.
Most people would probably try something.... The trick is to devise a method that is both robust (it worked 10 times), and the "obvious" method that should be used, assuming both people are exceptionally intelligent.

While your method may work, as may most of the others - they only work if both people have come up with the same method.  And since I see no reason why this method is any more "obvious" than the others, I don't think we can say it is correct.  Not that I think we can say any of the other methods are correct either.  I'd say this is still unsolved.

I like the series bulb connection idea (reminds me I must get the Christmas tree lights fixed!) but I do think the aliens might interpret the misuse of their wiring as communication ;)

BTW isn't it about time for a fiendish snoyes riddle?

Are these rooms DIRECTLY connected to each other or are there some form of hallways connecting them...?

"The rooms are connected in such a way that each room has two doors, and each door provides access to one of the other two rooms."

It says that each door provides access to one of the other two rooms, not to a hallway... but... If there are hallways, the problem would be much easier, something like:

lights turn on
man gets up;
the woman gets up, runs to: C, corridor between C and A, and stays there
lights turn off
man runs to: B, C
50 and some minutes later... lights turn on again
woman runs to: A, B
man waits 10 "seconds", run to A, sites
woman sits

>> if the rules are that the doors CAN'T be open at the same time, they can effectively use the doors as a way to determine she's left a room.  Meaning he wouldn't be ABLE to open a door if she still had the other door open.
I don't read it that way.  The rules must be followed by the 2 participants.  As I read it there are no constraints on anything but the people.  The woman opens a door.  She can leave it open the move to the other door and open it but that would violate one or more of the rules.  Just as a speed limit sets how fast you can legally drive down a road (the car and driver aren't restrained in anyway) the doors simply can be opened and must be closed.

mlmcc

Is their nationality of any significance?

>>Is their nationality of any significance?
I wondered that myself, whether a knowledge of each other's religion or culture was linked to their "intelligent" thought process. Both languages read from right to left. No connections come to mind, however.

Sorry, got some typo errors:

3. ...W knows that M is smart...

It's a good theory and it uses the additional information which no-one else has done yet

Yes very plausible

But does it breach rule 6-  "The man and woman are not permitted to communicate between each other in any way, or obtain from others any information allowing them to figure out where the other one is. They may not beat the walls or the doors, or try to generate any kind of shock wave. On leaving a room and entering another one, it is required to close the corresponding door. Initially all the doors are closed. Two or more doors may not be open at the same time. "

As this is a form of communication?

>Wwysdom...

Actually, that seems almost perfect...
I was trying to think of a variance whereby the woman would effectively signal herself just by the air moving because the man entered the next room (ie, laying the items at the doorsill so any draft under the door will be noticed)... but technically air movement IS a shock wave...

>> But does it breach rule 6-
Yes :) imo anyway

Besides, what if she doesn't have a scarf? ;)
And the lights might go off after just a second, so they cannot really be used as a reliable additional signal, I think.

I think this would be considered a form of communication... so it wouldn't work.

Also, you don't need the religion or nationality to make it work.  No matter what religion/nationality they were, we could probably assume they had some clothes on.  

Okay, going back and re-reading... It appears that whatever the solution, the two participants could be deaf and still perform it.  So:  no listening on doors...

Still, though, the distinction between communication and information gathering (surveillance) is valid.  I gather from the original post, however, that the solution does not rely at all on anything observable with the five senses.

>>>I am wondering, if the rooms are all sealed, solid and opaque with the only access going to the other rooms - How did these people get in there?
>>Teleported of course!

Although it is stated that there are doors and door knobs, and that the woman or the man cannot be in a room if the other touches the doorknob leading to that room,

but there is no rule saying that they must use the doors in traversing the rooms, or they cannot be in the same room at the same time.

Also, the order of sitting/ standing is stated but it's not stated that they have to stand up at all.

And although both are deaf and mute, the aliens manage to inform them of the instructions
- implying telepathy.

1. Signal lamp lights up, man (M) sitting in room A thinks telepathically to aliens "Please teleport me into room B, please!" Blink! M appears in room B.

2. Woman (W) gets a shock at seeing the man, but calms down in a while. She soon thought of how M got there. W now thinks thinks telepathically to aliens "Please teleport me into room C, please!" ...

3. They continue in this manner until they are in their original rooms. They shift to the center of the rooms and wait for the test to end...

>> 11-  The man is told that the woman is exceptionally intelligent.  
>> 12-  The woman is told that the man is exceptionally intelligent.

One other assumption that I think everybody here made: They are told that the other is exceptionally intelligent, but that may not necessarily be the case.

The part about the lamps is unclear.  However, if it's meant that there are two lamps, "one on each side of the door" in the sense of "one on the front side in Room X, and one on the back side, in room Y", then that means that by looking at the position of the lamps -- to the right or left of the door -- the person can ascertain some understanding of the layout of the rooms -- to wit, whether the rooms are linked in a clock-wise or counter-clock-wise manner, and which of the rooms one is in -- the room with two doors on one side, the first room (depending on if you're counting clock-wise or counter-clock-wise) after that, and then the next room after that one.

Unfortunately, the way the problem is written it's not clear whether or not they actually mean "a lamp on the right and a lamp on the left side of each door".  

Also, it's not written anywhere that the participants know which room is A, which B, and which C.  It's only stated that they must move in that direction, not that they know which door they must initially move through.  So far as i can tell, if they were able to do it right ten times in a row then they were just exceptionally lucky, because there's no possible way for them to ascertain from the information they've each initially, individually been provided which door leads where.

But again, if they know they're supposed to move clock-wise or counter-clock-wise, then:

1) Light flashes, Man immediately stands up, and starts to count to whatever number he thinks it will take him about five minutes to get to.
2) Woman waits a few seconds and then stands up herself;  she immediately moves to the door to room C and walks into it.  She immediately moves to the doorway to Room A and waits there.
4) Man waits a few minutes.  Moves into Room B and positions himself at the doorway to Room C.
5) Woman waits about 10 minutes;  it's not important *exactly* how long, because it will only take a few minutes for the man to move into her old room -- so any amount that allows for him moving into a room as quickly as he feels comfortable with is acceptable.  She moves into Room A and positions herself at the door to Room B (i.e. -- the last room).
6) Man commences to do something that will indicate that he has waited about half an hour.  This is more tricky, because he's not sure if the woman has moved out of the room yet or not.  He must give her time enough for her to feel confident to move into his room, and yet not wait until the next flashing of the light.  Anyhow, he moves into Room C and positions himself at the door to Room A.
7) Woman waits til the light flashes and jogs to the center of Room B.  She counts to ten very slowly -- which should take somewhere between twenty and thirty seconds (most "not extremely intelligent" people even know that, right?) -- to give the man time to sit down.
8) Light flashes -- Man counts to five or ten (however long he thinks the woman will need to get through the door -- just a few seconds, no?) and then sprints to the center of Room A (which is just a couple of meters away anyhow) and immediately sits down.
9) Woman sits down before the minute is up.

I think it's a pretty safe bet that someone who's reasonably intelligent will be able to peg a time span somewhere between 20 seconds and a minute, or between 20 and 40 minutes;  that's all that's required here.  The first few steps could probably be slept through by most people.  It's just step 6 that presents a challenge.

The real problem with this riddle (as has already been discussed), is that there's so many possible (equally intelligent) solutions, and that for each solution there's so many variables, that it's very unlikely that both people picked the same exact solution.

For example in your solution, the time spans you specify : 10 minutes, 30 minutes, count to five, etc. - how are you gonna ensure that both pick the same values (or at least compatible values) ?

I'm beginning more and more to think that my earlier 'they both run' suggestion is the better way.
We have pretty much decided that there is no safe timing method that can be safely decided upon by both parties.
Just imagine yourself in the situation:
You are sitting on the floor in a room waiting for a light to come on. You have been told that the other person must not be in any room that you even touch the door of. Neither must you be in any room that the other person touches the door of.
As soon as the light goes on you are going to want to get out of your room asap in case the other person comes in.
They are doing exactly the same! so you both start at a fairly brisk pace then run (just to keep in front).
I think I sorted out the direction earlier (with the hinges and the fact that the aliens had left a possible solution).
It's only 3 doors you have to get through and just less than 5 meters to run in each room.
I have yet to try a practical experiment but I think it is possible.

>> I think I sorted out the direction earlier (with the hinges and the fact that the aliens had left a possible solution).

If the direction is unknown to them, the hinges won't make any difference at all. How would they know whether to push the door into the next room, or to pull it into their current room?

It could also have bee a sliding door?

>> If the direction is unknown to them, the hinges won't make any difference at all. How would they know whether to push the door into the next room, or to pull it into their current room?

To elaborate, using the hinge idea, for the two doors in a room, one would be pushed to open, and the other pulled, they still would not know which one to pick.

>> Whether you wait 10 minutes  or 5 is irrelevant in the first few steps, and largely irrelevant for the woman as well.
It is very relevant, because if one picks 5 minutes and the other 10 to wait, they're no longer synchronized, and might run into each other.

>> She only needs to wait long enough for her to be sure the man moves from his room to the next
How can she be sure ? She has NO idea when the man will move out of the room. Except that it's gonna be before the final light signal.

>> the only really tricky step is step 6, where the man's basically gotta guess whether or not the woman's out of the next room.
You said it yourself, and still you claim that your solution will work ?

And you didn't take into account the range of other solutions that have been suggested in this thread (and that are equally intelligent). What if they both pick a different tactic ?

>> So really, the only problem i see with the riddle is that there's no way for the people to know which door they should open before they start off on their traversal.
I assume that's part of their knowledge before they start the challenge. The riddle isn't about knowing which direction to turn in, but about synchronizing your actions without knowing what the other one does.

>Hinges/which door

One of my earlier posts in here I described the layout of the rooms.

A supposition was that a solution exists.
If the hinges were arranged in a particular direction then it would give the occupants some clue - I feel a clue is neccessary.
One of the rules states 'always walking in the same direction'. So you use a door that opens away from you - if you open a door towards you then you have to step backwards as it opens after stepping forward to reach the handle.
So my assumption is that all the doors open either clockwise or anti-clockwise - the actual direction doesn't matter.

There is a difference in just one of the rooms - two doors on one side, whereas the other two rooms have doors in two walls.

>proof-thinkers
It looks like the problem has been built up after several successes. Each constraint added after a solution was found. This way, anyone 'passing' this section of the test has found a way that no-one had used before. I think that is why there are so many restrictions on the signalling possibilities - banging on the walls, shock wave, deaf participants, no-one else must tell them - all added after these were used for solutions. So maybe there is no guaranteed solution, they are still looking for one, and when it's found there will be a new rule added.

>> proof-thinkers
It sounds plausible heh :)

>>It is very relevant, because if one picks 5 minutes and the other 10 to wait, they're no longer synchronized, and might run into each other.

No. Not at all.

It goes like this:

A) Man stands up.  Waits a bit for the woman to stand up and walk through the door.  This won't take a lot of time for her to achieve.
B) Woman waits a bit and, confident that the man stood up as quickly as possible after the lights flashed, stands up and *immediately* walks to the door and moves to the next door of the next room.  She waits.

Now you're saying that here, she's in a terribly difficult position. Except that she's not.  She only needs to worry about whether or not the man is in the next room.  Now she knows that the man is aware that they only have an hour, and that the man *must* have waited a bit for her to move out of the last room (otherwise they'd be experiments by now).  So she only needs to wait for the man to walk into the next room.

The man, meanwhile, has waited a bit.  He is aware, however, that the woman knows he can't do anything until she moves out of the room, and that she knows this as well. Thus he knows that upon standing up she will *immediately* move to the next room.  So he only needs to give her a suitable bit of time to do so.  A couple of minutes might be cutting it a bit short -- what if she trips?  She's nervous?  What if the doors aren't as easy to open as they should be?  -- so he paces off the trek to the door a few times, and maybe mimes opening a difficult door a couple of times, and by that point maybe five minutes have passed and he can safely touch the doorknob.   At this point

C) he moves into the next room and to the next door.

Now the woman is standing at her door all this time, aware that the man hasn't walked in on her but *at any moment he will*, because he *must* come through the door she has just exited.  This is the *only* troublesome part of the problem for her:  she cannot wait too long, here, but she can't move too quickly, either.  What does she do?  Same thing the man just did -- pace back and forth a few times, miming the action of opening the door and walking to the next one, maybe four or five times.   Maybe ten.  How about twenty, just to be safe?  But regardless, she's not going to spend half an hour doing so because she knows that the man may well decide to come through that door in preparation for their last minute.  So it doesn't really matter how long she waits, just so long as it's 1) not too long, and 2) not too short.  How much is too short?  Not enough time for the man to get through the door.  Why might he not get through the door?  Because he's still waiting.  Except that she knows what the man knows:  that she got up after a few seconds (and isn't an experiment yet, so everything's o.k) and *immediately* moved to the door.  So now that ten or fifteen minutes have passed -- let's say she paces off the path to the door twenty times, as opposed to the man's few-to-five, and slowly --

D) -- she opens the door and moves into the next room.

Now the man is still waiting, right?  We're at the infamous "Step 6", now.  The woman has moved through her two rooms.  She only needs to open the final door, walk to the center of her room, and sit down.  In other words -- *there is no more question of how long she needs to wait*.  She's only waiting for the flashing of the final light.  So we don't need to worry about her at all.  The man, however -- how long does he need to wait?  Well, he's got two options;  one is to wait for the final flash and then move as quickly as possible -- jog, in other words -- through the next two rooms (only a total of 10 meters or so, which is basically 10 large strides for an average man) to the final room, or he can wait until he is confident that the light is *just about* to flash, and then move through the door.  Basically, if i were the guy i would say "I know that the woman is going to be next to her final door just before the light goes off, and if i want to maximize the chances of sitting down before she does then i'd best get to the next door as well -- but i don't *need* to, because in all likelihood i'll be able to do so even if i *don't* succeed."  So what do i do?  Pace up and down the pathway to the door, but this time *fifty* times.  Maybe count how many seconds it takes, and estimate how many times i'd need to pace off the space to make thirty minutes go by (because remember - they have some 44 minutes remaining, at this point).  Maybe sing "Jambalaya" twenty times, or do some routine task that i do every day and am pretty certain about the time it would take me (pushups, yoga routines, a very light nap, whatever).  

Like i said:  this is really the only tricky part of the problem, because the man needs to basically guess at how long the woman's going to wait before she enters room A.  But he's got a load of data that he can infer from his own situation:  1) that the woman immediately moved into room C, and will move into A as quickly as she feels comfortable, 2) that the woman would feel better -- and he would too -- if he were standing by the door that goes from C to A when that final light flashes, and 3) that she's aware how much that would increase the probability of their survival. So he *knows* that she will move into the next room as soon as she feels comfortable.

And as i've already pointed out, she knows that he's thinking these things as well and consequently she's not going to sit around waiting for that final light to flash.  After five minutes or so have past, barring that the guy's a sea-slug (or even only has the brain of one) it's basically a sure thing that he's not going to be in his room any more.  So while the problem may *seem* like a big gamble and risk at this point, so long as the man errs on the side of a *longer* wait, rather than shorter, there will be no problem.   So he waits a good, long time -- hopefully not until the next light flashes, but even so taking that risk is safer than not -- and then

E) moves to the next room.    If the light just flashed, he *runs* through the next two rooms;  if not, then he just waits a few moments -- however long it would take for someone to open the door to the next room -- and *then* moves into room C, to wait by the next door until the light flashes.  Either way, it's not really a big deal, because both he and the woman know that as soon as that light flashes she will get through that door and into the center of room B as quickly as she finds humanly possible.  

So by this time, if the man is sprinting he just continues his blind rush into the next room, because the time it will take him to move through room B will give the woman plenty of time to move into room B.

If he's standing by the last door, he simply counts to whatever number represents the time it takes to open and close a door (he's had two times to gather that information now, already) and the moves into the next room.

As soon as the man is in room A, he immediately moves to his spot and sits down.

When the woman gets into room B, she simply starts slowly counting to whatever number represents however long it would take to open *two* doors and quickly walk through *two* rooms (again, she's had two or more opportunities to make these observations), and then maybe tacks on a few extra numbers for safety's sake, and then she sits down.

Really, the *only* time there is any risky decision to be made is what i called "step 6" up there, where the man must decide at what point to move into room C.  After reviewing it just now, i think it might be safest for him to wait until the light flashes and then move through the next two rooms.  But he could just as easily choose the original solution i suggested, and do so at his own discretion.  As i've pointed out, the only thing he needs to be sure of is that he's about five minutes away from the *final* flashing light, and he's guaranteed to succeed.

After that -- during the final-flashing-light phase -- the observational evidence and knowledge of their mutual situation provides the two with more than enough information to predict the other's behavior and plan accordingly.

You keep referring to "a bit". How long does "a bit" last ? 5 seconds ? 10 ? 1 minute ? 5 minutes ?

>>And you didn't take into account the range of other solutions that have been suggested in this thread (and that are equally intelligent). What if they both pick a different tactic ?

The choice of any other tactic would be an arbitrary association that doesn't make use of the full range of information that they each share.  

For instance, dividing the time into three or four equal intervals and basing their movement on those would basically *guarantee* that they were scheduling their movements at the same time, and thus actually *increase* their probabilbity of failure.  Moreover, they don't have a time-piece and so they can't exactly measure time accurately.....

Most of the others involved communication of some sort, which the problem explicitly, universally prohibits.

The teleportation solution was, i thought, quite clever and as equally as probable as the solution i offer, but as you pointed out it doesn't really partake in the "spirit" of the problem, which is to provoke thought about how the two people will time their actions.

Also, "two or more doors may not be open at any time" makes any possiblity of staggering the opening and closing of doors impossible.

And as for "riddle isn't about knowing which direction to turn in" -- i actually mis-understood the problem to be about *exactly* that, up until i'd read most of this current thread.  $:-o  Thus i've made that criticism.  While i thought RobinD's "hinges!" rejoinder was also clever, i really don't think it is a clue that serves any reader reliably -- as one poster pointed out, the doors may slide;  also, there are hinges that move either inwards or outwards.  Finally, while the rooms must be traversed in a certain order i don't think there's anything in the problem that prohibits the man or woman from pacing about the rooms while they make their next decision to move.

Basically, what i've posted is just a detailed explanation of the same line of thinking Masqueraid and jkmyoung were following, as well.

"a bit" in this instance is basically however long it takes for someone to walk to a door, open it, go through, and close it.

Kyle - You're solution looks good, but unfortunately it's me in the other room and I have decided to run around as quickly as possible just in case you come in behind me.

(I'm not trying to be fascetious, just showing that you can't guarantee that the two people will come to the same conclusion).

Whether the man or the woman, neither will trust the other completely, no matter how intelligent they both are. And don't forget that they are two different nationalities - (although they might not have been told this). When it comes down to making a decision that could cause the premature end your life I think a form of controlled panic will take over.

See! I can't even get my post in the correct order :7)

It was supposed to be just after infinity's

>> "a bit" in this instance is basically however long it takes for someone to walk to a door, open it, go through, and close it.
And how fast do you do that. And how fast will the other do that ?

>> Most of the others involved communication of some sort, which the problem explicitly, universally prohibits.
I wasn't referring to those, rather to the different ways of timing your moves (pacing the length of the room, counting seconds, making a mathematical calculation, as fast as possible, "a bit", ...).

So essentially what you're saying is that you have decided on a course of action *without taking into any sort of consideration what i will be thinking or doing*.

It seems like an awful big assumption to stake your life on, eh?

You're right:  i'd be screwed.  But so would you.  But frankly, under any circumstances whatsoever we'd probably be screwed, because there's no way to guarantee that we run at the same pace, that you or i don't fumble at one or more doors, that we sit down at the right time or in the right order, or any of it.  So basically you're choosing the least-likely path to success.

When we get carved up as biology experiments, don't blame my attempt at a copascetic solution -- blame yourself.

My solution doesn't rely on either of them "coming to the same conclusion" regarding the behavior or strategies of the other;  it relies upon the presumption that both are going to be mightily concerned with self-preservation and so will try to maximize the probability of success.   For instance, if the woman jumps up immediately that's just stupid.  She knows she needs to wait for the man to get up.  The man knows that she knows this, too.  That little bit of wait introduces a considerable bit of uncertainty into the timing of their next decision, but not so much that a virtually guaranteed success can't be maintained.  I.e. -- they wait a bit, the woman then gets up and immediately moves to room C.  The man *knows* that she's going to do this.  The woman, however, has no idea when the man is going to move -- *but*she*knows*he*must*move*.  Thus, again, the *only* choice she can make is *when* to move .  

Again, the man knows this, because it's also *his* only choice.  And any rational human being, knowing that the other person is basically healthy and this isn't a rigged game, is going to presume that after a "bit" of time the woman whill have stood up and moved to the next room.  So the man waits *ten* "bits" of time, and if you want an explanation of how he estimates it then he walks back and forth from his spot to the door, ten times.  But once again -- the man *knows* the woman might come through that door at any moment, and if he's still there then they're screwed.  So he's got a pressure to get out -- and he's waited a good bit of time -- so he goes on in to the next room.

And the woman *knows* that he's going to do this, for the simple reason that if he doesn't then they will be faced with the exremely unlikely possibility of using that last minute to sprint willy-nilly through the remaining rooms while praying that the other one doesn't stumble, mismanage a doorknob, or sprain an ankle.  And in addition to that, they'll need to get seated in the proper order (remember that if you use that last minute to do a mad sprint, then there's no synchronization for the sit-down).


Basically, y'all are all interpreting this situation like it's some sort of measurement made on a quantum scale.  We're talking about walking to and from and opening/closing doors, sitting down and standing up -- that sorta stuff.  It's not rocket science, and the psychology here is simple.

I had already proposed a 'miming opening the doors' timing solution before. But someone correctly pointed out that while reliable enough, the chances of both parties picking this method was slight.

I've just thought of another timer though...
In the cowboy films they come upon a recently used camp site and identify how long since the people left by the warmth of the camp fire. These two have started out by both sitting on the floor and so will have created a warm patch. The man or woman will know when the other party has recently (5-10 minutes ?) left the room. Of course they need to assume that the other is using the same method...

>> "a bit" in this instance is basically however long it takes for someone to walk to a door, open it, go through, and close it.
>And how fast do you do that. And how fast will the other do that ?

The first few moves and last few moves are constrained by the timing of the lights, and at the beginning the woman doesn't need to worry about anyone in room C, only about whether or not the man has stood up yet.

The man knows this.  In this context, "a bit" is a descriptor sufficient to serve the solution of the problem.   Just because something is a fuzzy quantity doesn't mean it's without content or meaning.

The last few moves are equally constrained by similar logic.  Only in that one middle spot, where the man must make his decision to forge ahead or wait to the last light, is there any real question of what two thoughtful, rational, self-interested people would do.  Yes, you're right:  it's
because the fuzziness of the time-spans in question really do become an obtrusive problem.  

Even so, it's only a problem in the sense that the man cannot *move too quickly*, nor can he *wait too long*.  While it's also true for the woman, as she moves to room A, still it's not nearly so problematic for her as it is for the man.  The reason is that an hour is long enough for people without time-pieces to lose track of time.  If they both had watches, it would be a simple thing for them each to time themselves as they walk to/through the doors, and then to prepare themselves for that final minute when the man's gotta be in his place before the woman sits down.  

But elsewhere in this problem, the order of steps for the solution practically writes itself.

Remember:  the two people are intelligent actors working in their own best interest.  Once one makes that presumption, then there really isn't a second solution.

Another way to look at it is like this:

At the start, there is no pressure on the man to move because he doesn't have anyone behind him, while the woman knows she *must* move or else the jig's up.

Fortunately, the woman knows there's nobody in front of her and so she has absolutely no worries about moving into the next room.  Thus, doing so as quickly as possible is an act of self-preservation.

However, the man knows this is so.  Thus, he knows that if he stays in his room too long, the jig's up. Fortunately, he also knows that the woman will feel a similar pressure and so move into the next room at the earliest opportunity.  Thus, he's going to give her a safe bit of time to accomplish that, and then *he's* going to move to the next room.

Now they're back where they started, with the same pressures.  *Except* -- because of the short bit of time that's passed, the woman has no way of knowing definitively if the man has left the next room yet, or not.  She knows, however, that he will feel the pressure to do so.  So she's got to make a judgement call, here -- how long to wait?  Like i said:  tricky decision.  But there's one thing that's *certain* -- if she waits too long, then the usefulness of that final flashing light will diminish exponentially.  

Another thing is *certain* -- that the man knows this, as well, and that he has done his best to get out of the next room once he felt pretty sure the woman was already gone.  So when does she move on?  Tough question.  As i said above:  it's this and the next step where our thought-problem really becomes a problem, because once the two people are arranged at the final set of doors the rest of the schtick falls into place.

I really don't see how the woman could make any decision other than the one i've offered:  wait long enough to be sure the man could have moved into the next room, and then make her own move.

Now, we've got the woman poised at door A, and she's had two opportunities to observe how long it takes to open and shut one of the doors.  The man's in room B, still, waiting at the door to room C.  The question for me is only this:  does the man move into room C *before* the light flashes? Or does he wait for the light to flash and *then* make his move?

Tough call.  I can't make it.

@kyle_in_taiwan : there's no point in trying to reason with you, so I'm gonna stop here. If you feel up to it, read this whole thread for the reasoning everyone else has made, and you'll realise that basically your solution is the same as a lot of the other proposed solutions, but only differs in the timing. And since timing is crucial, and there's no way to be sure that both persons are gonna pick the same timing, this solution can't be the one they used, unless their success was solely based on luck.
I don't have the time for any more of this :)

>Thus, doing so as quickly as possible is an act of self-preservation

That's why they start by walking briskly and end up running. Whilst there is pressure to remain in a room for 'as long as seems enough', there is a far greater pressure forcing you to move on in case the other person catches up behind you.

But don't forget -- there's also a great pressure not to move too fast --

I see that I'd misread the bit about the woman having to stand AFTER the man... not a major problem since I'm not the man but oh well...
Anyway...
Let's consider the comments about:
11-  The man is told that the woman is exceptionally intelligent.  
12-  The woman is told that the man is exceptionally intelligent.  

Does being "exceptionally intelligent" mean you've got a good sense of time?  It doesn't seem to me that it would.  The point there being what good would it do even if both parties DID think of the same time frame if they can't both count it off correctly.
So, what if we assume that, being exceptionally intelligent, they both remain calm since they both trust in both of their ability to come up with a workable answer.
The use of their heartbeat would seem to be reasonable then.

A problem of the wording we're perhaps avoiding is that it doesn't say that either or both of them are knowledgable... you could be ignorant as all get out and still be exceptionally intelligent...
I also haven't noticed anyone mentioning their convertion to Zoroastrianism... I assume we can assume that means they DON'T have that in common at the time of these tests...
If they really ARE exceptionally intelligent, shouldn't they consider some common ground...?  Are there things that Arabs and Israelis have in common that could translate into a measurement of time?  I don't necessarily mean things they agree on but for instance wars or disputes or the like...

kyle - theses are the moves that must be made, in this order
1) man gets up
2) women gets up
3) women from B->C
4) man from A->B
5) women from C->A
6) man from B->C
7) women from A->B
8) man from C->A
9) man sits
10) women sits

As I understand your solution:  
1) happen immediately - man knows this has to be first
2) happens after a bit - lets give that "bit" a time - say 10 seconds
    this is plenty of time for someone to stand, so any longer would be *to long*
3) happens immediately after step 2, this takes lets say 20 seconds to walk
4) man goes from A->B.  He knows that the women will have moved as soon as she thinks it's safe, so probably after 10 seconds
    so he waits about 20 seconds then moves
5) womem moves from C->A.  She know the man would only wait about 20 seconds, but to be safe, she waits 60 seconds.
    any longer would be rediculous.  she knows it only takes 10 seconds to walk, and knows the man will be moving as fast as possilbe.

Now, suppose for step 4 the man decided to wait 40 seconds... just to be sure.  40 seconds isn't unreasonable, is it?  i don't think so.
And suppose for step 5, the women only waits 30 secons.   This isn't unreasonable, as it only takes 10 seconds to actually move, so she is giving *3 TIMES* the actual needed wait time.  waiting any longer would be rediculous, as the man could come in on her....

No, your solution isn't any more robust than any others.... you think so because you use the time "bit", and assume that both people consider a "bit" to be the same.

Rewrite your solution, giving actual times... and assume a 50% error (maybe more) on any times - some people naturally walk fast, or slow.  Or if they are counting, they could count fast, or slow.  One might be extremely nervous, and move even faster than normal, without knowing it... while the other can remain calm, and move at a normal slower pace.

As is pretty obvious, the two need to be fairly well synchronized.  If they aren't, then they die.  And since it has worked 10 times for them, their solution must be fairly robust to these timing errors.  Your solution doesn't fit that.  

Attention: Do not read if you're already tired of the door knob solution! :)

Quote RobinD:
"It looks like the problem has been built up after several successes. Each constraint added after a solution was found. This way, anyone 'passing' this section of the test has found a way that no-one had used before. I think that is why there are so many restrictions on the signalling possibilities - banging on the walls, shock wave, deaf participants, no-one else must tell them - all added after these were used for solutions. So maybe there is no guaranteed solution, they are still looking for one, and when it's found there will be a new rule added."

>I think that is why there are so many restrictions on the signalling possibilities

This is something that puzzles me somewhat. While they are explicitly ruling out all kinds of actions (banging on the walls etc) which undoubtedly have to be considered means of comunication, they fail to rule out precisely those cases that need to be ruled out the most - borderline cases like my favorite "holding the door knob for an extended period". While I agree that purposely delaying your actions without doing anything you wouldn't have to do anyway *can* be considered a form of communication, it is, I think, an arguably one, and I'm still convinced that a good lawyer would have a chance in court arguing that his client didn't break the rules ;)
As I have to assume that this solution did cross the author's mind(s), I can't really understand it wasn't clearly ruled out with a simple "...it is required to close the corresponding door *and instantly release the door knob*".

Especially as one information, which doesn't make very much sense otherwise, seems to hint to this (or a similar) solution:
"Each lamp is bright enough for a person to notice easily **even when he is not paying attention to it.**" There's not much in those rooms (as described) to pay attention to besides the lamps and, well..., the door knobs ;)

Also, the german version doesn't use the more general term "Tuergriff" ("door knob"), but "Tuerklinke", a term which only denotes the L shaped classical device you have to press in order to open a door. As one has to assume that members of a society of highly intelligent people are well aware of the hazards of translation, one must also assume that they made sure the translation is done by an equally intelligent person who knows the solution and is aware of relevant distinctions.

So I wonder why the author(s) would, on the one hand, rule out things that don't really need to be ruled out, as they clearly are covered by the term "communicate", and on the other hand leave a cloud of doubt lingering over possible solutions (possible at least for me, that is), that would otherwise be 100% safe. Why rely on the interpretation of
- "the moment x touches..." and
- is not doing anything special in a certain way communication or not...
to rule out a solution (thus setting up an unnecessary trap for moderately clever people ;), instead of simply and straightforwardly ruling it out like they did with more obvious cases of "communicating".

BTW, there are other differences between the English and the German version which really make me feel uneasy, e.g.:

English:
"or obtain from others any information allowing them to figure out where the other one is"

German:
"oder sonst wie Informationen über den momentanen Aufenthaltsstandpunkt zu bekommen"
("or otherwise obtain information about the momentary position")
Not "momentary position *of the other*", but simply "momentary position"

In the French and the Italian version this sentence is basically the same as in the English version though... Can't judge other versions (I guess the original version is the Portuguese one).

Thanks for the translations TName.

Can you verify for us, what you believe to be the meaning of 'The moment that the woman touches the doorknob of a room, the man cannot be in that room any more'?

I think most of us have taken this to mean that 'the man must have left the room before the woman touches the door knob (now a handle), else they fail the test'.

>I think most of us have taken this to mean that 'the man must have left the room before the woman touches the door knob (now a handle), else they fail the test'.
Yes, that's how I understand it also, but for me it doesn't mean that someone can't touch (start touching?) a knob before the other person enters the room.

We've discussed the situation earier in this thread.

My opinion was that, if the woman opens a door and then closes it but keeps the door knob pressed for a prolonged period, allowing the man (who enters the room she's just left at some point *while* she is holding the doorknob) to know when she will leave the room she's currently in (this will be seconds after she releases the door knob)  -  ...my opinion was/is that this scenario wouldn't contradict the rule 'The moment that x touches the doorknob of a room...'.

I understood "the moment that..." as the initial moment she touches the knob (when closing the door to the now empty room she has just left). At that very moment, the said room is empty. In my opinion the fact that she is *still* holding/pressing the door knob when the man enters the room she has left earlier doesn't break the mentioned rule.
Others were of the opinion that it does contradict the rule, and I admit that this different interpretation does have its own legitimacy, even if I tend to disagree :)

The idea was: if each of the two persons will keep the knob of the door to the room he/she has just left pressed until he/she sees the knob of the other door being released (plus an additional 30 seconds to 10 minutes, to allow the other person to change rooms and start observing the "own" knob), they couldn't fail.
In my opinion this doesn't really break any of the two rules in question, although I agree it's debatable:

"The man and woman are not permitted to communicate between each other in any way, or obtain from others any information allowing them to figure out where the other one is." (who's "others"?)
"The moment that x touches the doorknob of a room, y cannot be in that room any more."

It would be an extremely simple and safe solution, provided it's allowed. I may be plain wrong of course, but in my opinion it's at least debatable if any rules are being broken - it largely depends on precisely defining terms.

For instance: If the aliens/authors (who, I repeat, must have thought of this solution) understand delaying otherwise necessary actions (in other words, temporary lack of action) as communicating, why do they give as examples of forbidden communication only cler-cut actions (beat..., generate...) and even cite the fact that the two might as well be mute and deaf as the ultimate argument against any communication. Ok, but not blind...;)

Considering all this, my question is: if wrong, why wasn't this possibility clearly ruled out, as others were?

@Adam:

1) man gets up
2) women gets up
3) women from B->C
4) man from A->B
5) women from C->A
6) man from B->C
7) women from A->B
8) man from C->A
9) man sits
10) women sits

As I understand your solution:  
1) happen immediately - man knows this has to be first
2) happens after a bit - lets give that "bit" a time - say 10 seconds
    this is plenty of time for someone to stand, so any longer would be *to long*
3) happens immediately after step 2, this takes lets say 20 seconds to walk
4) man goes from A->B.  He knows that the women will have moved as soon as she thinks it's safe, so probably after 10 seconds
    so he waits about 20 seconds then moves
5) womem moves from C->A.  She know the man would only wait about 20 seconds, but to be safe, she waits 60 seconds.
    any longer would be rediculous.  she knows it only takes 10 seconds to walk, and knows the man will be moving as fast as possilbe.




>>Now, suppose for step 4 the man decided to wait 40 seconds... just to be sure.  40 seconds isn't unreasonable, is it?  i don't think so.
And suppose for step 5, the women only waits 30 secons.  

You're right.  If the woman only waited 30 seconds, she'd bump into the man.  But why in the world should she cut it so close?  She needs to give him only enough time to move into the next room, and she basically has a full hour in which to wait.  The next room she moves to will the be the *last* room she occupies before the last flashing light, so she literally has something like 57+ minutes which she can wait for.  Why would she move in only 30 seconds, knowing full well that doing so might cause her to bump into a man who hasn't yet decided to move?

However, there is an alternate pressure at work here as well, and one which i consider more troublesome.  The woman is not so much under pressure to move immediately, nor even quickly, but she absolutely cannot move too *slowly*, and there's where the rub comes in.  How slowly is too slowly?  20 minutes?  40 minutes?  That's why, the more i think about it,  i believe the final arrangement at the last flashing light would best be with the woman next to the exit from Room A, and the man next to the *entrance* to Room B.  In that circumstance, the woman simply moves through her door and starts counting to thirty or something, while the man sprints through the next two rooms and sits down as quickly as possible.  Because he's moving through two doors instead of one, there's no way he'll be able to overtake the woman as she moves through her one door.  And with the woman waiting for thirty seconds or so, it should give him plenty of time to get into place and sit down -- and it's about the same amount of time she'd wait if they were each standing beside their final doors anyway.

>>No, your solution isn't any more robust than any others.... you think so because you use the time "bit", and assume that both people consider a "bit" to be the same.

Well, estimation of time does depend on several subjective factors.  But if i ask ten intelligent people to estimate twenty seconds, and then give them each a watch to practice on twice before letting them attempt the feat, then i would think it's a pretty safe bet that they'll each be able to come within three to six seconds of each other when they make their respective attempts -- and that's a plenty large enough margin of error for our purposes here.

>>As is pretty obvious, the two need to be fairly well synchronized.

I dispute that.  With the two flashing lights they already have a basic synchronization.  Only the last two moves for the man are a real problem.

I somehow have the feeling that we are all moving in circles (like the woman and the man in the riddle) between 3 or 4 basic solutions and their endless variations.
I promise never to mention door knobs again :)

My feeling is that, as already inferred by Infinity08, this is a badly written puzzle, with poor translations and too many possible viable solutions. Outsmarting the aliens by finding a loophole in the rules, like teleporting (a good one!), would be the best way to find THE solution. If there is more than one solution... it really nullifies the two people following the same pattern. The problem with finding loopholes is that the rules are not distinctly clear through the translations.

If you check the source f this problem (an intelligence test for entry into an elite group) many of the problems are thought provoking and may have multiple answers.  Your score may be based on how weel you describe and defend the solution you present.

mlmcc

except that whatever solution you present is not a good solution :) Unless we assume that both prisoners were lucky.

Anybody here fluent in Português ?  Want to take a look at the original and see if anything got lost in the translation?

Um homem árabe e uma mulher israelense são abduzidos por extraterrestres. Os E.Ts. prometem devolvê-los incólumes à Terra, desde que eles sejam capazes de cumprir uma tarefa, que consiste no seguinte: três salas são designadas A, B e C. Cada sala é quadrada e tem aproximadamente 25m2. Elas estão unidas de modo que cada uma delas possui duas portas, e cada uma dessas portas dá acesso a uma das outras duas salas. As três salas são acusticamente isoladas, não possuem nenhuma mobília e nenhuma janela. As paredes, as portas, o teto e o chão das salas são maciços e opacos e não apresentam fendas, orifícios, passagens ocultas ou similares. Na sala A é colocado um homem e na sala B é colocada uma mulher. Tanto o homem quanto a mulher recebem as seguintes instruções:  
1 – Ambos terão o prazo de 1 hora para percorrer as três salas e voltar à sala de origem, sempre caminhando no sentido A-B-C-A.    
2 – Ambos deverão permanecer sentados, no chão, no centro de sua respectiva sala, até que seja emitido um sinal, indicando que a contagem do tempo foi iniciada. Esse sinal consiste no seguinte: em cada porta existem duas lâmpadas (uma de cada lado da porta), e o sinal é quando todas essas lâmpadas se acendem quase simultaneamente. Cada uma das lâmpadas é suficientemente luminosa para se fazer notar com facilidade, mesmo que não se esteja prestando atenção a ela.    
3 – No momento em que a mulher tocar na maçaneta da porta de uma sala, o homem já não pode estar presente nessa sala.    
4 – No momento em que o homem tocar na maçaneta da porta de uma sala, a mulher já não pode estar presente nessa sala.    
5 – A mulher precisa se levantar depois que o homem.    
6 – O homem e a mulher não podem estabelecer nenhum tipo de comunicação, nem obter de terceiros alguma informação que permita a um saber onde se encontra o outro. Não podem bater nas paredes ou nas portas, nem tentar propagar nenhum tipo de onda de choque. Ao sair de uma sala e entrar na outra, é necessário fechar a porta que lhe serviu de acesso. Inicialmente todas as portas estão fechadas. Duas ou mais portas não podem ficar abertas simultaneamente.    
7 – Nenhum deles dispõe de um relógio nem qualquer outro instrumento que permita determinar o fluxo do tempo.    
8 – Quando faltar 1 minuto para completar 1 hora, será dado novamente o sinal luminoso, indicando que o prazo está se esgotando.    
9 – Ao expirar o prazo de 1 hora, o homem precisa estar sentado no centro da sala A e a mulher precisa estar sentada no centro da sala B.  
10 – A mulher só pode se sentar depois que o homem.    
11 – O homem é informado de que a mulher é excepcionalmente inteligente.  
12 – A mulher é informada de que o homem é excepcionalmente inteligente.  
O homem e a mulher não se conheciam previamente, nunca tiveram nenhum contato antes e permanecem incomunicáveis entre si durante todo o processo (para tornar o enunciado mais claro, pode-se admitir que ambos são surdos e mudos). A experiência é realizada e eles conseguem cumprir a tarefa. A experiência é repetida 10 vezes e todas as 10 vezes eles cumprem a tarefa com sucesso, o que deixa claro que não foi por sorte. Então eles são devolvidos à Terra, convertem-se ao Zoroastrismo, casam-se e vivem felizes para sempre! Descreva o procedimento que eles tiveram e o pensamento de cada um.

"...nem obter de terceiros alguma informação que permita a um saber onde se encontra o outro"
I don't speak Portuguese, but I think this means: "or obtain from a third party any information allowing one to know where the other one is".
Please correct me if I'm wrong, but I think this differs slightly (but significantly?) from the English version, where "from others" might include the other person as well.

I'm fairly sure it isn't a trick of the wording.
I'm seeing this as a tour through three rooms by two people. They have to identify what will be a unique solution to the problem. It would be too easy if they could just signal to each other so this is banned - any form of signalling.
They have to complete the tour without meeting. I think the doorknob bit is again to prevent signalling and just adds complication to a fairly simple description.
Even the sitting/standing up bit looks like it is there to remove the use of the flashing lamp signals for moving rooms, as these 'timing marks' have now been used up before they can move.
The essence of it seems to be: The woman must tour through the rooms not catching up with the man. The Man must tour the rooms not catching up with the woman. Even if there were clocks on the walls they would be no better off as neither would know what interval the other would choose betwen moves.

TName's mention of the door Handle as opposed to the door knob made me wonder if it could be used for some information transfer, I don't believe it would be 'signalling' if for instance the woman watched a door handle on a room she had just entered to see if it moved. It would be signalling if the man deliberately delayed releasing the handle, but if she just saw the movement and he had walked through the door normally he wouldn't have deliberately signalled. Perhaps she could tie a bit of thread from her clothes to one of the handles, take it through the next door with her and by feeling it move would know when the man entered the room behind her, thus it would be safe for her to move on. I don't believe this would count as signalling. The man might even be unaware that she had done this, except that being equally intelligent would be doing exactly the same himself.
After ten goes they may be slightly undressed, what does Zoroastrianism say about nudity?

The sitting/standing bit is there to provide considerable complication to what would otherwise be a simple problem.

Without the sitting/standing up part, they could follow my outline and be guaranteed of success.

> provide considerable complication

More to narrow the problem down I think.
The only task is to traverse the rooms in the correct direction without meeting the other person.
No communication is allowed, or any tricks in the wording.

The solution must be one that would work for a single person (no communication or signalling), allowing that the other person will be using a compatible (not necessarily the same) strategy.

>> They did not communicate with each other during the whole process (to clarify the matter, it can be told that they both were mute and deaf).

To me, however badly translated the question is, this clarification of the non-communication premise seems to refer to only audible spoken communication, since they were mute and deaf, but not blind. If some kind of visual communication was disallowed, it might have been stated that they were mute, deaf, and blind.

But if they were blind, this whole question would not make any sense at all, as they could even take up to 2 hours or more just to find the doors...

dagesi >> I also haven't noticed anyone mentioning their convertion to Zoroastrianism... I assume we can assume that means they DON'T have that in common at the time of these tests

I did, earlier on.

>Wwysdom...
  So you did... my mistake... =]

kyle_in_taiwan>>Without the sitting/standing up part, they could follow my outline and be guaranteed of success.

Many of the solutions can be guaranteed of success *if they choose the same method*, even with the sitting/standing.  With the number of moves that must be made, and the amount of time, there is enough extra time that they could wait appropriate times (with errors), and make it.  And you can use the argument "I'm extremenly intelligent, and thought of this... so someone else who is extremely intelligent would think of the same method".  Once a particular method worked once, they woudl continue to use the same method.  But you have no way to be assured that they pick the same method.  You use arguments like there is no reason to wait longer or shorter... but of course there is: if they go to fast or to slow, they run into each other...

mlmcc>>If you check the source f this problem (an intelligence test for entry into an elite group) many of the problems are thought provoking and may have multiple answers.  Your score may be based on how weel you describe and defend the solution you present.

I'm starting to think this more and more.... I'd be impressed if anyone came up with a solution so obvious it is the only possibility for both people, but don't think that's going to happen.  Coming up with a solution that would work fairly reliably and defending it... that might be the main point.

This is actually one of the final questions in the test and to get to answer it you have to score sufficiently high on the previous sections.

Ok, so, in view that even being exceptionally intelligent they would possibly find different sollutions, they would begin to think that it is all about the interpretation of the rules, mainly the rules #3 and #4:

3 - The moment that the woman touches the doorknob of a room, the man cannot be in that room any more.
4 - The moment that the man touches the doorknob of a room, the woman cannot be in that room any more.

There are 3 rooms and 3 doors, each door have 2 doorknobs, one on each side. Let's suppose that the man is in room A and the woman is in room B. There is a door that leads from room A to room B, and the man touches the doorknob of this door, BUT he touches the doorknob at the side of the A room (not the B room), so, it is ok! From rule 4, the moment that the man touched this doorknob (of room A), the woman cannot be in room A anymore, but it is ok, because the woman is already in room B! So, the man stays on room A and closes the door (because there cannot be two open doors at the same time), waits a little and try again. If the woman moved to room C, he moves to room B. They keep following this pattern, until they are again at room A and room B.

About rules #5 and #10:

5-  The woman has to get up from the floor after the man.  
10-  The woman may only sit down after the man.  

It is easy. At the first signal, the man goes up immediately and opens the door. The woman will see he opened it and will get up. He will close the door (staying in room A), she will go to room C, etc. At the end, when the man is in room A again, before the second signal, the man will sit down and the woman will keep waiting standing up. At the second signal she will sit down.

Problem solved!

:)  May I remind you of this little episode earlier on in this thread:

Quote TName:
"@ e_tadeu
Just trying to clarify, especially as English is not my native tongue:
>The moment that [x] touches the doorknob of a room, [y] cannot be in that room any more.  
By this you mean that whenever someone  touches the doorknob of a door leading to another room, the other person cannot be in that other room, correct?"

Quote e_tadeu:
"@TName
>By this you mean that whenever someone  touches the doorknob of a door leading to another room, the other person cannot be in that other room, correct?

I think it is, otherwise it would be a very dumb problem, huh? :)"


>So, the man stays on room A and closes the door (because there cannot be two open doors at the same time), waits a little and try again
Well, why doesn't he walk into room B right away? There's no rule against both being in the same room. ;)

Yup, I thought about that "solution" since the beginning, and I was waiting to see if someone would come up with a better solution without needing to "reinterpret" the rules, but... maybe the problem is dumb after all =)

> Well, why doesn't he walk into room B right away? There's no rule against both being in the same room. ;)
But then, when someone touches the doorknob, the other person will be in the same room, and this is prohibited ;)

>But then, when someone touches the doorknob, the other person will be in the same room, and this is prohibited ;)
It's no big problem to *close* a door without touching the d.k. (I promised not to mention the word again :)
Just bang it shut!

Oh I see, they have to get out of the room again.  But why not re-reinterpret the rules back again then until the next door is open?

Forgot the smiley  :)

> Oh I see, they have to get out of the room again.  But why not re-reinterpret the rules back again then until the next door is open?

Well, maybe because you should have a consistent interpretation? You could interpret statement S as S' or you could interpret statement S as S'', but you can't switch between S' and S'' deliberately, this would be inconsistent :p

Changing the rules from room to room was of course a joke.

BTW, do *you* speak fluently Portuguese?
"The moment that x touches the doorknob of a room, y cannot be in that room any more" is such an unfortunate formulation, that a precise translation of
"No momento em que a mulher tocar na maçaneta da porta de uma sala, o homem já não pode estar presente nessa sala."
might shed more light on it's meaning (especially as that "any more" at the end adds to the confusion):

"já não pode estar presente nessa sala" (especially curious about the exact meaning of "já" and "nessa" in this context)

 

Yes, Portuguese is my native language!
The translation is correct, I will translate it step-by-step:

No ("Em"+"o" = In the) momento (moment) em que (that) a mulher (the women) tocar (touches) na maçaneta (the doorknob) da porta (of the door) de uma sala (of a room), o homem (the man) já (means "already", but in this context is the same thing as "since now" or "any more") não pode (can't) estar (be) presente (present) nessa ("Em"+"essa" = in this) sala (room).

"Nessa" is the conjunction of "Em Essa" that literally means "In This", there is no other meaning for this word.
"Ja" in the past is the same thing as "already", in the present or future is the same thing as "since now" or "since this event"

Thanks for the translation!

Does "touch" mean skin contact?   Is it permissible to open the door without "touching" the door knob/handle?

Besides, these could be star trek style doors that automatically open as you approach and the door knob/handles are merely ornamental?

>without "touching" the door...

Oh come on, it means 'Do not come into contact with a door when the other person is still in the next room.'

You have to be sure that they have not only moved on a room but have closed the door before you make your move.

Im not sure if anyone has posted this, I looked through about 2/3rds of the comments, but why couldn't the man stand up open the door to the next room and take of this shoe to prop the door open thus allowing him to see when the women entered the room behind him, when she enters the room behind him, he can move through the next door again proping it open with his shoe, this allows them both to see when he moves into the next room and then he can look through the proped door to discover if the women has moved to the next room, once she enters that room she uses one of her shoes to prop the door and they now can transverse the rooms to their little hearts content.

d@mn nevermin just reread line 6
My idea was destroyed

Does using your shoelace to tie the knobs of the doors together so that as you slam one shut behind you, it pops the other one open, count as communication?

Well, the implication of rule 6 is that one and ONLY one door can be open at a time... that would include his doors AND her doors... meaning if they did manage to do that, how would the other person get INTO the room you did that to?

No, here's what I mean. The signal appears, the man stands, the woman waits a tick and stands.  She opens the door (BC), ties her shoelace between the doors (BC) and (AB). When she enters room C and closes the door behind her, her shoelace pulls open door (AB), and the man knows it's time to move.

However, unless all the doors swing both directions, it will only work in at most one of the rooms (since both doors would have to open into that room). So never mind.

>her shoelace pulls open door (AB), and the man knows it's time to move.

I think that would be signalling - she is sending information to the man.

If she was able to use various bits of her clothing to trigger a signal to herself that the man had entered the room behind her then I don't think it breaks the 'no communication' rule.

As I mentioned before, one of the problems I see with this riddle is that we have less information than the two persons will have in reality.
If they are clever and flexible, they can adapt to the situation, and each will know that the other one is able to do the same.

What about this (a combination of several solutions posted in this thread):
When the light goes on, they both start counting their heartbeats (relying on the fact that their pulse won't change significantly during the test). If the light goes off after only a few seconds, they'll forget about this method, and think of something else. If the light goes off after, let's say, anything between 10 seconds and a minute, they could decide to use this (X=the number of counted heartbeats while the light was on) as time unit. And to be safe, they'll always count 2X when they know that (at the beginning of the count) the room behind them is empty, and 1X if they know that it's not. So, woman enters room C and counts 2 times X, man counts 1 time X in room A (similar to the numbers in my very first post).

This is just an example. The main idea is (sorry if I repeat it): Compared to them, we may lack knowledge of some important details, and even the best/ideal solution found by someone who answers the riddle (having to provide an answer that is valid under *all* circumstances) might be rejected by those clever people in reality (even if it was the solution they have opted themselves for in theory), as soon as certain details we know not of prove to have the right parameters at that time in those rooms, thus making a solution possible that we cannot provide, as it wouldn't always work.
So I really believe the best answer would be a (pretty complex) hierarchical list of possible solutions they will pick from in realtime.

>When the light goes on, they both start counting their heartbeats...
Or walk in a circle at a constant pace and count the steps ("Each lamp is bright enough for a person to notice easily even when he is not paying attention to it." would make some sense then). It doesn't matter. One could cout steps, the other one heartbeats if he wanted. The idea would just be to reproduce that amount of time (light on - light off) as accurately as possible, by whatever means each of them would deem fit.

I like the shoelace idea, although I suppose that *would* be classified as "signalling" -- plus if one of thedoors latches closed, the idea stops working.  Plus, I think they'd have to be wearing hiking boots to get long enough laces... :)

I'm wondering if she could construct/set a timing device to delay the man from moving for a calculable period. Not to signal to him (cuts herself and writes 'count 50 heartbeats' in blood), but to actually slow him down. Being highly intelligent he would be a sucker for a crossword puzzle or a small sudoku so she could leave something for him to solve. Or maybe something to block the door for a period, again not a signal but something to prevent him moving - can't think of much here yet.

Assuming that the aliens were not lying for instructions 11 & 12. (They are intelligent)
Assuming that the two know which room is which. (A, B, C)
Assuming that they both think in English.
And since the distance from the centre of the room to any of the doors is only less than 3 meters, I will assume they take three steps (S) to reach a door. I also assume the opening and closing the doors is a simple operation, and therefore will only take the same duration as walking three steps. (open door, cross over, close door)

Before the first signal is lighted, The man (M) thinks to himself, "What I only know about the woman (W), is that she is an israeli, and that she is exceptionally intelligent. The only info she knows about me is that I am an arab. If she is intelligent, she will think likewise."

W thinks to herself, "What I only know about M, is that he is an arab, and that he is exceptionally intelligent. The only info he knows about me is that I am an israeli. If he is intelligent, he will think likewise."

They both think, "the only timing that we may be able to agree on, is the count off of letters from the words arab, for a short length of time, and israeli, for a longer length of time.

The test begins.

1. The first signal lights, M gets up immediately, knowing that he has to do it before W. He thinks, "The safest time for W to get up is when the signal goes off, then she should be moving immediately into C, I should count off a longer length of time to make sure that she has done so after the signal goes off."

2. The signal goes off. W gets up and goes immediately into room C, which they both know is unoccupied. While moving, she thinks, "If M is intelligent, he will give me ample time to go to room C, so he should have counted off for a longer time. When I am in room C, I also should count off a longer time for him to leave room A."

3. M, after counting off 'israeli' goes to room B, and while moving thinks, "W must have known I was going to count off longer, so she will also  count off longer while in room C, to allow me to reach B. But as I will take some time to reach B's centre, I should be safe to count off a shorter time in B, as W will already be moving into A during my count.

4. W, after also counting off 'israeli' starts to move to room A, and thinks, "Okay, this is my second last room. M should be clearing out of B quickly, to let me go back to B, so he should be counting off 'arab', and I should do the same in A.

5. M after counting off 'arab' moves into room C, thinking, "W will be moving back to room B after this and staying put, it will be safer for me to count off a longer time in C. As I will have to sit down first, I should do so immediately when I reach A's centre. The safest time for W to sit down will be at the second signal."

6. W moves back to B after counting off 'arab'. She moves to B's centre and thinks, "The safest time for me to sit down will be at the second signal, while it is safe for M to sit down any time before that. The aliens must be sexists to make me stand so long!"

7. M moves back to room A after counting off 'israeli' and sits down. W sits down at the second signal.

To show the timing they took, below is a crude diagram. (time progressing left to right, starting form the second signal. 'x' stands for a step, 'o' stands for sequence of opening/closing of doors)

M     i s r a e l i x x x o o o x x x a r a b x x x o o o x x x i s r a e l i x x x o o o x x x

W     x x x o o o x x x i s r a e l i x x x o o o x x x a r a b x x x o o o x x x

If you get the above into an excel sheet or some other table format, please note that th 'o's do not coincide.

Actually, just pasting it into a notepad file will do.

>Or maybe something to block the door for a period, again not a signal but something to prevent him moving - can't think of much here yet.

W moves from B to C, closes the door and blocks the door handle (holding it, maybe even leaning against the door) in the closed position. M tries after some time also to go from B to C but finds the door blocked. She cannot help but notice/feel his attempt to turn the knob and she knows that he will try again from time to time, but in intervals long enough to allow her to leave the room after any of the attempts (she will always know when his last attempt was and he will know that she knows). Would it be signalling, a form of communication? I don't know. But I can't see a significant difference between her blocking the door with some device or with her own body. After all, her intention would be the same in both cases, and he could only guess (ok, a well founded guess) that it's really herself preventing him to enter the room, and not some device or attached string/rope/whatever.

Shoe laces? Fine, but what if they wear slippers or if they are bare footed? ;)
I don't think we can take any object/device/piece of clothing for granted.

Folks, we need to use the Occam's Razor here!

The more complex the solution, the less likely it is *the* solution, because the other person could always think in a different complex solution or in a simpler solution. Being both exceptionally intelligent, they know that, to be one "in accordance" to the other, they must choose the *simplest* solution in the solution space!

Wwysdom>>2. The signal goes off.

We don't know when this is... it might be after 100ms after it comes on (eg: it flashes on, then back off), or it might be after 49 min, 59 sec (eg: it comes on, then flashes off, then on at the end).

Also, saying "I'm exceptionally intelligent, and this is the method I thought of, so the other person, also exceptionally intelligent, must have come up with the same method" has been proposed and there is no reason to believe that it is true.

TName>>W moves from B to C, closes the door and blocks the door handle (holding it, maybe even leaning against the door) in the closed position. M tries after some time also to go from B to C but finds the door blocked.

If W is holding the door when M tries and finds the door blocked, he would have had to touch the doorknob (if he didn't, he would have no way to know it was blocked, as the door wouldn't move anyways), and touching the doorknob while she is in the room is prohibited.

Using something else to block the doorknob would probably be considered a form of communication/signalling.

I agree completely with the Occam's Razor approach. My interpretation of the "exceptionally intellgent" clue is simply that both will choose a method which statistically gives them the best chance of using the same system to escape.

If they are that bright they will also realise that there is a finite chance that the system will fail.

Once they have got through once they know that both are using the same system so from then on it is bound to be reproduceable.

In regards to any method that utilizes something external, consider this also...

>"The experiment is repeated 10 times and each time they complete the task successfully, making it clear that the first time was not due to mere good luck."

Clearly, if there were some form of visible method employed, you, as the aliens, wouldn't need to retest to see if there was luck involved...
It stands to reason then that the method used is entirely within the minds of the two individuals.

>If W is holding the door when M tries and finds the door blocked, he would have had to touch the doorknob
Correct, forgot about that...

Adam314,

>> Also, saying "I'm exceptionally intelligent, and this is the method I thought of, so the other person, also exceptionally intelligent, must have come up with the same method" has been proposed and there is no reason to believe that it is true.

Sorry, I did not imply that they will choose the same plan because they are intelligent. What I mean is that the only things they might know about each other at the beginning, is that the other party is an israeli woman/ arab man.

With this information, which they know the other party knows, and with the larger difference between the words 'israeli' and 'arab', the two also would have needed some kind of common seconds count-off plan, and these two words would have been the most logical to choose.

It also works with the Portugese words, árabe and israelense as in the question before translation.

Is token passing considered communication? Can they slide something under the door, and you're only allowed to move if you are in possession of this token?

Are there any airplane or railroad buffs in the audience? What is the emergency procedure for planes landing at an airport in low visibility with dead radios? How did trains keep from colliding prior to the invention of the wireless telegraph? If there were a solution, I'd expect to see a similar concept at http://en.wikipedia.org/wiki/Railway_signalling

Wwysdom>>these two words would have been the most logical to choose.
How about "women" and "man"? or "Female" and "Male"? or "Male Arab" and "Female Israeli"? or "Arabic" and "Israeli"?  or "Arab man" and "Israeli woman"?

Also, I would think the most logical is the one that has the highest probability of success.  This requires that they both use the same method.  Once you have that, the method that allows for the greatest error in counting speeds has the highest probability of success (eg: the most robust to timing errors).  Counting the words israeli and arab don't give the highest probability of success - as least I don't see how they do.

I'm jumping in rather late into this thread so at the risk of sounding stupid:

> An Arab man and an Israeli woman are abducted by extraterrestrials.

Has anyone brought up the notion that they might be travelling at faster-than-light speeds?  Or travelling through a worm-hole...  somewhere where the physical laws we take for granted may be warped in some way...

Well that killed it dead muso :)

Another late arrivee.. with a different take on it.

The key is the method to measure time .. that they know the other will use.

I think there is a clue in that after they are returned to earth they 'convert to Zoroastrianism, get married and live happily everafter'. Now why would they do that? .. because that was they key to their method.

As they are both exceptionally intelligent and they know each others nationality.. they would look for some link between Judaism and Islam.
And both having studied Mary Boyce they know that .."Zoroastrianism is the oldest of the revealed credal religions, and it has probably had more influence on mankind, directly or indirectly, than any other single faith... some of its leading doctrines were adopted by Judaism, Christianity and Islam".

They also know what the Zorastrian scriptures say about action.. which is their task..  "A thousand people cannot convince one by words to the extent that one person can convince a thousand by action." (Dk6.e15) "

Now they have their method to measure time.. based on 1000

light goes on .. man immediately stands.. and starts counting to 1000 (approx 16 minutes give or take)
woman waits 10 seconds..( one one thousand, two onethousand .. etc) stands and goes into room C.. and starts counting to 1500 knowing this will provide an 8 minute buffer ..( 24 minutes give or take).
At 1000 man goes into room B.. starts counting to 1000
At 1500 woman goes into room A. .waits
At 1000 man goes into room C .. waits
light comes on.. Man counts to 10 seconds (one one thousand, two one thousand..etc)
light come on.. Woman goes into room B .. knowing he will count to 10.. counts to 20
At 10 man goes into room A .. sits
At 20 woman goes into room B sits.

Fin

Z

Paradoxally, each new solution like this is just another solution in the pool of solutions that they can choose... leading us to be more distant to the one true solution... :p

I don't agree.. You are assuming that none in the pool of solutions is the 'true solution'.. when if fact one might be.. or the next one might be..so we are not being led more distant to the solution.. but nearer to it.. or the likelyhood of finding it.. if it has not already been found.
Go back and sit in your armchair. :_)

Z

The "convert to Zoroastrianism, get married and live happily everafter" part of the puzzle is interesting...
maybe god told them when to get up, move, and sit down... and while doing so also mentioned that Zoroastrianism is the religion that is correct.

That's good Adam.. nice and simple..
I think I like it better than mine.

"A single god Ahura Mazda who is supreme. Communication between Himself and humans is by a number of Attributes, called Amesha Spentas or Bounteous Immortals."

Z

> Well that killed it dead muso :)

Yeah, for a while it was like when you walk into an unfamiliar rural pub (American werewolf style), a glass is dropped, and everyone goes silent...

let me buy you a drink.. in case it happens again.
"eerk it's that muso agin an looks like he's ready ta draw"..
Larson spings to mind

Z

:-)

count to 1000, so easy.... but what language are they counting in? 'uno duos trios' takes longer than 'one two three'

there are large buffers around the counts to 1000 and 1500 ..so it souldn't matter
the counts to 10 and 20 are too short to cause any significant difference.. a second or two at most.

Z

Z,

>> light goes on .. man immediately stands.. and starts counting to 1000 (approx 16 minutes give or take)
>> woman waits 10 seconds..( one one thousand, two onethousand .. etc) stands and goes into room C.. and starts counting to 1500 knowing this will provide an 8 minute buffer ..( 24 minutes give or take).
>> At 1000 man goes into room B.. starts counting to 1000

You obviously forgot that at this point when the man opens the door to room B, the woman will still be counting, in room B that is...

oops, ignore my last comment please

Various solutions proposed, all of which would work if their proposers logic was used.  The problem here is we don't have access to either the original question setters rules or their solution.  Each offering could be equally valid.  As a result I propose we either keep the question and split the points amongst the 18 participants or agree to delete it.   - or move it to P&R :)

Any comments?

>Any comments?

Please don't delete it.
I vote to keep the question and split the points. This has been a very interesting discussion and it might be useful to keep in case anything similar turns up in the future. Reference to here could save some time as many different suggestions have been offered and then disproved.

RobinD > Please don't delete it.

I agree.  I haven't contributed anything worthwhile myself, but it's a fascinating thread and one that's definitely worth keeping.

MASQUERAID > or move it to P&R :)

Nooooo! Definitely *keep* it in P&R!

I agree with all above....Don't delete!

This has re-woken an idea I had been toying with. It goes back to one of my earlier thoughts that rules were added to the puzzle as each version of it was solved.
My idea was to start with a version of the problem that had most of the constraints removed, and gradually add them, solving in each case.
So, for instance, you MAY wiggle the door handles to signal to the other party - can we be certain that they will understand the signal?
and working through each of the problem versions then adding the restriction just might either find 'the' solution or allow us to prove it unsolvable.

Well, then for each presented solution a new restriction can be added, and that way the puzzle will NEVER be solved :)
It's just a badly formulated puzzle, that's all.

Inherent in each riddle should BE the answer to the riddle... if a riddle, in itself, doesn't give the information needed to solve it, it's not a riddle, it's just a confounded question.
It's not necessary that the information IN the puzzle be readily understandable, but it can't be of the bad mystery novel nature where you discover the real culprit was the evil identical twin that no one mentioned in any way in the book...

You have to consider the source of this one, it's from an IQ test - there may not be a known answer. My speculation is that every time the puzzle was solved, another constraint was applied to ensure a different solution next time.
In all the above we haven't been able to prove that it can't be done, just that we have been unable to do it (yet).

>> In all the above we haven't been able to prove that it can't be done, just that we have been unable to do it (yet).
Yes, but if someone finds a solution, the next version of the riddle will include new requirements that invalidate that solution ... oh well :)

>the next version of the riddle will include ...

It very well may do, but our task is to solve just this version.

The only "solution" that exists for this riddle, is for both the woman and the man to pick one of the possibilities, and hope that the other picked the same.

>> In all the above we haven't been able to prove that it can't be done, just that we have been unable to do it (yet).
We have effectively proven just that : the fact that we can come up with more than one equally intelligent solutions is proof that no unique solution exists, which is a prerequisite to solve this riddle.

>In all the above we haven't been able to prove that it can't be done, just that we have been unable to do it (yet).

>We have effectively proven just that : the fact that we can come up with more than one equally intelligent solutions is proof that no unique solution exists, which is a prerequisite to solve this riddle.

I think I have to agree and disagree with you both  ;)
In my opinion we have proven that we cannot come up with a solution we can all agree upon. That's all. There might be a solution we would all instanly accept (we cannot prove it's nonexistence). On the other hand, there might be a solution we (as a group) do not accept, but the author of the riddle would. Not all solutions fail on "technical" reasons, reasons that can be proven or rejected beyond any doubt. Or because they're as good or bad as other/similar solutions. Some depend on the precise definition of concepts, and these are fields of debate where equally intelligent people can strongly disagree. In such cases, the chances of one or two dozen people agreeing (more ore less unanimously) on a solution are of course not very high.