## Alien abduction

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ejsantos
Posts: 3
Joined: Wed May 22, 2013 12:49 pm UTC

### Alien abduction

Hey all, this is my first post here, but I've been following XKCD and the forum for some time.

This puzzle has been tormenting me for quite a while now. I don't really know the correct answer, but I'd like to think I got far before getting stumped.
So I decided to share with you guys and gals:

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.

Posts: 1267
Joined: Thu Jun 16, 2011 6:36 pm UTC

### Re: Alien abduction

Do they know the layout of the three rooms? The woman must initially pick a door to walk through, but I don't see how that could be anything but a 50/50 proposition unless they know the layout. So I'll assume they know the layout.

So if I understand the problem, there is a series of tasks, and each task must end before the next one begins:
1. Man stands up
2. Woman stands up
3. Woman goes from B to C
4. Man goes from A to B
5. Woman goes from C to A
6. Man goes from B to C
7. Woman goes from A to B
8. Man goes from C to A
9. Man sits down
10. Woman sits down

Spoiler:
The first and last step will be taken immediately following both lights. Therefore steps 2 and 3 can be taken immediately following the first light + a tic. Steps 4-9 are the trick. The man has to know how long the woman will take with steps 2, 3, 5, and 7, while the woman will have to know how long the man will take with steps 4 and 6.

If I were thrown in the situation, I'd simulate the other person's tasks (without actually touching doorknobs and stuff), and do everything a bit more slowly than would be natural. It's reasonable that they would do it right once, and then once they have a proven plan they can repeat it 10 more times easily enough.

If the woman can leave behind a note, then do that.

Lopsidation
Posts: 183
Joined: Tue Oct 27, 2009 11:29 pm UTC

### Re: Alien abduction

Can they
Spoiler:
open a door without touching the doorknob?

If the puzzle has general no-cheating rules, the only obvious thing they can choose is how long to wait between each door. They just have to hope the other person chooses a time close to theirs. So, the task is like a round from the not-very-fun Psychic Game. (Psychic Game: a group of people picks a category. You each secretly choose an object from it. The goal is to be in the plurality.)

Personally, I would choose
Spoiler:
1 minute. It's very common culturally, not hard to count to reliably, and also, the directions mention it in Step 8.

So, I'd wait 5 seconds before standing up and opening the first door, and then wait 1 minute between each subsequent door. (If I were the man, I'd stand up immediately, wait 30 seconds before opening the first door, and then use the same strategy.)

But it looks like I would die (?) if I were up with Adam H. I guess we should determine the answer to this puzzle by majority vote.

dudiobugtron
Posts: 1098
Joined: Mon Jul 30, 2012 9:14 am UTC
Location: The Outlier

### Re: Alien abduction

It seems like the puzzle wants there to be a solution where if both people did the right thing, then they are basically certain of victory. I don't think there can be one, though. If not, then as Lopsidation says, it's just the psychic game.

One question I have though - do they need to stand up? It seems like they could complete the puzzle sitting down and dragging themselves along the floor. I doubt this would make it easier, just wanting to clarify.

Anyway, here's what I would do:
Spoiler:
The man is intelligent so he will stand up immediately.
The woman knows that he will stand up immediately, and so can stand up with relative impunity after a short time.
Then since she is intelligent, she will go to the next room immediately.
The man knows the woman will do this, so, after waiting a short time, he knows he is free to go to the next room.
etc etc as per Lopsidation's answer.

The problem is that they can't necessarily tell time reliably, and they don't necessarily walk at the same speed etc... So really, it's just a guessing game.

And here's my guess at what really happened:
Spoiler:
They both chose a strategy, and the two strategies happened to align well. So the next 10 times they just kept the same strategy, since they were confident of its success.

wraith
Posts: 103
Joined: Mon Aug 06, 2007 6:58 am UTC
Contact:

### Re: Alien abduction

Does the signal last a noticeable amount of time?

If when the lamps are lit, they stay like that for 5-6 seconds, I could well use this to my advantage.

Let's say like so:

Spoiler:
-- begin signal --
man stands up
-- end signal --
man goes next to door to room b
woman stands up
woman goes to room c
woman goes right next to door to room a
-- wait --
-- begin signal --
man goes to room b
stays next to door
-- end signal --
man starts running to door to room c
meanwhile woman goes to room a as fast as possible
both run in the required direction
man enters c
woman enters b
man enters a
man sits down
woman waits for some time
woman sits down

Not perfect but I think it has fewer possibilities for making an error. I think I can make an even better one, provided the signal lasts for some time.
It's only when you look at an ant through a magnifying glass on a sunny day that you realize how often they burst into flames

ejsantos
Posts: 3
Joined: Wed May 22, 2013 12:49 pm UTC

### Re: Alien abduction

Well, I would say that you could break it down as two different problems:

1 - Which door leads where (layout)
2 - How to solve the timing issue

Problem #1 could be avoided as simply stating that they know which door leads where, but think about it for a second:
There is only one possible way to arrange 3 interconnecting square rooms. That way leads to one of the rooms being noticeably different than the other two.

Spoiler:
Where would you place the doors in that one arrangement? You could say that the different room is 'Z', and the similar ones are 'X' and 'Y'. Under certain door arrangements, 'X' and 'Y' are subtly different to each other, which causes one to be able to know which door leads where. That depends however on which room is room C, and the exact door location leading from 'X' to 'Y'.

This makes me think that under at least some conditions, problem #1 can be solved.
Spoiler:
If either the man or the woman begins in room 'Z' I don't think it is solvable.

But then,
Spoiler:
I guess that since the instructions say it is possible, it has to be one of the solvable door arrangements.

Now Adam H has a nice breakdown of the timing issue.
Spoiler:
You are right in that some steps have to be carried out immediately.

However, no communication allowed!
Also, wraith's idea is interesting, but it still does not avert the main problem.
And yeah, not standing up would make it more difficult. But I guess the stand up/sit down part is the easy one.

ejsantos
Posts: 3
Joined: Wed May 22, 2013 12:49 pm UTC

### Re: Alien abduction

I guess the trickiest part on Adam H's breakdown are steps 4 and 5:

1. Man stands up
2. Woman stands up
3. Woman goes from B to C
4. Man goes from A to B
5. Woman goes from C to A

6. Man goes from B to C
7. Woman goes from A to B
8. Man goes from C to A
9. Man sits down
10. Woman sits down

The rest is easy.

Posts: 1267
Joined: Thu Jun 16, 2011 6:36 pm UTC

### Re: Alien abduction

ejsantos wrote:I guess the trickiest part on Adam H's breakdown are steps 4 and 5
Spoiler:
Eh, you know that step 3 will be taken basically immediately, therefore step 4 is just a matter of waiting as long as you think step 3 takes plus a bit for margin, and then immediately doing step 4. Then since you know that step 4 will be taken basically immediately after step 3, step 5 will be taken as long as you think step 4 takes plus a bit for margin. I would imagine step 6 and 7 is much harder than 4 and 5. Imagine if you are the woman waiting in A, trying to determine whether it's safe to go in B (step 7). She needs to determine how long the man took to do step 6, which is based on how long the man thought the woman took to do step 5, which is based on how long the woman thought the man took to do step 4. So she is estimating how long the man thought the woman thought the man thought the woman took to do step 3.

Below are the steps and how long it takes for each step.

1. Man stands up (~0)
2. Woman stands up (~0)
3. Woman goes from B to C (tw)
4. Man goes from A to B (tm)
5. Woman goes from C to A (tw)
6. Man goes from B to C (tm)
7. Woman goes from A to B (tw)
8. Man goes from C to A (tm)
9. Man sits down (~0)
10. Woman sits down (~0)

tm=tw-e
tw=tm+e

The man knows tm, the woman knows tw, and e is the difference between the two that neither of them know.

So the man needs to do step 4 between time tm+e and 2tm+e. The woman needs to do step 5 between time 2tw-e and 3tw-e. The man needs to do step 6 between time 3tm+2e and 4tm+2e. The woman needs to do step 7 between time 4tw-2e and 5tw-2e. The man needs to do step 8 after time 5tm+3e and before the end light flashes.

If their estimates of e are reasonable, or biased similarly, I think this is quite doable. Example: if tm = 12 seconds, tw = 12 seconds, the man thinks tw is 15 and the woman thinks tm is 9 (pretty extreme example), then:
4. 15-27
5. 21-33
6. 42-54
7. 42-54
8. 69-end

Step 7 will naturally be taken at the high end of the range, since there's no reason for step 8 to be taken for a long time. So I think this is a worst case scenario that still gives a decent chance for success.

The above is over-simplified because it assumes that the time from touching the doorknob to flinging open the door to jumping in the next room to slamming the door is negligible.

Layout:
Spoiler:
Yeah, you can determine whether you are in X/Y or Z, from the layouts below. But the players can't distinguish between X and Y. Imagine you are one of the players in X or Y. You face the corner of the walls with the doors on them. There are two ways of distinguishing between the two doors in these rooms - right/left and the distance to the corner. But as drawn below, the left door in Y leads to not-Z, while the left door in X leads to Z, and the closest door to the corner in Y leads to not-Z, while the closest door to the corner in X leads to Z.

(Also, I'm assuming you aren't going to allow loopholes like long doorways/hallways, non-euclidean geometry, etc.)

And even if the doors were positioned in a way that the man and woman could tell they are in X, Y, or Z, and they also know which doors lead to X, Y, and Z, that says nothing about how [A, B, C] is mapped onto [X, Y, Z].

Code: Select all

` _____   |     |      |  X  |  |     |_____|__.._:     | |     |  Z  ||  Y  |     | |     :_____|      |_____|       `

I really think the solution is basically "they got lucky the first time, then repeated their strategy the next 10 times."

eulerIV
Posts: 29
Joined: Sun Nov 18, 2012 1:49 pm UTC

### Re: Alien abduction

I think I know the "solution", it helps to know that this was originally an item in a supposedly "extremely high IQ test", and also that I have seen this puzzle posted to many fora but noone has a clear solution (or none that I found when I googled this puzzle 3 years ago). So my guess is that its some experiment to test whether people with really high IQ would agree on their solutions, and if they did, the item could function as any other item in the test, maybe there are multiple levels of solutions correlating with IQ. In any case it would be an interesting experiment if you had a really large sample.

ThirdParty
Posts: 351
Joined: Wed Sep 19, 2012 3:53 pm UTC
Location: USA

### Re: Alien abduction

The puzzle was vague about whether we know the layout of the rooms. If not:
Spoiler:
Since the woman knows she's starting in B and the man knows he's starting in A, the only variable is whether the rooms are arranged clockwise or counterclockwise.

There's nothing to be done about the 50% risk of losing by guessing wrong. However, we do want to avoid the risk of losing by guessing something different from one another; we should try to coordinate on a salient direction.

The salient direction is clockwise, for various reasons including the following:
• Since we're trying to synchronize, we wish that we had clocks.
• Sitting in the center of the room waiting for the signal, and looking in a direction such that both doors are in my field of view at once, I naturally picture my partner coming out of the one on the right and moving to the one on the left, since the Hebrew and Arabic alphabets both go right-to-left.
• After passing through a door, I arrive in a room which is completely featureless except for its second door. I prefer that this single feature be on my right, because of the English expression "right is right" (English is a universal language), because cars drive on the right throughout the Middle East, and because most humans are right-handed.

Timekeeping:
Spoiler:
I'm going to time my actions in seconds, which are the SI unit for time and which can be measured by feeling my own pulse. A normal human heartbeat, when not engaged in strenuous exercise, has a frequency of about 1 per second.

Obviously, if I know that my heartbeat runs fast or slow, I will attempt to correct for that. And if there's some phrase, song, or prayer that I know takes me a certain length of time (e.g. the word "Mississippi"), I'll use that as a supplement.

Scheduling (the puzzle was vague about whether signals have duration, but I'll assume they don't):
Spoiler:
There are eight steps that have to be performed without overlapping:
1. The man stands.
2. The woman stands, walks about 3m to the door, and goes to the next room, which is hopefully C.
3. The man goes to the next room, B.
4. The woman goes to the next room, A.
5. The man goes to the next room, C.
6. The woman goes to the next room, B.
7. The man goes to the next room, A, walks about 3m to the center, and sits.
8. The woman sits.
There are unfortunately a lot of possible approaches that could be taken here, and we have no way to coordinate. Our only hope is to luck out by thinking similarly.

One option is to move (and allow my partner time to move) at a normal pace after the start signal, and hope to stay roughly in sync. I don't like this option. We might lose even if we both choose it, if our definitions of what's "normal" when one has just been abducted by aliens turn out to be too different from one another's.

A second option is to space the steps out in an arithmetic sequence across the available hour, so that there's as big a buffer between each one as possible. There's going to be a question of whether to allow a whole interval after Step 1, since it's relatively simple and since it occurs at the very beginning when the timing is easier, and whether to allow a whole interval after Step 7, since the existence of the warning signal after 3540 seconds makes it fairly safe to wait until the last moment to perform Step 8. And there's going to be a question of whether to allow an extra interval for Steps 2 and 7 since they're longer. So here are some arithmetic sequences that all strike me as plausible:
1. 0, 510, 1020, 1530, 2040, 2550, 3060, 3570 (arithmetic sequence)
2. 0, 010, 0605, 1200, 1795, 2390, 2985, 3580 (arithmetic sequence, without alotting significant time for "stand up" at the start)
3. 0, 010, 0715, 1420, 2125, 2830, 3535, 3570 (arithmetic sequence, treating "stand up" and "sit down" as non-steps)
4. 0, 395, 1185, 1580, 1975, 2370, 2765, 3555 (arithmetic sequence, with double intervals for the two complex steps)
I'd go with something like (b), which wins when paired with any of the above.

A third option is a geometric sequence. This is a good idea if we're not sure how reliable our timekeeping method is; it gives us good odds of success even if my "second" is significantly different from my partner's. If we're worried about timekeeping then we should definitely plan to perform Step 7 at the warning signal so that we don't have to count the high numbers. Here are some plausible geometric sequences:
1. 0, 10, 032, 104, 338, 1094, 3540, 3570 (anything steeper than this would risk failing to leave enough time to comfortably complete Step 2)
2. 0, 30, 078, 202, 525, 1363, 3540, 3570 (half a minute makes a good intermediate number)
3. 0, 60, 135, 306, 692, 1566, 3540, 3570 (sixty is a salient starting point because the "minute", while not an SI unit, is nevertheless widely used)
Once again, (b) wins when paired with any of the others, so something like that is the best choice.

I'm honestly not sure which of these to go with. "Move at a constant pace" is a fairly salient thing to do when trying to coordinate with someone--again, imagine yourself imitating the hands of a clock--but on the other hand the instructions specifically mentioned the lack of timekeeping and that raises the salience of a plan designed to ameliorate that problem.

ilpinto
Posts: 7
Joined: Thu Aug 08, 2013 6:50 pm UTC

### Re: Alien abduction

hi, i'm happy to see that i'm not the only one who struggled to solve this problem, long time ago i tried to solve it, but i'm still not so convinced about my solutions, i already came up with all the ideas you explained above, even the one related with the heartbeat to measure time.
i'd like to share my ideas and see what do you think about

the most straightforward solution is in my opinion the one with the use of 2 time scales, a short one and a long one:
Spoiler:
1. lights are on, the man stands, the woman wait a ''short time'' and stands up and walks in the C room, the man approaches B-room door
2. lights are off, the man enters B room, the woman waits a ''short time'' and goes in room A, after that the man waits a ''long time'' and goes in room C (the woman approaches B-room door)
3. lights are on, the woman goes in room B, the man waits a ''short time'' and goes in room A and sits in the center of the room
4. lights are off, the woman sits in the center of the room B

sadly, we don't know if the ''short time'' is bigger than the time for the lights to turn off, and we don't even know if the lights will turn off after they are lit on the 59th minute, so it's not a convincing solution. about this last problem the solution can still be modified to make it works even if the lights will not turn off..

second solution:
Spoiler:
the signal is said to be the lights lit almost instantaneously, but in the puzzle it is never said that the lights turn off simultaneously, this could give enough signals to separate in time every action to solve the puzzle, but given this, we should remember that we don't have the confidence that the lights behave in a determined way, they even can turn on and off randomly until the 59th minute when they have to give the simultaneous signal.. it's unlikely to be the right solution but certainly it is the one with the less arbitrariness

and finally about the room disposition:
Spoiler:
it is said that the rooms are square of 25m2, etc, but it is never said that they are all at the same altitude, if it can be considered a room ''square'' if the perimeter is square, than the C room can be a square that contains the A and B room that are disposed vertically, given that C room can be a square of about 5*2^(1/2) m side so it's area is 25m2 if we eliminate the 25m2 of the A and B room that cross inside C room, and it is possible that the doors are disposed in such a way that one inside room B or A can figure out which is the C room, because it has to be the one where you can sit at the center (the C room in this case doesn't have a center..).

i'd like to know your opinions about my ideas, maybe i have forgotten something, but this are things i came up something like a couple of years ago,
ps: sorry if my english is bad, i'm not used to it D:

Tormod
Posts: 5
Joined: Sat Apr 27, 2013 3:34 am UTC

### Re: Alien abduction

I think I'd die because my solution is different from all of yours :S

Useing Adam's breakdown the critical events are the room swaps. There are 6 of them and there are 2 signals. I'd split the moveing into 2 parts and do 3 switches at the first cue and 3 switches at the last cue.

1. Man stands up
2. Woman stands up
3. Woman goes from B to C
4. Man goes from A to B
5. Woman goes from C to A
6. Man goes from B to C
7. Woman goes from A to B
8. Man goes from C to A
9. Man sits down
10. Woman sits down

So signal:
Man stand, women count to 2 stand and move to next room, man walks slowly to the door and goes to the room, after a long delay the woman would go from C to A.

Then I'd wait for ~ an hour and when the 2nd signal comes, the man would imidiatly carry out step 6, the woman would wait a few seconds, carry out 7, the man would carry out 8 and 9, and the woman 10.
Trusting yourself to count the woman will be reasonable sure to sit after the man if she sits down with say ~10 sec left on the clock.

In my mind this would reduce the risk of ever beeing in the same room, my 2cents.

ilpinto
Posts: 7
Joined: Thu Aug 08, 2013 6:50 pm UTC

### Re: Alien abduction

the point here is not to choose a feasible solution, because many of the above options are acceptable if the man and the woman are allowed to communicate before the task, but it's not the case, so the right solution should be one that would be the most reasonable and rational, if the man chooses a solution that brings them at step 7 before the ending signal and the woman chooses a solution that brings them at step 6, both the solutions could seem feasible but at the end they would end up failing because they didn't thought the same solution.. so the right one not only has to be feasible but it has to be the least arbitrary of them

Who
Posts: 108
Joined: Wed Oct 02, 2013 2:53 am UTC

### Re: Alien abduction

1. Man stands up
2. Woman stands up and goes from B to C
3. Man goes from A to B
4. Woman goes from C to A
5. Man goes from B to C
6. Woman goes from A to B
7. Man goes from C to A and sits down
8. Woman sits down

Given how there is no reliable way to count time I would not count it arithmetically. My first instinct would be to perform 1 instantly, 2 after 5-10 seconds, 3 after 20-30 seconds, 4 after 50-60 seconds, 5 after one minute to 59 minutes, 6 immediately after the signal, 7 after 10-20 seconds, 8 after 30-40 seconds.

Ways this could go wrong:
Other person does things arithmetically or some other way. (Looking at everyone else's solutions, I would not go home)
Man takes more than 5 seconds to stand up (Shouldn't happen)
Other person performs step 2 after more than 20 seconds (No reason for them to wait that long)
Timing error on step 4 (Shouldn't conflict with step 5 because step 5 has a huge window, shouldn't conflict with step 3 because counting should still be reasonably reliable after 20 seconds. They shouldn't pick timing which makes it go wrong because assuming 5/3 step 5 happens after a long amount of time which doesn't matter, step 3 happens after some easily countable amount of time, they can assume that 2 should be done reasonably quickly so 3 is anywhere in between reasonably quickly and the upper limit of countable, 4 is at the upper limit of countable, 5 is arbitrarily long)
Other person decides that it is better to have a wider window but longer times (Does things on the scale of minutes, which I ruled out because counting is unreliable then)
Not given enough time to think it through (My first instinct was to do instant, after seconds, after minutes, but that did not give enough times. Had I been put into the room and told "go" I would have failed.)
Other person decides that 6/2 is better than 5/3

Craig Manson
Posts: 1
Joined: Thu Nov 14, 2013 7:51 pm UTC

### Re: Alien abduction

In order to deal with the time periods you have to consider the fact that any inaccuracies of the perception of time are multiplacative. Ie the man might count seconds 50% faster than the woman - this means using fixed 1 minute time periods will quite quickly fail.

Therefore the way to do it is with time periods which double - this should encompass the maximum expected difference between 2 peoples counting of seconds. In order to keep it simple you can do this starting with a 1 minute increment and you get the following:

Man stands up instantly
1m Women stands up and goes from B to C
2m Man goes from A to B
4m Women goes from C to A
8m Man goes from B to C
16m Woman goes from A to B

At this point the timing of when the man goes from C to A is unimportant - on 32 minutes or on the 1 min to go warning. The woman just has to wait 30s after the 59m light to sit down to cover either eventuality.

32m-59m Man goes from C to A and sits down quickly
59m+30s Woman sits down

Simple!

Posts: 1267
Joined: Thu Jun 16, 2011 6:36 pm UTC

### Re: Alien abduction

Dammit people, if your solution doesn't work with my solution (which is obviously the most intuitive solution), then you're killing me. So get your shit together.

SPACKlick
Posts: 195
Joined: Wed Apr 03, 2013 11:25 am UTC

### Re: Alien abduction

Craig Manson wrote:In order to deal with the time periods you have to consider the fact that any inaccuracies of the perception of time are multiplacative. Ie the man might count seconds 50% faster than the woman - this means using fixed 1 minute time periods will quite quickly fail.

I looked at this and figured as follows. There exists some n such that the rate at which 95% of individuals counts time x is between t/n and nt.
If we assume 0 time for completing actions, which we'll adjust later. And we lock action 7 to the 1m signal marker
Action 6 should be aimed for 59/n minutes.
Action 5 should be aimed for 59/n^3 minutes.
Action 4 should be aimed for 59/n^5 minutes.
etc.
Where n = 2 this gives Target time/earliest time/latest time
1 @ 0:00:00 / 0:00:00 / 0:00:00
2 @ 0:00:07 / 0:00:03 / 0:00:14
3 @ 0:00:28 / 0:00:14 / 0:00:55
4 @ 0:01:51 / 0:00:55 / 0:03:41
5 @ 0:07:23 / 0:03:41 / 0:14:45
6 @ 0:29:30 / 0:14:45 / 0:59:00
7 @ 0:59:00 / 0:59:00 / 0:59:00
8 @ 0:59:30 / 0:59:15 / 1:00:00

This slightly ignores the fact that counting a gap like (4) to (6) is more variable than the gap between (1) and (3). And as I said above you need to factor in movement times through doors. Traversing rooms can be done on others time (the tightest is 28seconds for the man to get up and get to the door). Now I can't comment on what n is sensible for people to choose but if my partner chooses an n significantly different from mine we're screwed. Without some population study on what peoples estimates of the time variance of others is I don't see how it can be mathematically improved.

twinsen
Posts: 82
Joined: Tue Jan 06, 2015 9:57 am UTC

### Re: Alien abduction

Spoiler:
1. Man is clever, he is up. M - W - C
2. Woman is clever, she stands after a moment, and runs to C. M - B - W
3. Man walks to the door, then goes back to the center, then walks to the door, then back to center, then back to door and enters. A - M - W
4. Woman walks to the door, walks to center ( 30 times.) Then enters A. W- M- C
5. One minute left signal, man is clever, he enters C immediately and runs to A. W - B - M. (Edit, or walk. I didnt get the layout, if there are no corridors, its walk)
6. Woman is clever, she enters room B after a moment and gets into the center. A - W - M.
7. Man quickly gets to A and sits. M - W - C
8. Woman waits a while and sits. M - W - C

What I expect.
1.Woman to be able to determine time in interval(1;3)s.
2.Woman to be able to determine time in interval(20;60)s.

In other words, if I ask her: how much time has passed since the light is on?
she should be able to tell me: " Between 1 and 3 sec." or "Between 20 and 60 sec".
I dont think I ask much.

Edit: Its actually more like asking her to turn on the lamp after 1 to 3 sec, or after 20 to 60 sec, becouse determinating time is harder,
than giving estimates. I want her to give estimate.

The Fantasist
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### Re: Alien abduction

Okay, maybe this is totally and thoroughly stupid, and maybe I'm just not understand something simple, but I'm asking anyway:
How are these rooms connected?
At first I assumed a circle, so each room could lead into both others. But then I reread the problem and read that they were all square and of equal size. Okay, this knocked out all my guesses as to their configuration. Are they bent through another dimension or something?

SPACKlick
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### Re: Alien abduction

The Fantasist wrote:Okay, maybe this is totally and thoroughly stupid, and maybe I'm just not understand something simple, but I'm asking anyway:
How are these rooms connected?
At first I assumed a circle, so each room could lead into both others. But then I reread the problem and read that they were all square and of equal size. Okay, this knocked out all my guesses as to their configuration. Are they bent through another dimension or something?

-[]-
[][]

The Fantasist
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### Re: Alien abduction

I feel stupid now.
Tehe, thanks. By the way, is there actually a solution to this? I see a lot of attempts but no straight answers.

Wildcard
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### Re: Alien abduction

Interesting that none of the solutions posted so far make use of the fact that the people are, very specifically:
ejsantos wrote:An Arab man and an Israeli woman

Given that the actual question in the puzzle is not "describe an optimum strategy" or "what strategy would YOU use?" but is instead:
ejsantos wrote:Describe the method they used and the way of thinking of both of them.

...it seems to me that it isn't SO much a logic puzzle or a game theory question as it is a cultural knowledge puzzle. I'm not criticizing its inclusion in the "Logic Puzzles" forum, by the way—just clarifying that I think the actual solution depends less on mathematical prowess or knowledge of game theory than it does on knowledge of the differences in cultures involved here. So maybe something about circling the room in some particular direction before opening the next door? Make use of the fact that the dimensions of the room are known?

That being said...I still think the answer is indeterminate. There's no way to "check" any given answer and I seriously doubt there is any answer that would be very obviously "correct". To me, that makes it more of a lateral thinking puzzle than a true logic puzzle.

Actually, you know what I think the real answer is? And it is a TOTAL lateral thinking type answer, but I feel it is exactly correct because it very specifically makes use of the info given in the puzzle. Here it is:
Spoiler:
Lopsidation is right. They open the doors without touching the doorknobs. There is nothing in the puzzle that disallows them being in the same room at the same time, or even seeing each other. There is only a clause that prevents them from TOUCHING the doorknob. It doesn't say they may not open the door of a room while the other person is in that room. Tricky wording, maybe. But that's the way it's written. SO...

The Arab man uses the cloth from his turban so he doesn't touch the doorknob directly.

Okay, having written all that, I came up with an even better method which, although it makes no use of the data about their ethnicity, is more intellectually satisfying to me. It still makes use of a loophole...
Spoiler:
Clauses 3 and 4 very specifically refer to the MOMENT when the doorknob is touched. Also, nowhere in the rules is it specified that you can't OPEN a door in the wrong direction, so long as you don't walk through it.

So, the man gets up in room A and TOUCHES the doorknob to room C. He waits for a minute or so, to allow the woman to go from room B to room C, and then opens the door. The woman then walks from room C into room A to join the man. He closes the door. They go together into room B and the woman stays there. Then the man goes from room B to room C to room A and sits down. Once the ending light signal shows, the woman sits down.

(Incidentally, if rule 6 is interpreted to mean that it is physically impossible to open 2 or more doors at once, rather than merely disallowed, this method becomes even easier because the "waits for a minute or so" becomes irrelevant as he physically can't break the rules if he tries to open it too soon.)

I think this IS the solution because (a) although using it as a strategy may not be a good idea, since the probability of the other person picking it also is low, we are given a fait accompli that they DID succeed 10 times and survive. So probability is irrelevant—we are asked to describe the method they *used*, not what they *should have* used in our opinion. (b) If the man's timing was right, he could make the strategy work even if the woman hadn't thought of it. If he just guessed correctly when she would have entered room C and then he opened the door before she could make them lose by touching the doorknob to room A, then he could pull it off.

I'd be interested to hear other people's thoughts on this.
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### Re: Alien abduction

Wildcard wrote:
Spoiler:
Clauses 3 and 4 very specifically refer to the MOMENT when the doorknob is touched. Also, nowhere in the rules is it specified that you can't OPEN a door in the wrong direction, so long as you don't walk through it.

So, the man gets up in room A and TOUCHES the doorknob to room C. He waits for a minute or so, to allow the woman to go from room B to room C, and then opens the door. The woman then walks from room C into room A to join the man. He closes the door. They go together into room B and the woman stays there. Then the man goes from room B to room C to room A and sits down. Once the ending light signal shows, the woman sits down.
Spoiler:
I don't know that the rules allow this. The man keeps touching the doorknob to room C, so there are lots of moments (up until the man stops touching the doorknob) that the woman cannot be in room C. The rules don't say the moment one of them FIRST touches the doorknob.

Also, they still have to get kind of lucky with the whole two doors at once thing. I think my answer of "just traverse the damn thing normally" is not significantly more difficult.

And lastly, nothing says these aliens are bound to uphold loopholes. I'm assuming English isn't their first language. Their solution to a misunderstanding might be to just kill both participants. A lateral thinking solution would have to be airtight. Using the turban to open the doorknob is pretty good because it seems intentional that the rules avoid saying that the two participants cannot be in the same room at the same time. But I don't like your interpretation of rules 3-4.

SPACKlick
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### Re: Alien abduction

Some thoughts,
Have we missed the step where they identify in the first instance which door is which?

Spoiler:
To the lateral thinking solutions above, I'd suggest you re-read rule 6) as I believe you violate it at times. The two of them seeing eachother is communication.

I think a solution might be to blindfold themselves and wrap their hands but that doesn't guarantee you rules 5 and 10 but it takes the 10 step solution above down to

1) Man stands
2) Woman stands
3) They both lap rooms without touching door handles or communicating
4) Man sits
5) Woman sits

Spoiler:
Should we be reading something into the phrasing of rules 3 and 4
The moment that the man touches the doorknob of a room, the woman cannot be in that room any more?

Wildcard
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### Re: Alien abduction

Wildcard wrote:
Spoiler:
Clauses 3 and 4 very specifically refer to the MOMENT when the doorknob is touched. Also, nowhere in the rules is it specified that you can't OPEN a door in the wrong direction, so long as you don't walk through it.

So, the man gets up in room A and TOUCHES the doorknob to room C. He waits for a minute or so, to allow the woman to go from room B to room C, and then opens the door. The woman then walks from room C into room A to join the man. He closes the door. They go together into room B and the woman stays there. Then the man goes from room B to room C to room A and sits down. Once the ending light signal shows, the woman sits down.
Spoiler:
I don't know that the rules allow this. The man keeps touching the doorknob to room C, so there are lots of moments (up until the man stops touching the doorknob) that the woman cannot be in room C. The rules don't say the moment one of them FIRST touches the doorknob.

Also, they still have to get kind of lucky with the whole two doors at once thing. I think my answer of "just traverse the damn thing normally" is not significantly more difficult.

And lastly, nothing says these aliens are bound to uphold loopholes. I'm assuming English isn't their first language. Their solution to a misunderstanding might be to just kill both participants. A lateral thinking solution would have to be airtight. Using the turban to open the doorknob is pretty good because it seems intentional that the rules avoid saying that the two participants cannot be in the same room at the same time. But I don't like your interpretation of rules 3-4.

Dammit, I just wrote a medium-length reply to this and my browser lost it. Here goes again.

Again I'll point out that any possibility that "in case X the aliens might have decided to just kill both participants" can be ignored, because the aliens didn't kill the participants. We're given a fait accompli, not a future situation to plan for. In essence, the true answer to the puzzle is that
Spoiler:
they got lucky, because aliens capable of dreaming up such arbitrary rules are obviously capable of arbitrarily changing their minds and killing both participants regardless of their actions.
Spoiler:
Rules 3 and 4 specify THE moment, not AT ANY moment. There are two definitions of "touch" which could apply; one is "to come into contact with" and the other is "to BE in contact with." Only the first definition can fit the context here. But I will grant that I'm ignoring the last part of those rules which say "any more"...because that phrasing involves assumptions which I am violating, though they aren't stated to be required.
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kamenf
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### Re: Alien abduction

Wildcard wrote:Interesting that none of the solutions posted so far make use of the fact that the people are, very specifically:
ejsantos wrote:An Arab man and an Israeli woman

Probably it is important not what those people are but what they are not - they are not native English speaking, while the instructions are in English (at least we read them in English).

Spoiler:
And in that line of thinking I am curious (sorry, I am not native English speaking too) how exactly 3 and 4 could be interpreted literally:
The moment that the woman/man touches the doorknob of a room, the man/woman cannot be in that room any more.

Can this be interpreted as: "If the doorknob of a room is touched by one and if the other is in that room, that other should go out of that room (sometimes) after this moment of touch."?

There are a lot of conclusions that the man and the woman can not be in the same room at the same time, but reading all very carefully (and especially having in mind the above) I can not see any indication that such conclusion is valid.

Further in the same line of thoughts:

rmsgrey
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### Re: Alien abduction

The answer is clearly that they each came up with a strategy that was compatible with the other's strategy. Since both intended timings and errors in timing are, to an extent, arbitrary, the best either can do in coming up with a strategy is to come up with one that's compatible with a wide range of reasonable strategies from the other person.

I don't think anyone has come close to coming up with a compellingly superior strategy for either participant, so I doubt it's possible to improve on a reasonable guess plus a bit of luck.

As has been observed, the repetition only matters if their strategies are only semi-compatible, with the errors in timing some actions potentially overlapping - with each having a proven strategy, there's no reason not to stick to it, so it's only the random variations in timekeeping that could mess them up.

XKCD member
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### Re: Alien abduction

I think this puzzle could be more symbolic than that there is an actual solution.
The puzzle states that an Arab and Israeli are in a complex situation with many constraints - mainly about communincation; this is resolved somehow and the 2 cultural antagonists live happily ever after and convert to a more or less obscure religion.

If you rewrite the puzzle:
Arabs and Israel are in a complex situation due to religious/historical reasons.
Given all constraints around this situation (communication hard; physical constraints; first mover-problem) we inform you that they have found a solution, made peace and have set aside their issues, eliminating root causes of the problem.

Now, provide a solution that enables this to-be situation.

quintopia
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### Re: Alien abduction

I agree that the puzzle is mostly symbolic, but it's still fun to think about.

Here is a possibility if we make some additional assumptions:

Spoiler:
1) The man stands up immediately and tears up his clothes (or unravels a turban or whatever) and binds the door handle of door C (which just happens to be the lever type) so that it is always held unlatched. Alternatively, he shoves bits of clothing into the latch catch so it can't latch even when it is closed. (The latter makes fewer assumptions, but is riskier because it requires opening a door to a room the woman may be in. He should not attempt it if it would take him more than a few seconds to accomplish.)
2) Meanwhile, the woman scoots on her tush to door C, opens it and goes inside. (She doesn't know whether the man is in good health, and so will put off standing until the last possible second that she can feasibly stand up and sit down again.)
3) Both know that the man couldn't know whether the woman had left B yet, and the obvious Schelling point is the one-minute-remaining signal, so she expects he will not assume she has left until this signal comes.
4) The man stands at the door B, eyes closed, with his head angled towards the light. He is waiting for his eyelids to light up, but he doesn't want to see anything that happens in the room. He is nearly blind, deaf, and dumb.
5) The woman scoots across room C to the other door, closes her eyes, and leans on it, hoping the man has orchestrated some method for her to get in without touching the doorknob. The fact that it works does not convey any information about where the man is, nor does it give her any information of any other sort, as she can't even rule out that the door latch is busted. At no point does she open her eyes or feel any part of the door or latch, just in case he has left something there that could constitute communication. After she scoots inside, she immediately pushes the door closed and sits facing it, her eyes still closed, angling her head toward the lamp.
6) The one minute warning light turns on and the man immediately enters room B and closes the door behind himself. He opens his eyes and heads to the door of room C. He doesn't know if the woman figured out the door trick, so he counts 20 seconds on the off-chance she was waiting for the warning light before entering room A. Then he opens door C, enters, and closes it. He spots the door to room A immediately, closes his eyes and charges toward it. He does not touch the knob, knowing the latch is still held open, on the off-chance the woman is still inside. He pushes it closed quickly with his shoulder again, in case the woman was still inside and is about to open door B. (If she happened to open door B when he came barreling in, they are sunk, but he spent no more than two seconds inside room C, so he thinks it unlikely.) He takes two paces toward the center of the room and sits down.
7) Upon seeing the warning light, the woman stands. There is no chance the man hasn't stood by now, and if he hasn't, they are screwed anyway. Squeezing her eyes tighter to block out even the light of the lamp, she stays pressed to the wall, moving towards the other door, just to avoid bumping into the man in case he is in the room. When she feels the edge of the door frame, she stops, avoiding feeling the door. Meanwhile, she has been keeping a mental count. When the count hits 45 seconds, she steps in front of the door, finds the handle, opens it, steps through, closes it, opens her eyes and runs to the center of the room to sit down.

As far as I can tell, this does not violate any rules, and at no point requires either man or woman to make unpredictable assumptions about the other. To summarize, here are the assumptions they made:
-The man assumes the woman takes less than 20 seconds to open a door, move through it, and close it. Even scooting on your butt, it should be possible for any healthy human under the age of 50 to achieve that.
-The woman assumes that the man can cycle the rooms in under 45 seconds, start to finish. Given that each room is only 5 meters across, even a relatively weak human under the age of 50 should be able to do the moving part in that amount of time.
-The man assumes the woman will try to open the door without touching its knob before she touches its knob. This is the riskiest bit, but he is told she is exceptionally intelligent and knows that she knows he is as well, so it is reasonable to assume that any person with even moderate intelligence that read the same rules we did would at least try the experiment.
-The woman assumes that the man will have stood up at some point before the warning light comes on. Well, duh!
-Both assume that the warning light will be their signal to begin completing their respective journeys. Everyone in this thread so far has agreed that this is an obvious Schelling point for timing things.

Elvish Pillager
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### Re: Alien abduction

Spoiler:
quintopia: I see a bit of a problem with that solution. Rule one says they traverse the rooms by "walking", and scooting might not qualify.

Reading the rules literally, there are even more difficulties. It seems almost impossible for them to not "communicate" – consider that, whenever they move, they receive SOME form of information about where the other person is not. They also cannot "try to generate any kind of shockwave" – perhaps they cannot try to walk on the floor, or even breathe?

Wait, wait, I've got it.

7- None of them has a clock or any other instrument that can be used to measure time.

Before accurate clocks existed, people used to measure time by their pulse. Thus, we must conclude that neither the man nor the woman has a pulse. Yet, according to rule one, they must "walk". Therefore, they are the walking dead – zombies!

Since they have no minds of their own, they cannot possess any knowledge at all, which explains how they can avoid communicating in any way. Instead, their bodies are animated by swarms of nanobots, which have been preprogrammed to use a sequence of motions that fulfills the other requirements. They themselves do not "try" anything.

Afterwards, the extraterrestrials use some sort of high-tech system to bring the bodies back to life, so that they can actually "live" happily ever after.
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quintopia
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### Re: Alien abduction

Elvish I think you have it solved!

Spoiler:
More seriously, the scooting was not a requirement of my solution. It could be removed in the way others have done. And a pulse not an accurate time-keeping device. The heart rate changes too much when walking around.

Elvish Pillager
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### Re: Alien abduction

Spoiler:
Ah, but it never said that it was only forbidding devices that could measure time accurately. :p
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quintopia
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### Re: Alien abduction

Spoiler:
But it does use the word "instrument", meaning "a device designed for measuring". Measuring time is hardly what the human heart was designed for, so it hardly qualifies as an "instrument".

Elvish Pillager
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### Re: Alien abduction

Spoiler:
Fair enough.
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