# Traversing three rooms

1. Sep 1, 2010

### LAF

A few years ago a tryed to solve this problem. A got some reasonable solutions and one very good solution (I think the central question is to obtain a accurate way to masure time) but I don´t know if it´s the best one. This problem is from sigmasociety.com:

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.

2. Sep 22, 2010

### Caracrist

a man is always sitting, and a woman does it with a signal...

3. Sep 28, 2010

### LAF

Do you think heart beat rate a usefull way for time measuring?

4. Sep 28, 2010

### JaredJames

That's what I was thinking. If they're both 'intelligent', I figured the woman would move straight away and then count a certain amount of beats (assume they know their own beats per minute) to give the man time to move and then she'd move again. The man would initially wait by counting a number of beats for the woman to move and then would move himself and wait.

Repeat this three times and you should have sufficient spacing to end up within your original rooms without breaching the rules.

5. Sep 28, 2010

### D H

Staff Emeritus
This is yet another stupid, ill-formed problem chock full of non-essential information by a bunch of wanna-be smart people.

"The moment that on person touches the doorknob of a room, the other person cannot be in that room any more." What does this mean? Read it "wrong" and there is obviously no solution. So, read it like a lawyer. Are the doors labeled? The problem doesn't say. If they are not it can still be done -- depending on how tricky one is in interpreting the meaning of "The moment that on person touches the doorknob of a room, the other person cannot be in that room any more."

6. Sep 28, 2010

### davee123

Problem is that while it's ~reasonably~ constant for yourself, it's probably not constant for both of you. Plus, given that both their lives are essentially on the line, it's pretty damn difficult not to keep your heart rate from jumping.

One thing that gets me is the part where their cultural backgrounds are specified. What difference does it make that one is Israeli and one is Arab? I'm not sure if that's some sort of silly red herring, or if they're intending (for example) both parties to be familiar with the Islamic practices of praying on a regular schedule, or some other cultural tidbit.

Any way I slice it, I can't think of or conceive that their COULD be an ideal process that the two could conceivably be expected to agree on without ever having even met or communicated. I could believe that it's POSSIBLE-- after all, people are relatively aware of how much time has transpired, even if they're not accurate to the exact second. But I can't fathom how that would be consistently repeatable with different sets of people that are all highly intelligent.

DaveE

7. Sep 28, 2010

### BobG

It doesn't specify how many times they have to traverse the rooms. Once is sufficient.

That gives them 10 distinct actions to perform in 60 minutes. The first action takes place immediately and the last action when there's 1 minute left. That leaves 59 minutes for the remaining 8 actions to be performed, with most of the time being taken to account for any errors in time keeping.

1) Man stands up at time 0:00. Both can be certain of the time the man stands up.
2) Woman stands up at time 1:00. She knows when she's stood up.
3) Woman enters room C immediately.
4) By this time, errors in time keeping could have taken place, or the woman could have tripped and fallen. Man waits until 3:00 to enter room B.
5) Woman can't be certain of man's time keeping or hers, so she waits until 6:00 to enter room A.
6) Man can't be certain of woman's time keeping or his, so he waits until 11:00 to enter room C.
7) Woman can't be certain of man's time keeping or hers, so she waits until 21:00 to enter room B.
8) Man can't be certain of woman's time keeping or his, so he waits until 40:00 to enter room A.
9) Man knows when he's entered room A, so he sits down.
10) Woman sits down at 59:00

Note: Action 8 is the only action that has constraints on both sides (the action has to be completed before 59:00), hence sitting down in the middle of the time period vs allowing a cushion at the beginning of a time period.

A person doesn't need to know their heart rate very accurately for the system to work. Neither has to know the other's time system; they just have to know the person is capable of coming up with a timing system and a logical time plan.

Seeing as how humans naturally think logarithmically, this is a solution that one could expect to be obvious to any intelligent person, which makes it a lousy brain teaser, since the best brain teasers are seldom obvious to anyone. (And not knowing how much time there is before the signal to start is given, only an obvious solution would be guaranteed to work.)

8. Sep 28, 2010

### D H

Staff Emeritus
how does she know which door goes to room C and which goes to room A?

9. Sep 29, 2010

### davee123

I guess I'd be willing to accept that as a solution-- in my heart of hearts I'm still hoping for a more logically fool-proof method. I think my problem in approaching this one is that I'm looking for something that's too perfect. My natural tendency is to throw out any approach that says "they should wait X minutes", since I can't guarantee that accuracy. But admittedly, if I were actually faced with such a problem, I might start thinking in those terms-- IE, not perfect, but good enough to work.

DaveE

10. Sep 29, 2010

### LAF

I bypass the minor "tricky" statements - no problem to identify the doors (and no problemas with the knobs). I try to see he questions as fair as logical.
So, it seems a matter of determine slices of time (8 unknown and 2 known - 10 slices). And to measure time we need a reference. So we can use a medium heart beat rate. The problem of a not sincronized heart beat (what should be the case) is that the difference is greater as the time goes by...

11. Nov 9, 2010

### LAF

Some parts of the solution:

1) there´s no problem to solve the starting and ending movements (stand up and sit down).

2) the man and the woman don´t have an accurate way to synchronize their moves. So they have to use some kind of time increment. Something like while the woman is walking to next room, the man is simulating her movements and “Double” the simulated time before starting his move.

3) the problem of not synchronized time leads to this assertive: they have to finish all moves as soon as possible.

12. Dec 15, 2010

think out side the box.....
the rooms are arranged in a circular pattern, shape is not important. the tip off is 2 doors to each room.

the doors are 'mantrapped' i.e. one doesn't open unless the room is empty.

If they travel in a circle they will satisfy the requirements very easily.

13. Dec 15, 2010

### JaredJames

Where does it say "one doesn't open unless the room is empty"?

It just says they aren't allowed in the same room as each other.

14. Dec 21, 2010

### dilletante

The woman has to make sure the man has stood up first but she knows he will stand up quickly. So she waits a minute or so, then stands up and proceeds directly into room C. The man realizes that the woman is intelligent and is not going to enter A anytime soon (because as you will see, they do have a timer), so he gives it 5 or 10 minutes and enters B.

Now the woman can wait as long as she wants before going into room A, as long as she does it before the one minute remaining signal. So she estimates maybe 30 minutes for safety and goes into A. The man remains in B until the one minute warning signal. So with one minute to go, the woman has long been safely in A and the man enters C immediately.

Now all the woman has to do is wait a few seconds, knowing the man is entering C as fast as possible when the warning light goes on. She then enters B. The man has the better part of a minute to enter A -- it would be perfectly safe for him to count to 30 and then enter.

The only timer they need with any accuracy is the one provided by the designers of the puzzle -- the one minute warning light.