# Room switching logic puzzle [closed]

How can one solve this logic puzzle?
I think the key ideas may have something to do with 11.,12. and common knowledge

An Arab man and an Israeli woman are abducted by extraterrestrials. The E.T.s promise to return them to Earth unharmed, provided that they succeed in the following task: three rooms are designated A, B and C. Each room is square and measures approximately 25 m2. 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. The three rooms are acustically isolated and have no furniture or windows. The walls, doors, ceiling and floor of the rooms are solid and opaque, and contain no cracks, holes, hidden passages or the like. The man is placed in room A and the woman in room B. They both receive the following instructions:

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.
2- The both have to remain seated, on the floor, in their respective rooms, until a signal would be emitted, indicating that the time count had started. The signal was as follows: on each door there are two lamps (one on each side of the door), and the nearly simultaneous lighting of the all the lamps constitutes the signal. Each lamp is bright enough for a person to notice easily even when he is not paying attention to it.
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.
5- The woman has to get up from the floor after the man.
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.
7- None of them has a clock or any other instrument that can be used to measure time.
8- 1 minute before the 1 hour period is up the light signal will be given again, indicating that the time is running out.
9- When the 1 hour period is up the man has to be sitting in the center of room A and the woman in the center of room B.
10- The woman may only sit down after the man.
11- The man is told that the woman is exceptionally intelligent.
12- The woman is told that the man is exceptionally intelligent.

The man and the woman did not know each other and had never been in any contact with each other before. 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). The experiment is carried out and they manage to perform the task. 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. Afterwards they are returned to Earth where they convert to Zoroastrianism, get married and live happily everafter! Describe the method they used and the way of thinking of both of them.

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I don't see what their nationality, religion, gender, or otherwise have to do with this. –  Asaf Karagila Dec 9 '12 at 9:08
nothing I would guess but I wanted to keep the puzzle verbatim –  user52336 Dec 9 '12 at 9:39
verbatim --- from what? What's the source? –  Gerry Myerson Dec 9 '12 at 11:55
I think condition $7$ needs to be made more precise. Even without a clock or other instrument, a human has some sense of time and knows whether approximately one, ten or fifty minutes have passed. Since it's unclear precisely how exact this sense of time is, the problem would be ill-defined if the solution relies on it (so presumably it doesn't?). You should specify more precisely how the humans are allowed to choose instants in which to act. –  joriki Dec 9 '12 at 12:27
@AsafKaragila They have to do with making it possible to remember who's who. Would you prefer if they were referred to as Character 1 and Character 2? –  Jack M Oct 9 at 14:20
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## closed as off-topic by user72694, Davide Giraudo, azimut, Tom Oldfield, Lord_FarinOct 9 at 15:14

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is not about mathematics, within the scope defined in the help center." – user72694, Davide Giraudo, Tom Oldfield, Lord_Farin
If this question can be reworded to fit the rules in the help center, please edit the question.

I have found the following solution on another forum, however it plays on rules 3 and 4 slightly... If this is not an intended solution (it doesn't fully satisfy me even though it is quite clever), you could say, to counter that use of rules 3 and 4, that, because there is a given pattern (A -> B -> C -> A), the doorknob is present only on one side of the door.

I think the key to this is in:
- the layout of the rooms
- the fact that the doors have doorknobs
- the assumption that when you turn a doorknob, the doorknob turns in both rooms

Each room is square and measures approximately 25 m². 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.

Note that the position of the doors were not stated. For this statement to hold true without a room arrangement, that was too obscure, I pictured it as follows:

The sequence of events is thus:

1) Both the man and woman read the instructions
2) Reading number 5, the man stands up immediately while the woman does not move until she knows the man is up
3) The man walks over to the door, and turns the doorknob
4) The woman sees the doorknob turn. This causes the woman to know that the man is standing up, so she gets up. Note that this does not contradict point 4, which says:

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

This is because the man is touching the doorknob of room A, and the woman is not in room A - she is still in room B.

5) The woman, knowing the man is in room A, opens the door to room C, goes into room C, and closes the door.
6) The man does not know where the woman is at this point in time, so he does not open the door to enter room B.
7) The woman then goes over to the door between room C and A, and turns the doorknob.

Note that this does not contradict point 3, which says:

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

This is because the woman is touching the doorknob of room C, and the man is in room A.

8) The man, seeing the doorknob turn, knows that the woman is in room C. He opens the door between room A and B with confidence.
9) The woman does not know where the man is at this point in time, so she does not open the door to enter room A.
10) The man then goes over to the door between room B and C, and turns the doorknob but does not open the door.
11) The woman, seeing the doorknob turn, knows that the man is now in room B. She opens the door between C and A with confidence.
12) The man does not know where the woman is at this point in time, so he does not open the door to enter room C.
13) The woman then goes over to the door between room A and B, and turns the doorknob but does not open the door.
14) The man, seeing the doorknob turn, knows that the woman is in room A. He opens the door between room B and C with confidence.
15) This pattern goes on until the woman is back in room B, and the man is in room C waiting to enter room A.

16) The woman goes over to the door between B and C and turns the doorknob but does not open the door.
17) The man, seeing the doorknob turn, knows that the woman is in room B. He opens the door between room C and A, walks to the middle of room A and sits down.
18) By this time, a lot of time should remain on the clock. However to be certain, the woman remains standing until the 1 minute signal. She then goes to the middle of room B and sits down.

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I am still very interested in finding a solution to this though... One of the most interesting puzzles I've read so far ! –  Saryk Oct 9 at 14:05
So basically the puzzle boils down to a silly semantic trick on what "the doorknob of a room" means. That's disappointing. –  Jack M Oct 9 at 14:32
Also, doesn't this break rule 6? They're communicating. –  Jack M Oct 9 at 14:33
Well I agree on the fact that they do break rule 6, however if there is no trick as to how they can "communicate" without breaking the rules, there is no puzzle anymore and the answer sums up to somehing like "they are guessing"... Of course there is a brilliant solution, but it upsets me not to have a clue as to how they're supposed to do it ! And this is not a valid answer because it breaks some rules and the solution can be criticized. A perfect solution would abide by all the rules with no nuance whatsoever. –  Saryk Oct 9 at 14:51