Can you solve this puzzle?
June 22, 2015 6:47 PM Subscribe

Downstairs in a house are three identical on-off switches. One of them controls the lamp in the attic. The puzzle is to work out which switch controls the lamp. The rules are as follows. You are allowed to manipulate the switches all you like, and then you are allowed a single trip to the attic. How do you do it?
posted by growabrain (364 comments total) 23 users marked this as a favorite

Turn one switch on for a bit, then turn it off. Turn the 2nd switch on and go to the attic. If the bulb is warm and off, it was the first switch. If its on, its the 2nd, and if its off and cold, its the third.
posted by hwyengr at 6:52 PM on June 22, 2015 [88 favorites]

Take the chicken over first, leaving the wolf with the seeds.
posted by johnnydummkopf at 6:52 PM on June 22, 2015 [134 favorites]

Yet another puzzle that has been rendered unsolvable by modern technology.
posted by phooky at 6:54 PM on June 22, 2015 [60 favorites]

Even in nitric acid?
posted by moonmilk at 6:54 PM on June 22, 2015 [1 favorite]

Go to the attic immediately and leave the door open so you can see the light.
posted by Mei's lost sandal at 6:55 PM on June 22, 2015 [7 favorites]

I was going to write "Please do not post the solution in the comments"... Oh well, late again
posted by growabrain at 6:55 PM on June 22, 2015 [8 favorites]

1. I hate it when these puzzles are put in terms of "Are you smart enough to solve this?" Like your ability to solve a specific brainteaser is somehow an objective measure of worth.

2. There is usually something, once the solution is revealed, that reveals some unspoken assumption that is key to solving it. Not knowing the solution to this yet, I ask: is the lamp on or off at the start? Is this important information?
posted by JHarris at 6:56 PM on June 22, 2015 [23 favorites]

But the plane still doesn't take off ...
posted by hwyengr at 6:56 PM on June 22, 2015 [4 favorites]

I was totally confused when I thought this was a post in Ask.
posted by obfuscation at 6:58 PM on June 22, 2015 [13 favorites]

On RTFA, my smart-alec answer is toast.
posted by Mei's lost sandal at 7:00 PM on June 22, 2015

And for a second puzzle. How do you pronounce Jo Nesbø?

I'll take a crack at his second riddle.

This is literally the very first thing that came to mind when I read that name.
posted by phunniemee at 7:01 PM on June 22, 2015

And 3. Is this intended to be an abstract logic puzzle, where the switches, lamp and attic are just metaphors for states? Or do the physical reality of the components of the puzzle matter? Because if hwyengr's solution is correct the latter is true, which is not something that is obvious from how the puzzle is printed on the page, but is important to being able to solve it properly from first telling.

One could take the fact that, on the linked page, it was a mystery novelist who was the only one who solved it as a clue this is the case, but again, that's not information given as part of the puzzle as stated.
posted by JHarris at 7:01 PM on June 22, 2015 [6 favorites]

Open all windows and doors. Do the test at night.
posted by blue_beetle at 7:02 PM on June 22, 2015 [9 favorites]

If there's a goat behind the third switch, changing your answer increases the probability of winning the Lincoln Continental
posted by prize bull octorok at 7:04 PM on June 22, 2015 [72 favorites]

I never did solve the lightswitch puzzle. Years later, when I finally heard the answer, the solution made sense but I felt just a little cheated.

I guess the best clue I can provide is that yes, it's a logic puzzle, but it's a very physical, real-world puzzle. It's not on the same level of abstraction as: "I know what color my hat is."
posted by postcommunism at 7:04 PM on June 22, 2015 [6 favorites]

Also, the version I heard gave three lamps in the attic, but that doesn't change the solution.
posted by postcommunism at 7:07 PM on June 22, 2015

A retort: What would Feynman do?

Meanwhile, when I first heard of this puzzle it had a slightly different set up. There were two light bulbs and three switches. Two of the switches corresponded to the light bulbs and the third wasn't wired to anything. In this case, I came up with a different solution. If you move a light switch very slowly in between the on and off setting, you can sometimes feel the sparking of the electrical connection. You can do this with all three switches and see which one doesn't spark. Then do the one-on, one-off with the other two switches.
posted by mhum at 7:07 PM on June 22, 2015 [22 favorites]

Presenting it as a mathematical problem is cheating, I believe.
posted by shakespeherian at 7:07 PM on June 22, 2015 [10 favorites]

Someone speculated what Richard Feynman would do with this puzzle, to chuckle-worthy effect.
posted by Maecenas at 7:07 PM on June 22, 2015 [49 favorites]

4. The unstated assumption is that you are DC's The Flash and can reach the attic before the light comes on
posted by shakespeherian at 7:09 PM on June 22, 2015 [4 favorites]

Also, the lamp was his mother
posted by prize bull octorok at 7:09 PM on June 22, 2015 [21 favorites]

Looks like once again, the most powerful move... is friendship.

This is why Steven Universe really is the most powerful Gem.
posted by JHarris at 7:09 PM on June 22, 2015 [6 favorites]

Would it help if I gave you a barometer to use in the experiment?
posted by sammyo at 7:10 PM on June 22, 2015 [8 favorites]

I also thought I was reading Ask at first and was going to chime in with how I did asynchronous attic electrical work - Hangouts/Facetime with a second phone or computer makes corresponding between different spaces way easier.

Alternatively drill holes in your house until you have line-of-sight. Homeownership!
posted by bookdragoness at 7:12 PM on June 22, 2015 [2 favorites]

I figured it out after a few minutes (and making some guesses about unstated assumptions, such as knowing which direction of a light switch means "on" ahead of time -- not always obvious in my basement)...but my real question is whether this post counts as eponysterical or not.
posted by uosuaq at 7:13 PM on June 22, 2015 [1 favorite]

Jaime Lannister was actually trying to steal the lamp from the attic the entire time.

Sorry, Jo Nesbø.
posted by infinitewindow at 7:15 PM on June 22, 2015

I guess we have the "correct" answer already here, which is too bad because I for one didn't come up with it yet. I was going like this:

0. Oh right, it's assuming you already know which position is "on" and which "off", which is not true of many of the houses I've operated light switches in.

1. You can't see the light in the attic, but there's nothing that says you can't see the house electrical meter. But okay, I guess that's not allowed either.

2. It says manipulate the switches "all you like", so wire one of them to 1000 volts. If the house burns down starting in the attic it was probably that one.

3. If for some reason you don't have a handy source of different voltages or other useful electrical stuff, I guess you could try to burn out the light bulb by rapidly flipping one of the switches on and off a few thousand times. You'd have to do some experiments with other lamps first to see how much it would take.

4. "use red wire on green wire" ... no, wrong puzzle...
posted by sfenders at 7:17 PM on June 22, 2015 [17 favorites]

Thank you so much, Maecenas for that link. It's great!
posted by willF at 7:18 PM on June 22, 2015 [1 favorite]

If you guys are into light bulb-related puzzles, here's another one for you:

You have a string of 100 Christmas lights that work on a toggle system (i.e. you flip the switch, all the lit lights turn off and all the unlit lights turn on). On your first switch, every first light (so, every light) toggles on. On the second switch, every second light toggles. On the third switch, every third light toggles. And so on until you’ve flipped the switch 100 times. At the end of 100 toggles, which lights are lit?

posted by phunniemee at 7:18 PM on June 22, 2015 [4 favorites]

Can you solve this puzzle?

I could if Richard Feynman was still alive. I’d just call him up and ask him for the answer. (Then we’d probably talk about bongo drums – or congas – for awhile.)
posted by LeLiLo at 7:19 PM on June 22, 2015

Trade the barometer to the former owner to tell you which switch is correct.
posted by fifteen schnitzengruben is my limit at 7:19 PM on June 22, 2015 [9 favorites]

If the wording of the puzzle as presented above is correct*, it doesn't say your trip to the attic had to be to look at the light bulb. So can't you cut the wires up there and then come back down and test all three switches with a multimeter?

*I don't want to rtfa in case it has the answer.
posted by lollusc at 7:21 PM on June 22, 2015

Set up mirrors as you go upstairs that will reflect the light down to the switches.
posted by double block and bleed at 7:21 PM on June 22, 2015

Oh! Oh! I know this one! It's the other door!

(gets goat)

FFFFFFFUUUUUUUUUUUU
posted by ostranenie at 7:23 PM on June 22, 2015 [4 favorites]

ok, first check your inventory and randomly try to combine things. Glue cat hair to a stolen ID to match your fake mustache. Put the brown pebble in the blue vase, and voilà! It's really quite simple if you think about it.
posted by dejah420 at 7:24 PM on June 22, 2015 [20 favorites]

I always run into trouble with these because I don't understand the question. Like I thought "so, the other two switches must be connected to some other lights, right? So just flip them on and see what other lights go on! No problem!"

Apparently, the other two switches were installed by a perverted logic puzzle fetishist just for the purpose of asking this question. Also, the door to the attic is one way. That's why you can only check once.
posted by Joey Michaels at 7:27 PM on June 22, 2015 [10 favorites]

And now that I do read it: you aren't allowed to go back to the light switches.

In that case, leave one on, one off, and do something horrifying to the wiring of the third, like shorting it or wiring something else onto the circuit. In the attic the light will either be on or off. If off, your multimeter should be able to tell you if it's connected to the shorted switch.
posted by lollusc at 7:27 PM on June 22, 2015 [2 favorites]

richard feynman
posted by shakespeherian at 7:28 PM on June 22, 2015 [1 favorite]

Here's another puzzle I came across the other day which (unlike the lightbulb one) I hadn't heard before, and I'm still puzzled. Eh, here's the full text:

A dragon and knight live on an island. This island has seven poisoned wells, numbered 1 to 7. If you drink from a well, you can only save yourself by drinking from a higher numbered well. Well 7 is located at the top of a high mountain, so only the dragon can reach it. One day they decide that the island isn’t big enough for the two of them, and they have a duel. Each of them brings a glass of water to the duel, they exchange glasses, and drink. After the duel, the knight lives and the dragon dies. Why did the knight live? Why did the dragon die?

posted by Wolfdog at 7:29 PM on June 22, 2015 [6 favorites]

I like this one. It's true that it isn't purely a logic puzzle - but logic immediately tells you that it isn't a pure logic puzzle. So you either work on it more or abandon it because you were hoping for a logic puzzle.
posted by ftm at 7:31 PM on June 22, 2015 [6 favorites]

I hate it when these puzzles are put in terms of "Are you smart enough to solve this?" Like your ability to solve a specific brainteaser is somehow an objective measure of worth.

Yeah, especially in this case, or it's the same with a lot of the Encyclopedia Brown sorts of things, where it's really not logical ability that does it, it's knowing a mechanical fact about something and being able to bring it to mind quickly.

It seems like this is really testing for how recently you've used incandescent or halogen bulbs on a regular basis. My family used compact fluorescent bulbs from basically the moment they became available. Not only do they get less hot, they need replacing far less often. I literally would not have been able to tell you unprompted that light bulbs can get noticeably hot within a time period that would be reasonable for the purposes of a puzzle like this. Every bulb I've ever had to change in the last ten years has been cool to the touch by the time I got to it. Which is basically in the vein of that Encyclopedia Brown story about the watch that expected you to know that jewelers often use IIII instead of IV when writing Roman numerals. Which was bad enough when it was written, but today would be, like--I don't even OWN a watch.

Why did the knight live? Why did the dragon die?

See, this kind I like! But I won't tell what it is because it's worth feeling good when you figure it out.
posted by Sequence at 7:32 PM on June 22, 2015 [4 favorites]

I was thinking you could flip one switch on for longer than the bulb's expected lifespan until it burns out (and maybe speed things up by flipping it on and off a bunch to thermally stress the filament). I figure that's close enough. Having the solution depend on unstated assumptions is kinda annoying.
posted by Wemmick at 7:34 PM on June 22, 2015

I had this with the house I used to live in with my ex wife. The switch in the basement that you could never find what it controlled? It's the light by the pond, 100 yards away. You're welcome.
posted by nevercalm at 7:34 PM on June 22, 2015 [13 favorites]

Go to the attic first and unscrew the bulb. Go back down, turn all the switches off, remove the wall plate, and use a voltmeter to check for line voltage across the switch. The switches whose loads are still connected will show line voltage across the open switch. The one with no load in series will show nothing. That's the switch that controls the light in the attic. Bonus: Works even if the light is an LED or CFL.
posted by Bringer Tom at 7:34 PM on June 22, 2015 [11 favorites]

At least it's not perfectly rational pirates dividing treasure. Those puzzles are the most rage-inducing.
posted by GuyZero at 7:35 PM on June 22, 2015 [2 favorites]

And my first thought was "skype cell phone from computer, go up to attic, place cell phone in attic, go back down, flip switches til forever."
posted by nevercalm at 7:35 PM on June 22, 2015 [1 favorite]

I absolutely hate puzzles of this sort and for a while it was fashionable to ask them in job interviews. They are terrible terrible puzzles that assume facts not in evidence. There are plenty of solutions above that probably are not strictly forbidden by the rules of the puzzle but that would not be accepted as answers. The freakin guy who gets off on the 30th floor and walks up 10 floors every evening, but goes from the 40th to the 1st every morning is another one that really, really pisses me off, deeply.
posted by RustyBrooks at 7:36 PM on June 22, 2015 [7 favorites]

My opinion was, upon reading the riddle, that there is not enough information to ensure there is only one "right" answer. Things that need to be clarified for this to be a true logic puzzle are, (some as noted above):
1. what position are the switches currently in? Are they all in the "on" position, "off" ? they can't be in the middle so which is it?
2. are these switches wired correctly? Does flicking one "on" really engage the circuit? this is important.

There's probably more but I kinda got bored after I realized how lazily this puzzle's introduction was.
posted by some loser at 7:36 PM on June 22, 2015 [2 favorites]

Oh, I had the opposite problem when I moved into my current house. There's a light fixture in a short side hallway that connects the vaulted ceiling living room, the laundry room, the master bedroom, and garage. Could never figure out how to turn that light on. Finally after a few years I went in the attic to see what was going on.

there was NO WIRE to the light. I looked around, and realized that there was another wire with a splice going to the living room ceiling fan. Apparently the renovators had "borrowed" the switched connection to control the living room fan, and just left the hall fixture unconnected to anything. I ended up putting a dual switch in the laundry room so I could turn the hall light on.
posted by Bringer Tom at 7:38 PM on June 22, 2015 [4 favorites]

Flip one switch on, flip one switch off, unscrew the cover of the other switch, and run a shedload of current through the wires. Do you hear a pop? Now you don't even need to go up to the attic.
posted by fnerg at 7:38 PM on June 22, 2015 [4 favorites]

Take a flashlight and a vacuum cleaner/hair dryer/radio/some other noisemaking device to the attic with you. Use the flashlight to locate the outlet where the lap is plugged in, and unplug it; plug in the other noisemaking thing, turn the power on the thing to "on" and make sure it's loud enough for you to hear.

Go back down to the lightswitches. Turn each one on in turn. When you hear the noisemaking thing switch on, you've found your switch.

Yes, you do need to go back up to the attic and disconnect the noisemaker and plug the lamp back in. But the puzzle said nothing about how a trip to the attic AFTER discovering the switch was forbidden.
posted by EmpressCallipygos at 7:39 PM on June 22, 2015 [5 favorites]

I always run into trouble with these because I don't understand the question. Like I thought "so, the other two switches must be connected to some other lights, right? So just flip them on and see what other lights go on! No problem!"

Yeah, that's what I thought, too. The one that doesn't turn on a light right there where you can see it is the one that's connected to the attic light, of course.

I find puzzles like this so confusing, because I usually come up with an answer, but it never turns out to be the right one!
posted by rue72 at 7:40 PM on June 22, 2015 [2 favorites]

That dragon was clearly not cut out for living on the island of logic puzzles.
posted by sfenders at 7:40 PM on June 22, 2015 [5 favorites]

Alternative answer: flick on one switch, leave it on for a thousand years, then flick on another switch and go up to the attic. You (or more likely your descendants, all of whom have lived their provincial lives in the basement in fear of your prophecy) can determine which switch is which depending on if the light bulb is off, on, or burned out.

Note: they will be unable to return downstairs from the attic since only one trip was allowed. They will be trapped for all eternity, their only consolation being this new knowledge that they could never share.
posted by cyberscythe at 7:41 PM on June 22, 2015 [34 favorites]

The Edison solution!
posted by clavdivs at 7:41 PM on June 22, 2015

I'm not clear what the dragon-knight puzzle assumes. Are the wells the only water sources, or is there normal, poison-free water? How long do you have to drink the poisoned water after the other poisoned water? If you drink 1, 2, 3, will you die or not? Are we supposed to assume that the dragon is an idiot who can't do normal logical puzzle thinking?
posted by jeather at 7:42 PM on June 22, 2015 [4 favorites]

I'm convinced this is actually a test to see how many people actually read the whole article before leaving a comment.
posted by I EAT TAPAS at 7:42 PM on June 22, 2015 [5 favorites]

Using this kind of thing for job interviews seems like bullshit for me, unless you're just looking to see if the interviewee asks things like "so can I assume that 'up' means 'on' for all the lightswitches?" and stuff like that that shows they're thinking carefully about it.

Of course it's bullshit. It serves several purposes though
1. the interviewer gets to feel smart, because he knows the answer
2. it gives some veneer of "there is a process that seperates good and bad candidates" even if it's a terrible metric
If you press people they're like "oh, we just want to see how people reason through the problem" but there's no such thing. There is the "right" answer gained through insight and then there's a million things you could say that won't be accepted as right.
posted by RustyBrooks at 7:42 PM on June 22, 2015 [5 favorites]

Note: they will be unable to return downstairs from the attic since only one trip was allowed. They will be trapped for all eternity, their only consolation being this new knowledge that they could never share.

Oh so wait, is this a metaphor for getting into heaven?

Attic = heaven
Switches = various flavors of religious salvation
posted by rue72 at 7:43 PM on June 22, 2015 [22 favorites]

The light bulbs in my last apartment were about 15 feet off the ground, and I'd have to borrow a ladder from my neighbors to change them. It was a big chore, so I'm giving myself a pass on this one.

Also, if this is semi-real world rather than a formal logic problem, why are the people in these puzzles always solving problems all alone? I'd imagine that the solution to "ask your spouse or kid or neighbor to help" is always considered cheating, which reinforces a mindset that asking for help is less virtuous than figuring it out all by yourself, when often it is the much more practical choice.
posted by tula at 7:43 PM on June 22, 2015 [3 favorites]

Send spouse or child to attic. Flip switch. Shout, "Is it on?" Unable to understand answer. Shout, "Don't you have a goddamned phone?" Spend 20 minutes listening for missing phone. Send spouse or child back to attic. Flip switch. Repeat.

I mean, mysterious breakers in my house flip weekly. What's all this bullshit about only testing one?
posted by Eyebrows McGee at 7:44 PM on June 22, 2015 [10 favorites]

Set the switches to the down position. Tape a pop-up turkey timer under two of them so that they'd flip the switch when they pop. Take two space heaters and pull out the heating coils (earlier, you timed how long it takes a coil to reach 165 degrees). Wrap a coil around each timer. Plug in one heater, wait ten seconds, plug in the other. Run up to the attic with a stopwatch and time how long it takes for the light to go off (in the FPP video, the down position is on). Based on the timing, determine whether the first or second heater triggered the switch. If nothing happens, the correct switch was the one you didn't rig up. Boom. Solved. *mic drop*
posted by prize bull octorok at 7:44 PM on June 22, 2015 [9 favorites]

But think how good you'll feel on a job interview if you know the arcane answer but pretend you don't and come across as effing srmt, suckas!
posted by parki at 7:45 PM on June 22, 2015

I assumed that the knight lived and the dragon died because the knight stabbed the dragon with his sword. Unless they're on the Island of Idiots Who Swap Water Glasses and Walk Away but Call It a Duel, that's how it usually goes down.
posted by phooky at 7:47 PM on June 22, 2015 [17 favorites]

So to be qualified for this job you want me to be familiar with obsolete incandescent technology when the whole world is moving to CFL's and LED's?
posted by Bringer Tom at 7:48 PM on June 22, 2015 [3 favorites]

I can't make my solution work unless the dragon is bad at fetching well-water.
posted by uosuaq at 7:52 PM on June 22, 2015 [2 favorites]

Webcam.
posted by Tell Me No Lies at 7:53 PM on June 22, 2015 [1 favorite]

So to be qualified for this job you want me to be familiar with obsolete incandescent technology when the whole world is moving to CFL's and LED's?

Maybe the answer should be updated. CFLs have an "afterglow" for 5 or 10 seconds after you turn them off. I can see them in the dark when I turn the light off before going to bed. Also, if the lights have been off a long time you can often tell the difference by shaking them.

They do get warm, though, too. LEDs, I dunno, don't have any.

What's funny to me is, "to be qualified for this job, you want me to make unwarranted assumptions" which, for a software engineer, is the definition of bad practice
posted by RustyBrooks at 7:53 PM on June 22, 2015 [1 favorite]

If I got this right does it mean I should start writing Norwegian detective fiction?

(How the hell did I get it right? I never get these things!)
posted by sallybrown at 7:54 PM on June 22, 2015

Using this kind of thing for job interviews seems like bullshit for me

The finance industry loves using logic questions in their interviews, particularly for quants. It's not about getting the right answer. It's about finding people who 1) enjoy trying to solve problems, 2) are able to articulate their thought process, and 3) don't have a meltdown when forced to think abstractly.

Depending on the kind of position you're hiring for they can actually be quite useful. I would much rather go into an interview and be given inscrutable puzzles than to get asked where I see myself in five years.
posted by phunniemee at 7:56 PM on June 22, 2015 [9 favorites]

I will require a Phillips head, a voltage meter and one flying squirrel.
posted by clavdivs at 7:57 PM on June 22, 2015 [7 favorites]

My guess on the knight/dragon puzzle: The knight gave the dragon plain water and drank from the first well just prior to the duel. The dragon gave the knight water from well 7 and immediately after the duel flew to well 7 to counter-act the non-existent poison.
posted by forforf at 7:58 PM on June 22, 2015 [23 favorites]

The best way to solve this would be to try it out yourself.

On another note, is anyone in the market for a dead light bulb and a drowned wolf?
posted by cacofonie at 7:59 PM on June 22, 2015 [3 favorites]

So, the second part of what I said, phunniemee?
posted by uosuaq at 7:59 PM on June 22, 2015

That puzzle and its solution is cheating. If I can get extra information, then yeah, I can just hook up a voltmeter.
posted by Cool Papa Bell at 7:59 PM on June 22, 2015 [1 favorite]

JOB INTERVIEWER: So, Mr. Octorok, tell me about the last work situation where you--

PBO: ASK ME ABOUT DRAGONS AND POISON
posted by prize bull octorok at 8:00 PM on June 22, 2015 [51 favorites]

Or you can yell at your second cousin tommy, who's been living in the attic all year because your mom has a soft spot for him, to yell the answer to you.
posted by cacofonie at 8:01 PM on June 22, 2015

The dragon brought water from well 7, but the knight used his opposable thumbs to turn the 6 upside down and form a 9, providing both the antidote for well 7 water and a poison from which the dragon could not recover.
posted by Pater Aletheias at 8:02 PM on June 22, 2015 [13 favorites]

If it's not too early in the thread for spoilers (which are only spoilers if I've got this right) on the dragon question, if you drink from *any* well you're dead sooner or later, so the knight got regular water for some reason.
posted by uosuaq at 8:03 PM on June 22, 2015 [1 favorite]

So, the second part of what I said, phunniemee?

Yeah, it wasn't a reply to you so much as a reply to everyone who's talking about it in the thread but you said it in a nice, tidy way that was easy to respond to.
posted by phunniemee at 8:03 PM on June 22, 2015 [1 favorite]

I'm generally pretty bad at brain teasers but got this one, but still don't love it because it requires too many assumptions. First off, I thought at first that the three switches were in unknown states, and we didn't know if the lightbulb was on already, I'm not sure if that's really made clear, but I just went ahead and assumed the bulb was off and the switches were all obviously in "off" position. Then I assumed we were in a "real world" scenario where I can tell if a lightbulb has been on for only 30 seconds because it's still pretty cool to the touch. But that really isn't always true with LED lights or some flourescents, and I can't always reach a lightbulb in an attic, so I wasn't sure if I was cheating. So I wasn't very satisfied, but that's where they want you to go.

Anyway, I don't think brain teasers are clever unless they don't require you to make anything but the barest assumption. This one was okay though.
posted by skewed at 8:05 PM on June 22, 2015 [1 favorite]

Or better yet we all die someday so what's the point anyway?

That has yet to work for me in a job interview, oddly enough...
posted by uosuaq at 8:07 PM on June 22, 2015 [4 favorites]

When the attic wraith strips the flesh from your bones, the eldritch vibrations of its low terrible keening filling not your ears but the tattered, denuded tapestry of your soul, the true meaninglessness of home electric wiring concerns will finally become clear to you. All logic has gone from the world; what remains is something older, darker, deeper than that, a puzzle lurking beneath all puzzles, a riddle as black as the void.
posted by cortex at 8:08 PM on June 22, 2015 [32 favorites]

"In my house there's this light switch that doesn't do anything. Every so often I would flick it on and off just to check. Yesterday, I got a call from a woman in Germany. She said, 'Cut it out.'"--Steven Wright
posted by Melismata at 8:08 PM on June 22, 2015 [10 favorites]

My guess on the knight/dragon puzzle: ...

> But the dragon, being a beast of ancient intelligence, knows that the knight knows that if the knight doesn't drink from a well before the duel, then the knight is open to the dragon's 7 trump. A smart knight will pregame. Knowing that, it makes sense for the dragon to bring 1 water to the duel, as it's the only one that won't counteract the knight's presumed pre-duel tipple.

And of course, the dragon only dies if there is a source of pure water on the island, which parameter we are not given by the question.
posted by postcommunism at 8:09 PM on June 22, 2015 [8 favorites]

When the attic wraith strips the flesh from your bones, the eldritch vibrations of its low terrible keening filling not your ears but the tattered, denuded tapestry of your soul

We have such brain teasers to show you.
posted by shakespeherian at 8:11 PM on June 22, 2015 [5 favorites]

Ergo: upwind, faster than the wind. QED
posted by simra at 8:14 PM on June 22, 2015

With the dragon/knight puzzle: can either of them feel the effects of the poison coming on?

If yes -> then the dragon can drink from well 6 after the duel. If it starts to feel any effects, then it can drink from well 7. If it doesn't feel any effects, then it's fine.

If no -> then the dragon could give the knight regular water. The knight has no idea if he should be drinking from another well or not. It's a toss-up whether he lives or dies.
posted by naju at 8:17 PM on June 22, 2015

They both got poisoned, but obvs the knight made his saving throw and the dragon didn't
posted by prize bull octorok at 8:19 PM on June 22, 2015 [13 favorites]

> But the knight is quick enough to realize that the dragon has done this, and after the duel takes a sip from well 6 to cure himself.

But the puzzle doesn't ask to find the optimal move for each duelist, just to explain one particular outcome.
posted by eruonna at 8:19 PM on June 22, 2015 [2 favorites]

I laughed at the Yahoo answer that said the Dragon died because it couldn't count and didn't know which well to go to.
posted by mrbigmuscles at 8:19 PM on June 22, 2015 [4 favorites]

But, well 7 is poisoned too. They're all poisoned. Aren't your days numbered no matter what you drink? The only way to survive drinking from a well is to drink from a higher-numbered well, but that itself is also poison. And 7, being the highest-number, is the one without a cure! I mean this is just so full of holes.
posted by JHarris at 8:20 PM on June 22, 2015 [18 favorites]

Exactly, JHarris, which is why I think the knight must have somehow been served a glass of regular water. The dragon either doesn't understand about the wells or can't get water out of them.
posted by uosuaq at 8:22 PM on June 22, 2015 [3 favorites]

Or it had a change of heart
posted by mrbigmuscles at 8:22 PM on June 22, 2015 [4 favorites]

There's a detail missing from the telling of the knight-dragon puzzle in this thread: A drink from the seventh well will cure any of the other poisons but is only itself lethal if the drinker has NOT been poisoned by one of the other wells.

So drink from any well 1-6, you can cure yourself with 7. But drink only from 7 and you cannot be cured.
posted by crush-onastick at 8:22 PM on June 22, 2015 [3 favorites]

If so, that's a hugely annoying missing detail. I quit.
posted by uosuaq at 8:25 PM on June 22, 2015 [12 favorites]

Probably the Sons of the Harpy ran up and killed the dragon. Ridiculous.
posted by batfish at 8:28 PM on June 22, 2015 [2 favorites]

The dragon either doesn't understand about the wells or can't get water out of them.

Either way is tragic.

1. The Dragon doesn't know the wells are poison, so it thinks it is just playing a game. A fight, with glasses of water, haha! On this reading the Dragon is a good natured goof, like a big winged serpentine Labrador.

2. The Dragon DOES know about the wells, but is physically incapable of accessing them. It frantically tries to get water out of them, before the duel to poison the knight, and after the duel to save itself. But it can't. It won't back out of the duel out of pride.

Now I'm kinda sad
posted by mrbigmuscles at 8:30 PM on June 22, 2015 [14 favorites]

Flip the first switch about 100,000 times, then leave the 2nd in the "on" and the 3rd in the "Off" position, then go up and see if the bulb is on, off, or burnt out.

Even works with fluorescent and LED bulbs, they all burn out based on on/off cycles.
posted by Blackanvil at 8:31 PM on June 22, 2015 [6 favorites]

Hodor.
posted by stltony at 8:32 PM on June 22, 2015 [2 favorites]

So you're saying the second switch?

CAN'T SPELL "SWITCH" WITHOUT "WITCH" AND ALSO THE "S" SOUND OF THE VEIL BETWEEN YOUR WORLD AND THEIRS BEING QUIETLY BUT IRREVOCABLY TORN ASUNDER
posted by cortex at 8:32 PM on June 22, 2015 [2 favorites]

put mail on satchel
posted by rouftop at 8:36 PM on June 22, 2015 [7 favorites]

If you don't solve this puzzle your attic-bound grandma is going to get eaten by a grue.
posted by grumpybear69 at 8:38 PM on June 22, 2015 [2 favorites]

First, assume a spherical dragon ...
posted by mon-ma-tron at 8:38 PM on June 22, 2015 [12 favorites]

I said bury the survivors in Canada and I meant it, dammit.
posted by destro at 8:41 PM on June 22, 2015 [12 favorites]

I'm going to be honest, the kind of dragon that decides to spend its time drawing up an ironclad dueling contract, operating a well (itself a fairly comical image), and drawing a glass of possibly poisoned water for a goddamned knight instead of swooping down and biting him in half deserves to die to some B+ level mind games. Talk about needlessly and pointlessly crippling yourself.
posted by Copronymus at 8:46 PM on June 22, 2015 [21 favorites]

The problem with brainteasers like these that rely on real world knowledge of unstated properties is that there are tons of other obvious solutions that you won't be able to carefully define away.

E.g. the linked scenario says that you can't see light from the attic from the switches, but it doesn't say you can't set up a series of mirrors from a position where light is visible.

It says that you can only go into the attic once and can't return to the switches, but it doesn't say that you can't ask someone else to go up and tell you if the light is on.

There's no way to say that either of these solutions is less legitimate than the "real" solution, which is why I've always thought that this was a pretty lame puzzle.
posted by zixyer at 8:49 PM on June 22, 2015 [9 favorites]

I worked out the logic of it and said "I don't think this is solvable ... fine! I'll solve it in a stupid way." -- and whaddaya know, that's almost the "right" solution:

My annoyed solution: I can flick the switch as much as I want? And the drawing shows an incandescent bulb? Alright! I will spend two years doing nothing but turning the switch on and off. I assume this is enough time for the filament to break, because everyone puts shitty bulbs in the attic.

Then I turn one of the other switches on. I go up in the attic and look at the bulb. If the light is on, I know which switch it is. If the light is off and the filament is not broken, I know which switch it is. If the light is off and the filament is broken, I know which switch it is.

And I've wasted two years of my life. But that's only slightly stupider than this exercise!
posted by barnacles at 8:50 PM on June 22, 2015 [2 favorites]

Just thought of another solution. You can't go into the attic, but you can go around to the back of the house to check the electric meter. Just check that while the switches are on and off.
posted by skewed at 9:00 PM on June 22, 2015

Borrow your spouse's phone. On your one trip to the attic, call yourself on facetime and point the camera at the lightbulb. Then go downstairs and flip each switch until the light comes on.
posted by George_Spiggott at 9:00 PM on June 22, 2015

On didn't read the whole thread, okay, everybody already thought of that.
posted by George_Spiggott at 9:01 PM on June 22, 2015 [1 favorite]

the kind of dragon that decides to spend its time drawing up an ironclad dueling contract, operating a well (itself a fairly comical image), and drawing a glass of possibly poisoned water for a goddamned knight instead of swooping down and biting him in half

One of my favorite things about the weird little narratives that set up logic puzzles, as a genre of writing, is how many of them have this kind of question-writer proxy figure. Dragons or kings or trolls or whatever else, they're almost always deeply malevolent (or at least barely veiled sadists), often nearly omnipotent beings, yet they have a compulsive fixation on enforcing rules rigidly even to their own detriment, and they are very prone to obsessing over tiny, fussy little details. Part of what made Lewis Carroll's writing so great was that, unlike most logic-puzzle aficionados, he understood that this made for a psychologically rich and kind of troubling and creepy terrain, not just some innocent window dressing for the real abstract stuff.
posted by RogerB at 9:10 PM on June 22, 2015 [30 favorites]

My default response for mental chicanery.

With that said, the correct response is clearly to a) get a hammer, b) make eye contact, c) break your leg with the hammer, then d) make it very clear that solving the riddle is now Their Problem and e) do you have any ibuprofen?

(With that said, the obvious answer is to get some insulated gloves, then manipulate all three switches so they're wired in parallel.)
posted by mikurski at 9:14 PM on June 22, 2015 [3 favorites]

Considering the unstated assumptions here, I feel like my answer is equally valid:

Play with the switches all you like, while figuring out which two of the three trigger lights outside of the attic.
posted by Navelgazer at 9:14 PM on June 22, 2015 [9 favorites]

Hey y'all. I'm just a minimally intelligent device controller on your attic light bulb. What the heck you want this thing on for right now anyway? Just put your needs in your calendar and I will make sure to be all bright and shiny for when you need me baby. Switches are for bitches, hun.
posted by yesster at 9:14 PM on June 22, 2015 [1 favorite]

Play with the switches all you like, while figuring out which two of the three trigger lights outside of the attic.

Damn. All joking aside, I think I would be most impressed with this answer if it were given to me in a interview situation.
posted by skewed at 9:20 PM on June 22, 2015 [5 favorites]

Okay everybody.

So here goes.

The big one.

The actual one brain teaser to rule them all.

I always think of it when I hear the 3-light-switches-feel-the-bulb one because this one makes that one sound puny. No externalities, just the abstract principles at play:

You and 99 others are imprisoned in a dungeon (there is no well or dragon, and they treat you pretty well, all things considered).

The terms of the imprisonment are as follows: Each day, one person is randomly selected and brought to a room that contains a single lamp. The prisoner is free to alter the state of the lamp (turn it on or off) if they wish. The guards won't mess with the lamp, so it's always in whatever state it was last left in by a prisoner. And the light from the lamp is visible only from within the room: none of the other 99 prisoners can see it, ever, except when they are in it.

The deal is that anytime a prisoner is in the room, he or she is offered the chance to wager that all 100 prisoners have already visited the room. If this is correct, then everyone goes free. But the stakes are high: if a prisoner wagers this and is wrong, everyone is killed.

Got it? You and the other prisoners are permitted to discuss a strategy before being escorted to your cells. How do you stay alive?

Yes, it's doable. Yes, it's awesome.
posted by So You're Saying These Are Pants? at 9:22 PM on June 22, 2015 [8 favorites]

Take the wager on day 101?
posted by prize bull octorok at 9:26 PM on June 22, 2015 [1 favorite]

can the prisoners be selected multiple times? I'm guessing you don't mean for the prisoners to be chosen randomly, but each exactly once, because then you just wait until the last day. But if each prisoner could be selected multiple times, then it could takes years before everyone has been selected. I guess just wait 3-4 years until everyone is apathetic between continued imprisonment and death.
posted by skewed at 9:28 PM on June 22, 2015 [1 favorite]

Throw the glass of poisoned water the dragon gave you at all the light switches?
posted by el io at 9:28 PM on June 22, 2015 [4 favorites]

Most switches can be in an in between position where the light flickers. That's one answer.

Also, in my toolbox I have a device that looks like a pen and beeps when it gets near a wire that's turned on (even through walls). They cost about $15 at the hardware store. Very nice for checking the wiring. Also you could just find whichever switch controls a wire that seems to go upstairs.
posted by miyabo at 9:29 PM on June 22, 2015 [1 favorite]

This puzzle made me feel cheap and stupid when I read the solution. The video confirmed that this is what I was supposed to feel.
posted by Bistle at 9:30 PM on June 22, 2015 [2 favorites]

I dunno I flip switches until I have enough light to read Martin Gardner's Aha Insight! and sit in the basement, content to lead a life of calling out outlandish "Are you smart enough!?!?" logical exercises for their general isomorphism in that they all require a meticulous examination of the assumptions or specific circumstances, and for being able to understand where true mathematical thinking takes over in silly exercises like this.
posted by Theophrastus Johnson at 9:30 PM on June 22, 2015 [4 favorites]

Yell for your little brother to go get the cake that's hidden in the attic. When you hear him get up there, try the switches until you hear him trip over something and yell "Fuck!"
posted by pracowity at 9:33 PM on June 22, 2015 [2 favorites]

How do you stay alive?
Well the trivial answer is everyone agrees not to take the wager, but everybody dies eventually, man.
posted by juv3nal at 9:35 PM on June 22, 2015

The knight plays "I DRINK YOUR MILKSHAKE!" by tapping well #7 underground at an angle and draining it dry. The dragon is forced to use a lower number well and the knight has an antidote for himself and an unbeatable poison for the dragon.
posted by jason_steakums at 9:35 PM on June 22, 2015 [7 favorites]

You and the other prisoners are permitted to discuss a strategy before being escorted to your cells. How do you stay alive?

Interesting. I've heard a version of this with two switches, but not just one before. So... my answer would be this:

Wait 2 years. Odds are 1/600 that there's someone who *hasn't* visited. Adjust the duration based on the odds of success you prefer. (This is much more preferable to the "Choose an arbiter, have everyone else flip, count, etc." answers, which tend to take somewhere between 20 and 200 years.
posted by CrystalDave at 9:37 PM on June 22, 2015 [1 favorite]

guys can't we come up with a solution to a logic puzzle that DOESN'T involve waiting for two years
posted by DoctorFedora at 9:38 PM on June 22, 2015 [17 favorites]

First time you enter the room leave a drop of blood on the lamp, then count the drops.
posted by otherchaz at 9:39 PM on June 22, 2015 [1 favorite]

Infest the attic with lampreys. Reposition underwater. Drown.
posted by Bistle at 9:41 PM on June 22, 2015 [1 favorite]

The terms of the imprisonment are as follows: Each day, one person is randomly selected and brought to a room that contains a single lamp. The prisoner is free to alter the state of the lamp (turn it on or off) if they wish. The guards won't mess with the lamp, so it's always in whatever state it was last left in by a prisoner. And the light from the lamp is visible only from within the room: none of the other 99 prisoners can see it, ever, except when they are in it.

The deal is that anytime a prisoner is in the room, he or she is offered the chance to wager that all 100 prisoners have already visited the room. If this is correct, then everyone goes free. But the stakes are high: if a prisoner wagers this and is wrong, everyone is killed.

Count the days and only take the wager on the last day?
posted by jason_steakums at 9:41 PM on June 22, 2015

Isn't it clear? You flip the second switch, and on the 100th day all the Knights with blue eyes leave the island, while the ones with brown eyes stay behind. Then the dragon eats the prisoners and sets a second forest fire downwind of the first one.
posted by brecc at 9:42 PM on June 22, 2015 [10 favorites]

Ah, that only works if prisoners are taken out of the pool of random selections when they visit the room though.
posted by jason_steakums at 9:43 PM on June 22, 2015

Yeah, the riddle teller is always satisfied that any assumptions that need to be made are obvious, and then the riddlees spent all their time trying to figure out what those assumptions are.
posted by skewed at 9:45 PM on June 22, 2015 [8 favorites]

Wire switch 1 in series with a loud alarm bell.
Flip on switch 1 & 2.

Go up to the attic. If the light is off, it's switch 3. If the light is on, unscrew the bulb. If the alarm cuts off, it's switch 1, otherwise it's switch 2.
posted by fings at 9:47 PM on June 22, 2015 [2 favorites]

Wire switch 1 in series with a loud alarm bell and a small kitten.
Flip on switch 1 & 2.

Answer to your god.
posted by Bistle at 9:49 PM on June 22, 2015 [2 favorites]

Any entity capable of imprisoning 100 people, while offering the logical puzzle as proposed, is inherently diabolical. Why are those people imprisoned? What is the system of justice in this universe? Why would "guards" participate?

If rule-breaking were off the table, why would the whole genre involve criminality?
posted by yesster at 9:51 PM on June 22, 2015 [1 favorite]

Burn it down, is what I say. Burn it all down. It's bad wiring, bad people, it's a mess. Salt the earth and start over.
posted by the uncomplicated soups of my childhood at 9:52 PM on June 22, 2015 [14 favorites]

Felines and Dames in flames will hardly serve your aims.
posted by otherchaz at 9:54 PM on June 22, 2015

I use a microcontroller with built-in Bluetooth, three solenoids and some duct tape.
posted by ryoshu at 9:54 PM on June 22, 2015 [4 favorites]

I'm pretty sure the answer is that the dragon had an undiagnosed heart problem. The knight and the dragon fought, but after a short while realized the foolishness of their situation and resolved their problem through discussion (they agreed that the knight manipulates the switches and the dragon checks the attic). Unfortunately, it later turned out that the dragon had sold its hoard to buy the knight a new suit of armor, but the knight had renounced his knighthood so that he could stay on the island! Years later, as the knight and the dragon sat together before the coals of the fire on which they'd roasted one of the island's wild pigs (left there by conquistadores who had become frustrated with the difficulty of transporting pigs, truffles, and wolves on the same boat) they would reminisce about this and laugh and gaze into each others' eyes. That night the dragon, its heart grown soft from years of leisure and kalua pork, passed away in its sleep. The knight decided to leave the island and its now-painful memories, and flagged down a passing ship, which happened to be Ponce de Leon's… but that, O King, is a story I don't have time to tell tonight, unless of course you decide not to kill me for another day?
posted by hattifattener at 9:56 PM on June 22, 2015 [28 favorites]

The 100 prisoners solution:

-Every time a prisoner returns from the room, the other prisoners kill them.
-The last one to enter to room will incontrovertibly know they are the last.

It's a pyrrhic victory.
posted by His thoughts were red thoughts at 10:01 PM on June 22, 2015 [25 favorites]

This one didn't seem difficult to me at all, and I wonder if it has anything to do with how many times I've burned my fingers on lightbulbs.
posted by lastobelus at 10:03 PM on June 22, 2015 [2 favorites]

1st problem: the switches are all those indecisive types that sometimes tell the truth and sometimes lie so you can't rely on them for anything. Your only solution is to replace them with a single switch that works.

2nd problem: when they had switched the glasses, the knight said "Look, what's that over there!" and while the dragon was looking away, quickly dumped some iocaine powder into his own glass. It is not terribly well-known that iocaine powder, while poisonous in its own right, actually neutralises other, lesser poisons. And since the knight was from Australia, this was no problem.

3rd problem: the prisoners talk to each other. Not rocket science, really. Before heading up, the one selected each day says "so has anyone not been to the lamp yet?" If someone says yes, then you don't take that bet. Who's going to lie unless they're suicidal? And since the conditions are actually pretty comfy, that seems unlikely.
posted by Athanassiel at 10:05 PM on June 22, 2015 [10 favorites]

All of the presumed "best answers" require truckloads of spherical pigs.
posted by yesster at 10:09 PM on June 22, 2015 [1 favorite]

3rd problem: the prisoners talk to each other. Not rocket science, really. Before heading up, the one selected each day says "so has anyone not been to the lamp yet?" If someone says yes, then you don't take that bet. Who's going to lie unless they're suicidal? And since the conditions are actually pretty comfy, that seems unlikely.

Pah!

[Returns to polishing murder rock]
posted by His thoughts were red thoughts at 10:09 PM on June 22, 2015

Sorry for leaving the thread, got caught up.

Yes, prisoners can be selected more than once. No leaving any clues in the room, the only way to communicate anything is by switching the light on or off.
posted by So You're Saying These Are Pants? at 10:14 PM on June 22, 2015

CrystalDave: Adjust the duration based on the odds of success you prefer.

Yep, but I prefer 100% odds : )
posted by So You're Saying These Are Pants? at 10:15 PM on June 22, 2015

100 prisoner problem: are the prisoners told whether the light is initially on or off when the first one enters the room? I can posit a solution if yes, but not otherwise.
posted by George_Spiggott at 10:15 PM on June 22, 2015

Well, that point would be somewhat trivial ... they could just agree that the first prisoner selected should initialize the light to whichever state you like, and start your solution on day 2.
posted by So You're Saying These Are Pants? at 10:16 PM on June 22, 2015

At that point, the only way to communicate is with the lamp, and thus they'll have to elect a leader as someone else suggested, who is the only one to turn off the lamp. Once he does it 99 times, he's sure he's got everyone.

But that could take years and years, with the leader having to visit hundreds or thousands of times to turn off the lamp 100 times. Long enough that the leader would probably lose count and screw up. I think inherent in this kind of puzzle is that there should be some devious trick that allows for theoretically maximum efficiency (i.e., being able to make the wager as soon as each person has been to the lamp room).
posted by skewed at 10:17 PM on June 22, 2015

Good puzzle, but it's kind of cheating. "It's not a logic puzzle. It takes place in the real world."

Okay. But in the real world, the initial constraints wouldn't exist. I'd be able to make as many trips between the attic and the switches as I like.
posted by Ratio at 10:21 PM on June 22, 2015 [1 favorite]

Per the preceding two comments, if we take the "this is the real world" escape clause of the toplinked puzzle, statistically speaking a very sizable percentage of prisoners would die of natural causes long before you counted them all and we have no way of knowing how many, or tracking whether they contributed to the solution before they went, so unless we're back to dealing in abstract ideals that's not going to work.
posted by George_Spiggott at 10:23 PM on June 22, 2015

Yep! nice job, you can do it by electing a leader, who is the only one allowed to turn off the lamp, and everyone else turns the lamp on only on their first visit to the room.

You've got the right idea though, you can come up with some pretty clever algorithms that will speed up the time to completion. I would highly recommend that write up just to see how sophisticated the strategies can get.

What I love about this puzzle is that at first blush it seems so impossible to communicate certainty using just the binary state of the lamp, but not only is it doable, there are some amazing solutions.

edit: oops, I had the wrong pdf in here at first
posted by So You're Saying These Are Pants? at 10:24 PM on June 22, 2015 [2 favorites]

(it seems like I should have played up the drama that, yeah, you have no idea how many years it will be until #100 is selected...oh well...)
posted by So You're Saying These Are Pants? at 10:25 PM on June 22, 2015

Go up into the attic and unplug or otherwise disconnect the lamp and then go back downstairs.

That one switch controls the lamp in the attic is now a false premise, and since any conclusion follows logically from a false premise, any answer you choose to give will be correct.
posted by jamjam at 10:34 PM on June 22, 2015 [10 favorites]

There's a difference between cleverness and deliberate obtuseness.
posted by kafziel at 10:35 PM on June 22, 2015 [1 favorite]

clever
posted by So You're Saying These Are Pants? at 10:42 PM on June 22, 2015 [2 favorites]

As a real world problem, I hypothesize it would play out this way...

Person: "Hey, Samizdata, there's three switches and a light in the attic..."

Samizdata: "Fuck you and your problem. I don't go in the attic because I don't have an attic. Wait, who are you and why are you in my home?"
posted by Samizdata at 10:43 PM on June 22, 2015 [4 favorites]

I know there are 162 other comments in this thread, so I apologize if someone already mentioned this, BUT:

My answer before watching the video of the actual answer was that you should flip the first switch 100,000 times, turn the second switch on and leave the third off. When you go up the stairs, if the light is on it's #2. If it's off it's #3. If it's burned out it's #1.

Clearly not as good as the real answer but I like my thinking anyway.
posted by shmegegge at 11:03 PM on June 22, 2015 [1 favorite]

I don't think there's any reasonable way to say that's a less good answer than the "real" answer. It's just as unrealistic as the prohibition against going up to the attic twice.
posted by skewed at 11:07 PM on June 22, 2015 [1 favorite]

A dragon and knight live on an island. This island has seven poisoned wells, numbered 1 to 7. If you drink from a well, you can only save yourself by drinking from a higher numbered well. Well 7 is located at the top of a high mountain, so only the dragon can reach it. One day they decide that the island isn’t big enough for the two of them, and they have a duel. Each of them brings a glass of water to the duel, they exchange glasses, and drink. After the duel, the knight lives and the dragon dies. Why did the knight live? Why did the dragon die?

Either of them would need to drink more than once to survive the poison, so the knight didn't survive because he drank from a higher-numbered well, he survived for some other reason; similarly, the dragon died from something other than poisoning. The answer is that the knight lives because he won the duel, which wasn't the water-swapping-and-drinking, but an actual duel. The poisoned well business is a distraction from the fact that trading glasses of water doesn't constitute a duel.
posted by clockzero at 11:12 PM on June 22, 2015 [5 favorites]

I send another guy up to the attic. I flip the first switch once, the second twice and the third three times. Then I tell him to come back and ask him how many times the light went on.

I know from previous interactions whether he always lies or always tells the truth and ask appropriate questions. And I know he is willing to work with me, because I personally made sure the missionaries didn't convert him when we crossed the river. If it happens that we are paid with 12 identical coins, I have a scale to find out if there is a counterfeit one.
posted by tykky at 11:15 PM on June 22, 2015 [6 favorites]

What kind of creep is sending me on a one way trip to the attic? Get out of the house asap. Maybe call the police.
posted by ODiV at 11:28 PM on June 22, 2015 [4 favorites]

I've heard this as a differently-stated puzzle: You have a box with a fan in the middle, mounted parallel to the ground, and there's four switches. One turns the fan on; the rest do nothing. You also have a pouch full of black pepper. You can only look inside the box once. How do you find which switch controls the fan?

Solution: First, you turn on one switch and pour the pepper in. You turn the switch off and wait a while. Then, you turn on another switch, and wait a bit; then, you quickly turn that switch off and another one on. If the pepper's scattered, but the fan's not moving, the first switch controls the fan. If the fan's slowing down, the second switch controls the fan. If the fan's still moving, the third switch controls the fan. And if the pepper's in a pile, the fourth switch controls the fan.
posted by LSK at 11:31 PM on June 22, 2015 [3 favorites]

I thought the phrase "you are allowed to manipulate the switches all you like" was a pretty big hint that it wasn't just a matter of choosing a certain combination of on and off and then going up.
posted by L.P. Hatecraft at 11:38 PM on June 22, 2015 [2 favorites]

Since it does not say you can't go outside the house it would be pretty likely that the attic would have a window or one of those slat vents since it is big enough to warrant a light bulb.

1; turn on each light in turn and walk around the house and look for light from the attic at night (at this point the person posing this test will say something like "the house has a attic with no windows or vents", you inform them of the building code regarding such things) if you still can't see the light proceed to step two.

2; Turn off and unplug everything in the house, go outside make note of the meter reading.
Turn on each switch in turn for 4 hrs (this is to get a meaningful reading from a low watt bulb)
Did only one switch show a reading? then that is your switch, if not than the other switches are hooked to something and you will need to investigate.

If you don't want to go with the hot bulb route you really need more data (and a tester who is not being a dick).
posted by boilermonster at 11:52 PM on June 22, 2015

I go to the building owner and say "Hey, I'll give you this lamp if you tell me which switch controls that socket in the attic."
posted by Spatch at 12:00 AM on June 23, 2015 [2 favorites]

Got it? You and the other prisoners are permitted to discuss a strategy before being escorted to your cells. How do you stay alive?

Hmm, each time a prisoner is in the room, they lift the lamp off the ground and start digging a tunnel. They use the lamp as as source of light in the tunnel. When they're tired, or when the guards come to collect them, they'll have to scramble out and somehow put the lamp over the loose tile or board they're using to cover the hole. The guards can't mess with the lamp, so they will have to leave it alone. Someone will eventually dig their way out, and their job will then be to send help to rescue the rest of the prisoners. Whether this is by sending documents that incriminate the warden or doing a recon of the surrounding area to then be intentionally be recaptured in preparation for a greater escape will be up to the prisoners to decide.
posted by FJT at 12:03 AM on June 23, 2015 [3 favorites]

"Never go in against a Sicilian when death is on the line"! Ha ha ha ha ha ha ha! Ha ha ha ha ha ha ha! Ha ha ha...
posted by rum-soaked space hobo at 12:06 AM on June 23, 2015 [2 favorites]

A more extreme version of shmegegge's answer: flip the first switch on, wait thirty seconds, flip the switch off, wait fifteen seconds, flip the switch on, and from then on wait half the amount of time you waited previously before flipping the switch again, thus flipping the switch an infinite number of times in one minute.

If the universe is destroyed from the logical contradiction of a switch that can be neither on nor off, then it was the first switch. Otherwise, flip the second switch on and the third switch off and check the attic.
posted by J.K. Seazer at 12:24 AM on June 23, 2015 [2 favorites]

The knight puzzle is kind of stupid because it assumes that

a)the knight and dragon are not terribly smart
b)You can't tell if you've been poisoned
c)That the poison is rather slow acting...

A solution here and a nicer version of the puzzle (and solution) here
posted by Cannon Fodder at 12:42 AM on June 23, 2015 [2 favorites]

What I love about this puzzle is that at first blush it seems so impossible to communicate certainty using just the binary state of the lamp, but not only is it doable, there are some amazing solutions.

Well you don't have just the binary state of the lamp: in the solution described you also have one binary variable for each non-leader prisoner, and a counter on the leader.
posted by Dr Dracator at 12:48 AM on June 23, 2015

SOSTAP, the pdf explains the puzzle (and solutions) much more clearly. I wasn't sure what the puzzle or first answer was from just the comments.

So clearly the best interview question is to have the applicant write a brain teaser.
posted by halifix at 1:11 AM on June 23, 2015

I absolutely hate puzzles of this sort and for a while it was fashionable to ask them in job interviews. They are terrible terrible puzzles that assume facts not in evidence.

No, they're wonderful puzzles for job interviews. It doesn't really matter if you get the answer. What matters is your reaction when you don't get the answer. Broadly, there are two types of people:

"Ooooh, I get it now! Heh, that's pretty cool. I wasn't thinking about it that way."

"BUT THAT'S NOT FAIR THE QUESTION WAS WRONG AND YOU'RE TESTING THE WRONG KIND OF INTELLIGENCE AND THAT'S NOT A REFLECTION OF MY TRUE WORTH AND IS THIS A REAL LIGHTBULB OR A VIKING LIGHTBULB AND I'M GOING TO HEAD UPSTAIRS AND COME BACK DOWN AGAIN AND THEN CHANGE THE SWITCHES EVEN THOUGH THE RULES SAY I CAN'T"

Guess who gets the job? Hint - it's not the person who has a massive fucking sulk when things don't go their way, justly or not.
posted by obiwanwasabi at 1:49 AM on June 23, 2015 [5 favorites]

So instead, it's measuring how likely the interviewee will sit and take whatever bullshit judgement is made about them by an authority figure?

All the criticism from above on these kinds of problems are completely valid, and it's not sulking to point that out. They shouldn't be used as a basis for hiring, full stop.
posted by JHarris at 2:09 AM on June 23, 2015 [6 favorites]

The UK driver's exam apparently grades technique much lower than awareness. Someone who notices oncoming traffic will live long enough to perfect parallel parking, but not vice-versa.

I use this example a lot when defending the "softer" hiring techniques that look more concrete when you first approach them. Someone can learn skills and details on the job, but it's much harder to change someone's temperament to fit the role.
posted by rum-soaked space hobo at 2:10 AM on June 23, 2015 [5 favorites]

"The janitor will stop hitting you with his new barometer the instant you tell us which switch controls the lamp."
posted by sebastienbailard at 2:24 AM on June 23, 2015 [2 favorites]

Depends on how deep the skill set is, and the consequences of failure: you probably don't want brain surgeons figuring it out as they go.
posted by Dr Dracator at 2:24 AM on June 23, 2015

Regarding the UK driver's test, certainly when I did it the one thing my instructor always drummed into me was that the tester was basically really looking to make sure you weren't going to kill yourself or someone else, and that you could do the basic manoeuvres to some degree.
posted by GallonOfAlan at 2:32 AM on June 23, 2015

So, I flipped the light switch and went up into the attic, only to be confronted by a bedraggled man, long beard, and leg irons. He's angry, really angry, and shouting some crazy shit. "DID YOU JUST TURN THAT LAMP OFF? YES OR NO? DON'T MESS WITH ME BOY, THIS IS A LIFE OR DEATH SITUATION. I'M SUPPOSED TO BE THE FUCKING LEADER!"
posted by Thing at 2:44 AM on June 23, 2015 [22 favorites]

Also, my solution to the knight and dragon duel was that the knight mixed water from wells five and six, making a super level eleven poison the dragon didn't know how to cure, but would cure the knight of water from well seven. Crafty, literally.
posted by Thing at 2:47 AM on June 23, 2015 [1 favorite]

Count me in with those who think either this should be a pure logic problem or should carefully and also naturally specify what is allowed.

Yes, in a practical sense using the warmth of the bulb as an extra state indicator is easy and elegant but the problem already has some unreasonable assumptions (why can you not see or infer what happened in another way such as visually? Why only one trip up?) that it seems crafted to only allow that one solution - so it is contrived.

You also don't need to leave one switch on. Turn them all on and off, one at a time in sequence. Since you know cool-down rates for lightbulbs, you can tell which switch it was by measuring the temperature of the bulb. The advantage of my solution is it works even if you have 10 light-switches and one bulb - at least to the limit where the thermal curve is flat.
posted by vacapinta at 3:28 AM on June 23, 2015 [2 favorites]

The correct solution is firstly plan to rewire your house so that you don't control the light in your attic with a switch in your basement because seriously? What?!
If that's too much effort (and it will be I suspect), then at least go and buy a battery LED light for the meantime.
Also, if it's your house, label the switches and/or make a note in your house wiki to indicate what each switch does.
Also install a sensible attic door, because a one way attic (or basement door) is clearly a major hazard.
If it's not your house then you can either get your landlord to make these fixes or seal up that attic because it is dangerous!

Like others have said if it's a logic puzzle then it's one with unstated assumptions (i.e. incandescent bulb and one way doors) if it's a real world puzzle the solution is not to find out what switch does what but make some goddamn changes to your living conditions.
posted by Just this guy, y'know at 4:02 AM on June 23, 2015 [1 favorite]

One of my favorite things about the weird little narratives that set up logic puzzles, as a genre of writing, is how many of them have this kind of question-writer proxy figure. Dragons or kings or trolls or whatever else, they're almost always deeply malevolent (or at least barely veiled sadists), often nearly omnipotent beings, yet they have a compulsive fixation on enforcing rules rigidly even to their own detriment, and they are very prone to obsessing over tiny, fussy little details.

And what a contrast between such figures and the senior management that condone using such questions in interviews. Oh, wait....
posted by rongorongo at 4:05 AM on June 23, 2015 [1 favorite]

The "leader" solution to the prisoner problem takes on the order of 27 years (100x100=10,000 days). If it's a real world type of problem, there's significantly more danger of someone dying before the leader's count is complete than of making a wrong guess after 7 years (math here). It's a rather silly problem, like most of these.
posted by graymouser at 4:36 AM on June 23, 2015

Manhole covers are round because manholes are round.
posted by thelonius at 4:50 AM on June 23, 2015 [3 favorites]

Don't mind me. I'll sit in the dark.

(all this thread, and not one lightbulb joke? Come on, people!)
posted by Devonian at 4:51 AM on June 23, 2015 [2 favorites]

Dirty Harry has just discharged several rounds from a colt 45 in your proximity. He is now pointing the weapon at your head. He informs you that this is one of the most powerful handguns ever made and that a single bullet could blow your head off. How can you determine if he has discharged all 6 shots or only 5. Do you feel lucky?
posted by humanfont at 4:58 AM on June 23, 2015 [12 favorites]

I'm not smart enough to solve much of anything. I have, however, read a lot of puzzles.
posted by box at 5:31 AM on June 23, 2015

Take your one trip up to the attic immediately and rig up a webcam. Go back downstairs and flip the switches until you can see the light come on.

The dragon gave the knight ordinary water, expecting him to be poisoned by trying to counteract it, but the knight fatalistically assumed it was poison from well 7 and chose to do nothing, waiting to suffer a fate which proved not to happen. The knight gave the dragon ordinary water laced with arsenic. The dragon assumed that the knight would give it ordinary water in an attempt to poison it by drinking from well 7 to counteract a non-existent poison and likewise chose to do nothing. The knight and the dragon sat there glaring at each other until the dragon died from arsenic poisoning.
posted by talitha_kumi at 5:38 AM on June 23, 2015 [3 favorites]

I doubt that the amount of poison in one glass of water would be anywhere near the LD50 for something as large as a dragon.

Also, who the hell wants to own an island where all the groundwater is toxic?
posted by kewb at 5:41 AM on June 23, 2015 [4 favorites]

MONSANTO
posted by Aya Hirano on the Astral Plane at 5:59 AM on June 23, 2015 [4 favorites]

The more I think about this distinction between "true" logic puzzles and the real-world kind, the less I buy it.

I can see the argument that this light bulb puzzle would benefit from one more sentence in the setup: "You can't use any other people, objects or superhuman powers." But after that, if you go wrong by assuming it was a "true" logic puzzle, that's on you, I'd say – this is exactly the kind of unquestioned assumption that a good puzzle can root out.

And of course there's no such thing as a puzzle with zero assumptions anyway; even a true logic puzzle assumes "that the laws of logic apply" and "that the puzzle-setter is using words in their normal meanings", etc. So while you may of course prefer that kind of puzzle, I don't think you can really justify that on the grounds that they're "pure" while real-world puzzles aren't…
posted by oliverburkeman at 6:02 AM on June 23, 2015

Seal all the exterior windows and doors. Break the glass in all the lightbulbs in the attic. Fill the house with an explosive gas. Hide under a cast iron bathtub in the basement, and flip the switches with a long stick.
posted by blue_beetle at 6:04 AM on June 23, 2015 [6 favorites]

Why bother with a trip to the attic when you can download an app which will tell you whether a cable's carrying current. The rest is easy.
posted by ambrosen at 6:10 AM on June 23, 2015

"You can't use any other people, objects or superhuman powers."

What if I need a step-ladder to reach the light bulb in my attic?
posted by kithrater at 6:16 AM on June 23, 2015 [1 favorite]

I remember this from job interviews during the .com boom 20 years ago, when trick questions were all the rage. I told one interviewer (for CNet, I think?) that I already knew the answer, and he had literally nothing else to ask me.
posted by xthlc at 6:19 AM on June 23, 2015

The more I think about this distinction between "true" logic puzzles and the real-world kind, the less I buy it.

The fact that the average US light bulb would not work in the puzzle is enough to distinguish it from both a logic and a physics puzzle. If the puzzle specified that the light bulb was incandescent, then it's at least a physics puzzle. If the puzzle specified that the light bulb was incandenscent and then explained what that means (for all of those people who have never encountered one) then it would be a logic puzzle.

Think of it this way. There are a series of matchstick puzzles that my students enjoy. There are also a series of matchstick puzzles where you're supposed to break the matchsticks. That's fine when you're dealing with real physical objects, but if you put that on the board, the students will assume that it's a geometry problem, not an engineering problem.

Now, in the world most things aren't puzzles, they're problems. And there's some reason to believe that puzzle-solving destroys problem-solving, so perhaps we should prefer physics puzzles to logic puzzles, and engineering problems to geometry problems. I dunno.

I'd much rather see businesses start using trolley-problem variations for their interviews, anyway.
posted by anotherpanacea at 6:28 AM on June 23, 2015 [2 favorites]

Flip all three switches.
Go up to attic and confirm that light is on.
Say "yep, it's one of those."
Go on with your life like a normal person.
posted by sexyrobot at 6:28 AM on June 23, 2015 [5 favorites]

I told one interviewer (for CNet, I think?) that I already knew the answer, and he had literally nothing else to ask me.

That's mediocre! He could have at least asked you the one about the doctor who refuses to operate on the son.

These fads in interviewing come and go. I remember reading a piece about an era when investment banks and the like were fond of asking applicants to open the window, which couldn't be opened, to observe how they handled that. The same article said that one company ended up judging applicants on how well they picked up references to "The Big Lebowski", though.
posted by thelonius at 6:29 AM on June 23, 2015

There are three lightswitches marked on/off. Two of these switches control the attic light, but one of them is reversed (i.e. the attic light is on when that switch is off) The third switch swaps the two others, making the normal one reversed and the reversed one normal.
The attic light is a hyper advanced LED and so produces negligible heat and will never break.
The attic stairs are poorly built and everytime you go up there they have a chance of breaking (but you need to figure this light thing out before you can get round to replacing them). What's the fewest times you can visit the attic to determine exactly which switch is which.
posted by Just this guy, y'know at 6:39 AM on June 23, 2015

The wired switch will give off a faint spark...
posted by judson at 6:42 AM on June 23, 2015

The only questions like this I've ever been asked in interviews were a) for entry level jobs straight out of college and b) designed to see how well you could estimate or understand basic physical facts. No trickery, just some basic knowledge required.

Not all of which I had, apparently. I remember one question was to estimate the weight of sand poured into a football field to a depth of one foot. I told the interviewer I didn't know anything about football or the size of its field. He told me to estimate. I persisted a little bit - to the point where I admitted that I had actually never even watched a football game. I did some gross estimations anyway, but I could tell he wasn't terribly thrilled. Mind you this was in 2006; not quite ubiquitous-smartphone-era, but definitely Wikipedia-all-the-facts-era and it seemed unreasonable to me to not allow for looking up data in references (especially when most of engineering involves referring to the handbook anyway).
posted by backseatpilot at 6:45 AM on June 23, 2015

Flip all three switches.
Go up to attic and confirm that light is on.
Say "yep, it's one of those."
Go on with your life like a normal person.

I like this solution. It is a solution that requires ZERO trips to the attic.

All three switches must now be turned on and off together. Call this new switch "the light switch". So I have solved the problem. If I turn on "the light switch" the light in the attic will be on, according to the terms of the problem. If I turn it off, the light will be off. Thus, its a switch. The fact that other lights may also be on somewhere is extraneous to the problem.
posted by vacapinta at 6:45 AM on June 23, 2015 [3 favorites]

Invert your house. Now YOU'RE in the attic and can observe the effect of any switch.
posted by blue_beetle at 6:49 AM on June 23, 2015 [2 favorites]

At least I got the 'Number under the parked car' one, so I'm qualified to be a Hong Kong 6-year-old
posted by MtDewd at 6:50 AM on June 23, 2015 [1 favorite]

The point is simply to reason out that two states of the bulb aren't sufficient to distinguish between three switches, which can easily be done by brute force reasoning, and then to consider if there might be a third state to exploit. It's a nice little problem.
posted by thelonius at 6:50 AM on June 23, 2015

Oh, jeez, why didn't I think of this before? We're investigating the lightswitches, so we need to approach it with an appropriately investigatory praxis. Who investigates? Scooby-Doo and the gang. How do they investigate? They examine the premises. The lightswitches are on the premises; the lightswitches are the premise.

Pause for Scooby Snack.

Now, let us resume: the question is which lightswitches to switch. To switch is to move. What is a thing that moves? A thing that is colored poorly. There are three switches, but only one must move to turn on the attic light; only one will be colored poorly, a mismatch against the richer matte painting of the other two. QED.
posted by cortex at 7:00 AM on June 23, 2015 [6 favorites]

So what does it mean if my first thought was just to follow the romex back to the circuit breaker to see which one is connected to the breaker marked ATTIC? As opposed to the breaker marked KOINE?
posted by ROU_Xenophobe at 7:04 AM on June 23, 2015 [2 favorites]

The more I think about this distinction between "true" logic puzzles and the real-world kind, the less I buy it.

But the problem with this kind of logic problem is that it constrains creativity rather than testing it: we've had loads of different answers in this thread, some practical, some funny but all of them falling within the parameters of this question. However, if you replied with any of them you'd be told you were wrong for failing to follow the pedantic prescriptive line of thought that the questioner was after. If you enjoy solving problems within these artificially constricted scenarios, that's fine, but to claim it's an indicator of any skill broader than 'can solve problems in an artificially constricted scenario' is probably a mistake.
posted by Ned G at 7:04 AM on June 23, 2015 [2 favorites]

Turn on switch one for 10 seconds, then turn it off. Turn on switch two for 20 seconds, then turn it off. Turn on switch three for 30 seconds, then turn it off. Run to the attic and hold the bulb firmly in your hand. If it's hot as hell and burns the crap out of you, it's switch three. If it's kinda hot and hurts a bit, it's switch number two. If it's kinda warm it's switch one.
posted by ChuckRamone at 7:05 AM on June 23, 2015

Someone speculated what Richard Feynman would do with this puzzle, to chuckle-worthy effect.

Proving the point that in any job interview, they're interviewing you but you are also simultaneously interviewing them to see if they are a good fit . . .
posted by flug at 7:12 AM on June 23, 2015 [1 favorite]

It's times like these that we need a filthy light thief.
posted by dances_with_sneetches at 7:31 AM on June 23, 2015 [3 favorites]

I'd just go outside and see Alice and Bob, who are on their contractually-obligated fifteen minute smoke break between logic puzzles, and ask them.
posted by dr_dank at 7:35 AM on June 23, 2015 [2 favorites]

Rewire it so that all three circuits are controlled by whichever switch you choose. Then go have a stern word with whoever designed your crazypants house with its ridiculous electrical system and single-use doors.

I bet it's really frustrating to schedule this meeting, though. "Oh yeah, we can talk if you can figure out my schedule. I'm free one day in the morning and one day in the afternoon. If I'm free on Tuesday morning, I'm busy on Thursday afternoon. I'm never free on two consecutive days ..."
posted by obscure simpsons reference at 7:49 AM on June 23, 2015 [14 favorites]

The way you all are pissed about these puzzles in the exact right way is why I come here so often.
posted by MCMikeNamara at 8:08 AM on June 23, 2015 [3 favorites]

Take the elevator to the second floor and walk up the stairs to the attic, unless it's raining, in which case you can take the elevator to the attic.
posted by rocket88 at 8:16 AM on June 23, 2015

I used to have a poorly labeled breaker box in my basement, and I am lazy about going up and down stairs. The actual real-world solution to this problem is to have an assistant who hollers down the stairs when you find the right switch. There are other solutions, but they tend to be slower, or they rely on extra equipment. At no time should you consider waiting for a light bulb to heat up (seriously?! That takes too much time, doesn't help you if the attic bulb is burnt out, and if the attic is so hard to get to that you can only go once, chances are that the light may have cooled by the time you arrive.)
posted by surlyben at 8:16 AM on June 23, 2015

1) Go to Metafilter. Get the "correct" answer.
2) Reading the comments, realize the question, the whole category of puzzles, is suspect. Decide the question doesn't need solving.
3) Read the minority opinion, strongly expressed, that it is a a good puzzle and useful. Consider.
4) Get distracted by the jokes
5) What was the problem again?
posted by librosegretti at 8:25 AM on June 23, 2015 [3 favorites]

What we need to add to this puzzle, along with Monty Hall to reveal a goat behind light switch #3, leaving you and your friends to argue interminably about whether or not the odds of finding the correct answer have been changed just because the house's wiring has been eaten by the goat, is:

The stairs to the attic are a sort of downward escalator arrangement that moves downwards at the exact same speed that you are trying to climb upwards.

NOW try to get up to the attic to check that lightbulb, puzzle-solver!
posted by flug at 8:28 AM on June 23, 2015 [1 favorite]

The knight's glassful was normal water of the kind he'd be drinking until time of duel.

I mean, he couldn't be drinking from the wells until that point. He'd be already dead. So there's obviously some unstated water source here.

That is not necessarily true. The knight (and the dragon for that matter) could always drink from a well as long as they then followed it with water from a higher numbered well. There is no need for a fresh water source on the island.

I suppose given that its an island, there is water all around them - but that is going to be salt water or lake water, both which should be readily discernible from well water.
posted by rtimmel at 8:35 AM on June 23, 2015

That is not necessarily true. The knight (and the dragon for that matter) could always drink from a well as long as they then followed it with water from a higher numbered well. There is no need for a fresh water source on the island.

That doesn't follow. At least, it won't hold true for long. You could start off by drinking from well 1 and follow up with well 2 to neutralise the poison, but you'll then have to drink from well 3 to neutralise that and so on. Sooner or later you've drunk from the highest numbered well in order to neutralise the previous poison, and then you've got nowhere left to go. The only way to not be killed by the poisoned wells sooner or later is to never drink from any of them. For someone to live on the island without dying of dehydration within the first fortnight, they must have an alternative, non-poisoned source of water.
posted by talitha_kumi at 8:40 AM on June 23, 2015

Talitha kumi

That can't be how it works. If it was, the "official" solution - that the knight drink from well 1 before the duel - would be a non-starter. He would have to progress up the wells and die after he hit well 6. In fact, the duel itself would be a mutual suicide pact.
posted by rtimmel at 8:53 AM on June 23, 2015

Go back down to the lightswitches. Turn each one on in turn. When you hear the noisemaking thing switch on, you've found your switch.

In every house my family (me, my brothers, my parents) moves into, one of the first things we do is debug the electric panel. This involves one of us flipping breakers, while another moves room to room checking lights and plugs for power. Only one visit per room is usually required.
posted by bonehead at 8:55 AM on June 23, 2015

What's the water table like on this island? Surely these wells are contaminating each other and mixing poison + antidote up in some fashion that makes dosage extremely important, it can't just be as simple as a cup of well 2 neutralizing a cup of well 1, as well 1 is surely contaminated with whatever is poisoning wells 2-7 in addition to having its own local source of poison. If any well has enough contamination from other wells it could go past the point of having its local source of poison neutralized and become poisonous again due to too much contamination. Well 7, being the highest, shouldn't be contaminated by the other wells, so it will work as the only pure source of antidote for any other well provided you can figure out the required dosage.

Another thing to take into consideration is that the dragon has its own powerful and finely-controlled source of heat, and can therefore manufacture steam-activated carbon with easily-available resources on the island. He may be able to create effective filtration systems for every well to remove the poison.
posted by jason_steakums at 9:00 AM on June 23, 2015 [5 favorites]

Spend two years building a resistance to iocane powder, then poison both glasses.
posted by Anticipation Of A New Lover's Arrival, The at 9:05 AM on June 23, 2015

Is it a red dragon, or a white dragon, or some other color?
posted by librosegretti at 9:05 AM on June 23, 2015

how is the dragon able to hold a glass small enough for a human to use for drinking? how is a dragon able to turn the little handle to winch water up from a well. why aren't they both already dead from well poison far before this stupid duel takes place.

where is this island and how can i gather up all the people who use logic puzzles in job interviews and send them there to die
posted by poffin boffin at 9:10 AM on June 23, 2015 [3 favorites]

No, I don't remember last weeks puzzler!
posted by Four Flavors at 9:11 AM on June 23, 2015 [2 favorites]

If the attic/lightbulb question came up in a job interview I'd have to point out that placing a single person constraint on the project is not the best use of the company's resources since the single person solution requires more total man hours than the team approach does, and having me fart around with light switches is a waste of my salary. Then I'd round up the intern or the most junior staff member and have them go stand in the attic with a cell phone.

Also: my house doesn't have an attic. My parents' house has an attic with a single light bulb that can't be reached to test its temperature (replacing it is difficult). Some houses have the light switches installed upside down. This puzzle assumes too much about the initial state of things and depends on physical properties (e.g. waste heat, the idea you can reach the bulb in order to feel how hot it is, a steady air temperature in an attic and not something so hot or cold that the temperature test wouldn't even work anyway).

I would probably refuse to work for a company that asked me this question.
posted by fedward at 9:13 AM on June 23, 2015 [1 favorite]

The question as posed is unanswerable, so you need more data. At that point, it's a guessing game as to which unstated set of conditions is also in effect (as the Feynman piece so beautifully illustrates). Look for a spark? What if the other two light switches are connected to lights elsewhere? Feel the bulb? What if it doesn't get warm when on? And so on, and so forth.

So, what is the point? That's why I got very bored with logic games very early on - the ones that can be solved with the information given tend to be either easy, once you've learned deductive and inductive reasoning, or require a lot of slogging through "Anne lives next to Bob, but the house with the brown door has an even number" combinatorial bollockry. Like crosswords; once you've learned the rules then you've got to enjoy the work for its own sake, and I've always been bad at that. Or it's a 'can't get this, but let's see you try' test, when I'm with Kirk (in the computer lab with the OS manual).

The one exception, and one where I'd gladly spend more time, is the class of logic problem that reveals rules I don't know - specifically, that huge swathe of maths where I'm functionally... illiterate? I would say innumerate, only I'm fine with numbers. That's why I'm edging towards learning Haskell, because I can't think like that and I'd like to have the option. But if there was a set of well-written stories that led me to understanding how, say, Maxwell's equations actually work (as opposed to describing them in ways that vanish from my mind a minute after I've stopped reading them), I'd sign up.
posted by Devonian at 9:14 AM on June 23, 2015

why the fuck would you want to POISON A DRAGON THAT CAN VERBALLY COMMUNICATE WITH HUMANS USING AN ADVANCED LEVEL OF COMPREHENSION AND UNDERSTANDING

i'm so mad
posted by poffin boffin at 9:19 AM on June 23, 2015 [6 favorites]

Look when the only tool you have is poison wells everything looks like a contrived poison well-water duel
posted by jason_steakums at 9:25 AM on June 23, 2015 [10 favorites]

Turn all three switches on and off every five seconds. Win the Turner Prize. Buy a better house.
posted by oulipian at 9:29 AM on June 23, 2015

The dragon gives the knight water 6. The knight gives the dragon plain water. The knight pretends to die immediately, the dragon brings the corpse back to its lair on the mountain, where the dragon drinks water 7 and dies. The knight then drinks water 7 and lives.
posted by milk white peacock at 9:29 AM on June 23, 2015 [1 favorite]

Also that's a strange dragon that can communicate with a knight in order to come up with rules for this water-drinking duel, but lacks the ability to solve a simple logic puzzle. Poor dragon didn't deserve that fate. The knight who takes advantage of the dragon's difficulty with logic is kind of an asshole. I thought knights were supposed to adhere to a code of honor.
posted by fedward at 9:32 AM on June 23, 2015

I can't see how the knight lives and the dragon dies. Any strategy I can find that absolutely guarantees the knight's survival depends on the ability to survive drinking two glasses of poison before drinking an antidote, but under this condition the dragon can also ensure its survival.

If you can't drink poison twice before being cured, then the dragon can't guarantee its survival, but nor can the knight, as far as I can see. I'm stumped.
posted by Zeinab Badawi's Twenty Hotels at 9:34 AM on June 23, 2015 [1 favorite]

Dragon flies away from pirate adventure b-plot island and leaves knight to deal with it.
posted by jason_steakums at 9:35 AM on June 23, 2015

How can one keep one's vows to one's liege lord when one hies off to an island uninhabited save by monstrous beasts in league with the Devil? This man is no knight, I say! I rebuke your logic puzzle!
posted by prize bull octorok at 9:37 AM on June 23, 2015 [1 favorite]

At that point, it's a guessing game as to which unstated set of conditions is also in effect […] So, what is the point?

If this is an interview question, that's exactly the point. Your job probably involves being told to do things by people who don't tell you everything you need to know, who embed bizarre assumptions in their requests, and who ask you to do something other than what they actually want you to do, if they even know what they want you to do. (Depending on your job, these people may be higher-ups or they may be customers.) How you deal with that is the question. Are you able to converse with the questioner in a way that extracts the real requirements without annoying them? Are you able to probe around for those unwarranted assumptions and pick up cues as to their nature ("this person looks about 45; they probably assume all light bulbs are incandescent")? Are you able to make your thought process understandable to coworkers? That kind of thing.

I think some of the grumpiness surrounding these kinds of interviews stems from the assumption that the way to do well in the interview is to correctly solve the puzzle or write bugfree code on the whiteboard or whatever. In the interviews I've participated in, it really isn't.
posted by hattifattener at 9:37 AM on June 23, 2015 [1 favorite]

No, wait: Before the duel, the knight drinks water 5. The dragon, knowing the knight can't get to water 7 for an antidote, gives the knight water 6, which neutralizes water 5 and the knight lives. The knight gives the dragon plain water. The dragon drinks water 7 to counteract what it believes was poison, and dies.
posted by milk white peacock at 9:43 AM on June 23, 2015 [1 favorite]

lies, lies.. Do not be deceived.

THERE.. ARE... FOUR.. LIGHTS...
posted by k5.user at 9:46 AM on June 23, 2015 [1 favorite]

I think some of the grumpiness surrounding these kinds of interviews stems from the assumption that the way to do well in the interview is to correctly solve the puzzle or write bugfree code on the whiteboard or whatever.

My personal grumpiness about these kinds of questions is that for them to work in the theoretical way you're proposing requires that the interviewer have both the skill and intent to follow through with it. Unfortunately, I have seen quite a lot of times that questions like these get used by people who more or less googled "tough interview questions" or something similar, and instead of viewing it as a way to learn how a person thinks, go into it thinking there's one singular correct answer that, if not found, means the candidate is no good.

Perhaps more broadly: I don't think these questions work at all if the interviewer wasn't smart enough (and knowledgeable enough of the intent of the question, and the myriad paths the answer could take) to come up with it on their own.
posted by tocts at 10:00 AM on June 23, 2015 [2 favorites]

The knight, whose sworn duty is to rid the world of dragon, even at the cost of his own life, goes first. He drink the poison offered by the dragon. When the dragon drinks, the knight strikes, knowing that at that moment the dragon will both be slightly distracted by the challenge and unable to produce flame due to the water in its mouth. A single swift slice beneath the dragon chitinous breastplate silences the dragons heart.

The knight is resigned to his own death , knowing it was the only way to get the dragon close enough to slay. But unbeknownst to the knight, St. Michael sees the knight's purity of intent and, spare him from his fate.

(A knight that would resort to trickery would never have survived long enough to to be part of the duel)
posted by rtimmel at 10:08 AM on June 23, 2015 [3 favorites]

The reason so many people get this question wrong is because the dragon is actually the knight's MOTHER.
posted by poffin boffin at 10:11 AM on June 23, 2015 [4 favorites]

Do you think in the Layton universe, people are asked to debug code in hiring interviews?
posted by halifix at 10:40 AM on June 23, 2015

one company ended up judging applicants on how well they picked up references to "The Big Lebowski", though.

They're not wrong, they're just assholes.
posted by ambrosen at 10:53 AM on June 23, 2015 [1 favorite]

Have we considered the possibility that the dragon is on a treadmill?
posted by cortex at 11:05 AM on June 23, 2015 [1 favorite]

The answer has some idiosyncratic presumptions about what is "real world" and what is not. In the "real world" bulbs get warm, but apparently also people can only go upstairs once and can't come back afterward.

Also, for cultural completionist purposes, I offer the following additional criticisms just because nobody's done it yet:

Check your privilege, maaaaaaaaaaan. The question assumes you live in a country that has electricity more than four hours per day on average and / or at predictable times. Not everybody can flip a switch an assume power is going to the bulb when they can't see it. Also, the answer is ablist. What if you can't get up the stairs to the attic at all, or at least quickly enough to catch it while the bulb is warm?
posted by George_Spiggott at 11:07 AM on June 23, 2015

A wizard has trapped you in a cell. "There are two kinds of logic puzzles," he says. "Ones where you have to derive some sort of mathematical solution, like the 99 prisoners puzzle, and ones where you have to 'out-think' the conditions of the puzzle and provide some answer outside the original stated parameters, like the light bulb in the attic puzzle. What kind of puzzle is this? If you answer incorrectly, you will be killed. Also, everything I say to you is a lie."

Solve this puzzle. Our hiring decision will be based on the quality of your answer.
posted by prize bull octorok at 11:20 AM on June 23, 2015 [4 favorites]

In other words, are you a Spock or a Kirk? Does Star Fleet Academy award you a first place in math or a commendation for original thinking?
posted by George_Spiggott at 11:22 AM on June 23, 2015

Kill the wizard, steal his job, profit.
posted by poffin boffin at 11:24 AM on June 23, 2015

Kill the ~~wizard~~ asshole interviewing you for the job, steal his job, profit.
posted by oulipian at 11:35 AM on June 23, 2015

yes that is the joke.
posted by poffin boffin at 11:37 AM on June 23, 2015

The answer has some idiosyncratic presumptions about what is "real world" and what is not. In the "real world" bulbs get warm, but apparently also people can only go upstairs once and can't come back afterward.

That's part of my problem with these puzzles as well. And I'm not asking for much. In this instance it would help to just add a line that says something like "You are too lazy to go up to the attic more than once." That not only makes it totally realistic and also a puzzle I would find important enough to solve.
posted by MCMikeNamara at 11:38 AM on June 23, 2015 [1 favorite]

“logic immediately tells you that it isn't a pure logic puzzle”
Yeah.
1. Turn off power in the house
2. Go to attic, connect wire to bulb fixture
3. Connect lead from ohmmeter to light switches sequentially. Voila.

Alternatively, find out why the electrician is such wiseass.

"why did the knight live? Why did the dragon die?"

The dragon fell victim to one of the classic blunders, the most famous of which is: "never get involved in a land war in Asia," but only slightly less well-known is this: "Never go in against a Sicilian Knight when death is on the line"! Aha ha ha! Ha ha ha! Ha ha ha...*thump*

The dragon dies because if there’s a non-poisoned well on the island (and the knight can slip the dragon pure water) than there are certainly plant toxins such as Oleander which is fatal to lizards, the knight can harvest, and slip as pure toxin which no well will cure.

The knight lives because before drinking what the dragon will give him he drinks from well 1. Then after drinking what the dragon gives him he drinks from well 1 again then well 2. No matter what the dragon gave him, the knight lives because the first dragons failed undergraduate chemistry and over the generations traditional opposition to chromatography became a moral imperative and anyway dragons can neither fit in lab coats nor handle test tubes with their claws.
posted by Smedleyman at 11:51 AM on June 23, 2015 [1 favorite]

Another problem with this interview question format is that it's testing for people who happen to have heard about the right way to approach the question. It's yet another layer of "don't answer this interview question the way a normal person would; answer it how someone who would answer it the 'right' way would answer it." So someone who is clued in will emphasize the show-your-work aspects, and play up the cleverness of their thought process and their willingness to think outside of the box and brainstorm solutions, etc, rather than arriving at a correct answer. Someone who isn't clued in might try to silently work through permutations and processes in their mind (which is natural, after all) and get frustrated that they're being put on the spot, and feel pressured to present some answer. It's entirely about whether you're coached into understanding this is a specific lateral-thinking interview question. In that respect, it's yet another way that companies secretly test for culture fit (as a proxy for class and other things).
posted by naju at 11:54 AM on June 23, 2015 [4 favorites]

prize bull octorok: "A wizard has trapped you in a cell. "There are two kinds of logic puzzles," he says. "Ones where you have to derive some sort of mathematical solution, like the 99 prisoners puzzle, and ones where you have to 'out-think' the conditions of the puzzle and provide some answer outside the original stated parameters, like the light bulb in the attic puzzle. What kind of puzzle is this? If you answer incorrectly, you will be killed. Also, everything I say to you is a lie."

Solve this puzzle. Our hiring decision will be based on the quality of your answer."

Hire this.

- BLAM! -

drops gun on floor mike style and walks out
posted by Samizdata at 12:02 PM on June 23, 2015

naju: "Another problem with this interview question format is that it's testing for people who happen to have heard about the right way to approach the question."

Yeah. Although, for the record, while this kind of lateral thinking puzzle (see also: why are manholes round? bleh) gained notoriety in tech circles around the time of the first dot-com boom (I'm looking at you, Microsoft circa 1998), as far as I can tell, no large tech company uses them now. They're considered hopelessly passé, like a personality test or a phrenological study. Not that other, non-tech companies aren't using them but definitely in tech circles their usage has definitely dropped off.
posted by mhum at 12:29 PM on June 23, 2015 [4 favorites]

The funny thing is that the first switch always tells the truth, the second switch is always lying, and all three switches are able to change their position.

The third switch? THE THIRD SWITCH IS YOU.

(did I blow your mind?)
posted by Sunburnt at 12:36 PM on June 23, 2015

Special fun note: Googling "why are manholes round?" displays an answer from www.careerfaqs.com.au.
posted by MCMikeNamara at 12:37 PM on June 23, 2015

Adding to the interview-question tangent: these lateral-thinking problems were commonly referred to on Usenet as "Microsoft problems" in the 90s. Whether that was ever accurate or not, I don't know. Two friends first interned at and then got hired by Microsoft within the last year and I can confirm that neither of them was ever asked to, e.g., estimate the weight of a 747 or escape a blender, so things must have changed.

Certainly, two years ago, Google's senior VP of people operations (about the most Googlesque job description I can imagine) confirmed to the New York Times that brainteasers are a

complete waste of time. They don’t predict anything. They serve primarily to make the interviewer feel smart.

I have no idea whether whatever Google are asking instead these days is a better predictor, and I don't know that they do either, but I'm not sorry that this style of cargo-cult hiring is on its way out.
posted by Zeinab Badawi's Twenty Hotels at 12:42 PM on June 23, 2015 [2 favorites]

Sorry, mhum, missed that as I was writing. Er, what mhum said!
posted by Zeinab Badawi's Twenty Hotels at 12:45 PM on June 23, 2015

> Solving the 100 light string problem using a 10 bulb string got the pattern 1, 4, 9. Is the 100 solution 1, 4, 9, 16, 25, 36, 49, 64, 81, 100?

And here's another two for you guys to wrangle:

A group of people with assorted eye colors live on an island. They are all perfect logicians -- if a conclusion can be logically deduced, they will do it instantly. No one knows the color of their eyes. Every night at midnight, a ferry stops at the island. Any islanders who have figured out the color of their own eyes then leave the island, and the rest stay. Everyone can see everyone else at all times and keeps a count of the number of people they see with each eye color (excluding themselves), but they cannot otherwise communicate. Everyone on the island knows all the rules in this paragraph.

On this island there are 100 blue-eyed people, 100 brown-eyed people, and the Guru (she happens to have green eyes). So any given blue-eyed person can see 100 people with brown eyes and 99 people with blue eyes (and one with green), but that does not tell him his own eye color; as far as he knows the totals could be 101 brown and 99 blue. Or 100 brown, 99 blue, and he could have red eyes.

The Guru is allowed to speak once (let's say at noon), on one day in all their endless years on the island. Standing before the islanders, she says the following:

"I can see someone who has blue eyes."

Who leaves the island, and on what night?

There are no mirrors or reflecting surfaces, nothing dumb. It is not a trick question, and the answer is logical. It doesn't depend on tricky wording or anyone lying or guessing, and it doesn't involve people doing something silly like creating a sign language or doing genetics. The Guru is not making eye contact with anyone in particular; she's simply saying "I count at least one blue-eyed person on this island who isn't me."

And lastly, the answer is not "no one leaves."

(XKCD source)

Problem two:

A wizard has shrunk you down to the size of an ice cube [about 2" tall] and thrown you into a blender! The wizard will turn the blender to "mince" in 60 seconds, how can you escape? The blender walls are too slippery to climb, but the wizard has not sealed the top.

Show your work.
posted by LiteS at 12:51 PM on June 23, 2015

This book about puzzles in interviews was kinda fun to read at the time, and has probably aged as well as the average business book.
posted by box at 12:54 PM on June 23, 2015

i escape because magic is pretend, and my work is shown by expansively gesturing to the surrounding world where nothing is magical and everything is an endless tuesday afternoon in 96 degree heat.
posted by poffin boffin at 12:56 PM on June 23, 2015 [2 favorites]

Interview puzzles should involve situations that will actually come up, like "you have a colleague who sucks technically but is tight with the founding team and a million times better at office politics than you would ever even want to be. This colleague is heavily invested in a subsystem which is a source of most of the product's bugs, has never been properly documented and is a massive sink for engineer-hours. You have created a staggeringly robust and relatively futureproof replacement for that subsystem which is only five lines long. Describe how you would go about introducing this change into the product."
posted by George_Spiggott at 12:58 PM on June 23, 2015 [3 favorites]

otherwise i think it would be lovely to be part of a frozen daiquiri and if any wizards would like to make that happen i am at your disposal.
posted by poffin boffin at 12:59 PM on June 23, 2015 [2 favorites]

Problem one: I make an impassioned speech before congress, pleading with my country to declare war on the Archipelago of Logic Puzzles.

Problem two: I lie as flat as I can so that the blender blades pass above me, but let's face it, this isn't going to solve my wizard problem in the long term.
posted by prize bull octorok at 1:01 PM on June 23, 2015 [4 favorites]

A wizard has shrunk you down to the size of an ice cube [about 2" tall] and thrown you into a blender! The wizard will turn the blender to "mince" in 60 seconds, how can you escape? The blender walls are too slippery to climb, but the wizard has not sealed the top.

Is there anything else in the blender besides me? Cubes of fruit waiting to be blended, for instance? If there's anything else solid in the blender that isn't me, then I'll climb it to get out.

If there's nothing else in the blender, then I'll lie down flat in the bottom so that when the blades get switched on they whizz over the top of my head and fail to do any damage. Eventually the wizard will get bored of trying to kill me with a weapon that can't hurt me, and will pull me out so they can try something else.
posted by talitha_kumi at 1:03 PM on June 23, 2015

The second puzzle almost certainly relates to the volume / weight / muscle mass ratio thing that's actually behind the famous "ants can lift twelve times their body weight" thing that comic books always get wrong. The answer is you jump out.
posted by George_Spiggott at 1:06 PM on June 23, 2015 [1 favorite]

You give the wizard what he wants, don't be a hero
posted by jason_steakums at 1:10 PM on June 23, 2015 [5 favorites]

They're considered hopelessly passé, like a personality test or a phrenological study.

I wish that personality tests were no longer done. Since phrenology seems a lot like a head massage, I'd be cool with those.
posted by jeather at 1:19 PM on June 23, 2015

bruce willis storms in and shoots the wizard in the head. "anybody else want to negotiate?"
posted by poffin boffin at 1:20 PM on June 23, 2015 [1 favorite]

Based on science, I know that if I were shrunk by a Wizard, I would not retain proportionate strength, but rather absolute strength. So I'd just jump out of the blender and punch him in the face, since Wizards are invariably frail little nerds.
posted by skewed at 1:23 PM on June 23, 2015 [2 favorites]

> Well that one didn't last long at all. I also would have accepted "In a world where there is magic, I also have magic, and I use magic to defeat the wizard."

Here's another one for y'all to much on.

One rope bridge, four people. One flashlight. The Fallen will consume them if they do not cross before midnight.

The bridge is long and rickety, and requires a flashlight to navigate across alive. The two most athletic of the party can cross the bridge in one minute and two minutes, respectively. The third is an older woman, a doctor, who takes five minutes to cross. The fourth of the party is an injured mechanic who can fix the vehicle at the safehouse in the morning. It takes him ten minutes to cross the bridge.

Only two people can safely cross the bridge at once, lest they risk the bridge collapsing, and the bridge cannot be safely crossed without the flashlight. When The Fallen arrive at midnight they will be forced to cut the bridge to keep the remaining party safe for the night. It is too far to throw the flashlight across. When two cross the bridge simultaneously, it takes the longer time for them to cross. For example, bringing the two athletic individuals and the flashlight across takes two minutes.

The party approaches the start of the bridge at exactly 11:42 pm. Can everyone cross before midnight and survive? If not, who lives?
posted by LiteS at 1:32 PM on June 23, 2015 [1 favorite]

COME ON this is so easy, it's me, I live, because I leave everyone else to die.
posted by poffin boffin at 1:33 PM on June 23, 2015 [3 favorites]

> I'll have to remember never to get into a hypothetical situation with poffin boffin.
posted by LiteS at 1:41 PM on June 23, 2015

LiteS, that's a good one, thanks! I think I'll call it "Greedy algorithms have no place in the zombie apocalypse".
posted by Zeinab Badawi's Twenty Hotels at 1:44 PM on June 23, 2015 [1 favorite]

10 + 1 + 5 + 1 + 2 = 19
posted by kewb at 1:56 PM on June 23, 2015

Ace Mcsprintly (1 Minute)
Jack FastPants (2 Minutes)
Dr Sarah NormalSpeed (5 Minutes)
Ryan "WrenchFace" Slowcrawl (10 Minutes)

Ace and Jack cross (2 minutes)
Ace Returns (1 minute)
Dr NormalSpeed and Wrenchface cross (10 minutes)
Jack Returns (2 minutes)
Ace and Jack Cross (2 minutes)

17 mins

1 minute to chop the bridge, we're all safe from zombies.
posted by Just this guy, y'know at 2:10 PM on June 23, 2015 [6 favorites]

All of these are less obnoxious than morality puzzles where you choose to flip a switch to kill one person and save several others or you can only rescue a baby or the last remaining copy of the complete works of Shakespeare from a burning building. Situations are just as ridiculous, but with added guilt!
posted by chaiminda at 2:22 PM on June 23, 2015 [1 favorite]

Do you save 100 poisonous dragons or 100 babies that are in jail for tiny murders, think fast because a wizard will break your lamp in 10 minutes and you can't solve riddles in the dark with a flashlight that only works under unreliable, arbitrary circumstances
posted by jason_steakums at 2:28 PM on June 23, 2015

ObTheToast: How To Tell If You Are In A Logic Puzzle
posted by Zeinab Badawi's Twenty Hotels at 2:34 PM on June 23, 2015 [5 favorites]

True story: the master bedroom in my apartment has one switch which has no apparent effect. There is also a solid circular plate in the middle of the ceiling of the master bedroom, which looks like the sort of place where a ceiling fan might be installed.

The puzzle: can I get a reduction in rent because my apartment came with a substandard mindteaser?
posted by DevilsAdvocate at 2:38 PM on June 23, 2015 [3 favorites]

George_Spiggott: "Interview puzzles should involve situations that will actually come up, like "you have a colleague who sucks technically [...]"

Interestingly enough, this is actually one of the main trends in (tech) interviewing right now -- behavioral or situational interviewing. Sometimes the question is phrased as a hypothetical ("how would you deal with a crummy colleague"), sometimes it's about prior experience ("tell me about a time when you had to deal with a crummy colleague").
posted by mhum at 2:50 PM on June 23, 2015 [3 favorites]

this is actually one of the main trends in (tech) interviewing right now

I got trained on doing a STAR interview 10 or 15 years ago... and it's a hell of a lot more useful than a brain teaser.
posted by GuyZero at 3:02 PM on June 23, 2015 [1 favorite]

dragons always babies NEVER
posted by poffin boffin at 3:57 PM on June 23, 2015

The guru and the brown-eyed islanders can never get off, since their actual eye colors aren't even available to them as guesses.

1. Supposing there was one blue-eyed islander, she would know her eye color immediately from the guru's pronouncement and leave.

2. Supposing there were two blue-eyed islanders, each would deduce her own eye color from the other's not immediately doing so as per 1., and both would leave on the second raft.

3. Supposing there were three blue-eyed islanders, each of the three would deduce her own eye-color from the fact that the other two blue-eyed islanders do not deduce and perform as per 2. All three would leave on the third raft...

It iterates out to 100, and all and only the blue-eyed islanders leave at the same time, I'm going to say on the 100th or 101st raft.
posted by batfish at 4:40 PM on June 23, 2015 [1 favorite]

Also, this puzzle is totally set in the house we just moved into. There are light switches that do nothing, and there are light bulbs with no switches. There are entire rooms with no light switches (hello lounge!). For any given light switch, it is a 50/50 chance that it is wired backwards or upside down. There are even two light switches on the same panel which are each wired the opposite way to the other.

We are having an electrician in to check all of the wiring VERY CAREFULLY. (Which also has something to do with the fact the dishwasher has clearly been leaking into its own power socket.)
posted by lollusc at 5:03 PM on June 23, 2015 [2 favorites]

Supposing there was one blue-eyed islander, she would know her eye color immediately from the guru's pronouncement and leave.

Damn I hate that one. My objection is the same as it was when I first heard it in middle school from a teacher who loved giving us these things. Everyone on the island knows already that there isn't only one blue-eyed islander, because they can already see at least 99 of them. The statement from the guru gives them no new information at all. Therefore they do nothing. Unless they all want to get off the island, and are convinced by logic beyond human understanding that the most logical signal to start counting days is this inspirational utterance from their guru, rather than some other random event.
posted by sfenders at 5:32 PM on June 23, 2015 [1 favorite]

So instead, it's measuring how likely the interviewee will sit and take whatever bullshit judgement is made about them by an authority figure?

I didn't say anything about sitting and taking it, and to be fair, 'bullshit judgment' is your perspective of the solution, and it's not one that's widely shared as far as I can tell.

I'm sure if you were able to say something like 'hmm, I guess I was thinking about it this way instead', and maybe talk more about your problem-solving preferences, that'd be seen as positive. As I said, the answer is irrelevant. So is your agreement or disagreement with the solution, for that matter. What's important is how you talk about those things - whether you show a capacity for reflection and calm reasoning, and whether you can do that without getting really defensive or lashing out.
posted by obiwanwasabi at 5:50 PM on June 23, 2015

2. Supposing there were two blue-eyed islanders, each would deduce her own eye color from the other's not immediately doing so as per 1., and both would leave on the second raft.

I don't see how step two follows. I looked at explanations, and I'm not saying they're wrong, I'm just saying I don't really see how step 2 follows. If there are two blue-eyed people, Amy and Betty, seems like they could both say "wow, guru says she can see blue eyes, no shit, I've seen Amy's/Betty's blue eyes every day for years." If they both know that the number of blue eyed people is either 1 or 2 (just the other person, or the other person plus themself), what's the next step? It just seems that could hold forever.

Oooooooooh, damn, I just got it. Awesome. Will probably have to re-think it several times to be able to articulate it though.

It seems to me that having so many people in the riddle makes it much harder than it needs to be. It would be (in my opinion) a cooler, cleaner puzzle if it was just three people, Amy, Betty and Guru, with both Amy and Betty having blue eyes. Because once you get to step 2, all the other steps obviously follow.
posted by skewed at 6:00 PM on June 23, 2015

The statement from the guru gives them no new information at all.

Hmm, really? Then why can't the brown-eyed islanders do the same thing?
posted by batfish at 6:01 PM on June 23, 2015

But really, if they are all perfect logicians, then why would the Guru waste her one pronouncement saying something so illogical? Just say "I see 100 blue-eyed people", and everyone goes home that night. Except for the Guru herself, but she was fucked anyway. I guess she's just being vague out of spite? The hundred brown-eyes certainly aren't going to be very good company after they've figured out what she did.

They can all guess they have brown eyes at this point, because if one of them had different colored eyes, that would probably have been the more pertinent thing for the Guru to mention, but she's already proven she can't be trusted to give useful facts. The Guru's days are numbered. But, they are numbered 1 through 7, and each day can neutralize the the poison from the lower numbered days...
posted by team lowkey at 6:02 PM on June 23, 2015 [3 favorites]

I mean, the import of the guru's message must actually be "although we all know there are many blue-eyed among you, I want you all to please imagine that it possible there is only one. I tell you now, there is at least one. Please behave accordingly." Everyone is logical enough to get that message just from "I can see someone who has blue eyes." He might as well have said "my favourite colour is blue." Or shorten it further to just "blue". That's all these poor people are waiting on, some way to agree on which colour to use first and when to do it. Do they have the same astonomy as us? Do they have the concept of a "blue moon"? Maybe the guru could just point at the moon on the appropriate night and they'd get the same message. Maybe the ferry gets a new brown coat of paint one day and they all take that as the sign they've been waiting for. The puzzle would be easier actually, if the guru just said "blue". It's only misdirection to think there's meaning in the rest of his message.
posted by sfenders at 6:02 PM on June 23, 2015

Imagine there are just three people, Amy, Betty (both have blue eyes) and Guru Genevive (green eyes). Guru says "I see blue eyes".

Amy thinks "Yeah, obviously. I already knew there were either one or two blue-eyed people." Betty thinks the same thing.

Crucially though, Amy thinks "I wonder if Betty is surprised by the fact that there are blue eyed people on the island? She might not have known, since maybe I have brown eyes. Of course, if I do have brown eyes, then Betty will be very surprised that there are blue eyes on the island, and then she will realize that she is the blue eyed person, and then leave."

Amy waits a day, and it turns out Betty doesn't leave the island, so Betty must not be surprised by blue-eyedness. So Amy can infer that she herself must have blue eyes if Betty isn't surprised by blue eyes. So she leaves the island that night.

Betty comes to the inverse inference at the same time. That night they leave the island, and Genevive cries herself to sleep.
posted by skewed at 6:10 PM on June 23, 2015 [2 favorites]

I don't see how step two follows. I looked at explanations, and I'm not saying they're wrong, I'm just saying I don't really see how step 2 follows. If there are two blue-eyed people, Amy and Betty, seems like they could both say "wow, guru says she can see blue eyes, no shit, I've seen Amy's/Betty's blue eyes every day for years." If they both know that the number of blue eyed people is either 1 or 2 (just the other person, or the other person plus themself), what's the next step? It just seems that could hold forever.

When they each see that the only blue-eyes they can each see isn't sure if she's a blue-eyes, they know that the unsure other must be seeing another blue-eyes, which, by process of elimination, must be self.
posted by batfish at 6:13 PM on June 23, 2015

Amy thinks "I wonder if Betty is surprised by the fact that there are blue eyed people on the island?

Yes, but she would have no reason to think anything like that if there are more than two blue-eyed people.
posted by sfenders at 6:15 PM on June 23, 2015

Yeah, sfenders, I get what you're saying, and it is paradoxical, but, then, why can't the brown-eyed islanders do the same thing on the same utterance that there is at least one blue-eyes?
posted by batfish at 6:25 PM on June 23, 2015

Yes, but she would have no reason to think anything like that if there are more than two blue-eyed people.

The process for three people is basically the same. Just imagine the third blue-eyed person, Clara. They get the pronouncement from Genevieve, and so:

Amy: "Of course, I already knew that there were either two or three blue-eyed people. At the least, Betty and Clara are blue-eyed, but maybe me as well. If I have brown eyes, then Betty and Clara are the only two blue-eyed people on the island, and they’ll figure that out in a couple of days and then leave."

When two days passes and Betty and Clara don’t leave, she realizes that she must have blue-eyes as well. Amy, Betty, and Clara all come to this conclusion after no one leaves on the second day, and they all leave on day three.
posted by skewed at 6:30 PM on June 23, 2015

team lowkey: "But really, if they are all perfect logicians, then why would the Guru waste her one pronouncement saying something so illogical? "

Just because she's logical doesn't mean she's not a jerk.
posted by mhum at 6:31 PM on June 23, 2015

A wizard has shrunk you down to the size of an ice cube [about 2" tall] and thrown you into a blender! The wizard will turn the blender to "mince" in 60 seconds, how can you escape? The blender walls are too slippery to climb, but the wizard has not sealed the top.

Show your work.

Not sure what the rules are here but my attempt would be to run around the inside and up the wall of the blender in a spiral. This assumes that I can run any better at that size than I can now.
Either up and out or the whole thing falls over if for some reason I still weigh 200+ lbs.
posted by boilermonster at 6:32 PM on June 23, 2015

but, then, why can't the brown-eyed islanders do the same thing on the same utterance that there is at least one blue-eyes?

That's not so easy to guess, but since the historical records are clear about what happened, we may as well assume that it's because they're all perfectly logical, so it's natural that whatever conclusion they reach about the most logical way to proceed will be identical for each.
posted by sfenders at 6:35 PM on June 23, 2015

If I have brown eyes, then Betty and Clara are the only two blue-eyed people on the island, and they’ll figure that out in a couple of days and then leave.

Does it make a difference if there's one person who can see only one set of blue eyes? I'm not even sure any more.
posted by sfenders at 6:39 PM on June 23, 2015

No, in my scenario Amy sees both Betty and Clara, and all three of them have blue eyes. All three of them go through the same process of choosing whether it's two people or instead three people who have blue eyes. There doesn't need to actually be a person who can only see one, they just need to be able to consider that possibility and see that it is not true. Each person on the island considers the others as a set, and has to wait for the same number of days as there are members of the set to determine that since they didn't all leave already, that she herself has blue eyes. It works for 3, or 4, or 100.
posted by skewed at 6:44 PM on June 23, 2015

The statement from the guru gives them no new information at all.

It is pitch black. You are likely to be eaten by a guru.
posted by Smedleyman at 7:13 PM on June 23, 2015 [5 favorites]

That's not so easy to guess, but since the historical records are clear about what happened, we may as well assume that it's because they're all perfectly logical, so it's natural that whatever conclusion they reach about the most logical way to proceed will be identical for each.

Ha! Anyway, I think your point is really interesting. My thought process was the same as yours--the guru's utterance doesn't make a difference, but then: under what circumstance would it make a difference? and then: you see how to leverage that difference into the cascade of inferences. But then, you couldn't obviously get the same thing going from, say, having everybody just silently say to herself "there is at least one blue-eyed islander," so what is the difference between that and what the guru does? I think you're right that the puzzle is "leaky" in some really peculiar way.
posted by batfish at 7:17 PM on June 23, 2015

Is there another version of this puzzle? I've been stuck, because I don't understand it the way it's written. Logically, if you can set and observe the output once, then you only obtain 1 bit of information, and that's not enough to distinguish between 3 possible configurations of a system. So is this puzzle supposed be a mathematical problem or a trick question, or what? Clearly I'm still missing something. I don't have an answer, let alone a wrong answer.
posted by polymodus at 7:53 PM on June 23, 2015

batfish: " I think you're right that the puzzle is "leaky" in some really peculiar way."

It's pretty subtle but it boils down to the fact that each islander is thinking not only about the physical state of the world (i.e.: who actually has what eye color), and not only about their own mental state (i.e.: what do I know about who has what eye color), but also about each other's mental states (i.e.: what do I know about what everyone else knows). In particular, they use each other's actions (or inactions) to determine clues about each other's mental state.

Let's revisit the skewed's simplified case. Initially, Alice knows the following: 1) there is at least one person on the island with blue eyes (because she can see Betty's eyes), 2) Betty either thinks that there is at least one person on the island with blue eyes (i.e.: if Alice has blue eyes) or that there could be zero people with blue eyes (i.e.: if Alice doesn't). After the Guru's pronouncement that at least one person has blue eyes, you'd think that Alice has no extra information since she already knew that there's at least one blue-eyed person on the island. And in a strictly limited sense that's correct. It doesn't provide an extra information regarding the minimum number of people on the island with blue eyes. However, she gets a clue into Betty's mental state after Betty doesn't leave. If Betty left right away, then she'd know that the Guru's declaration actually provided new information regarding the minimum number of people with blue eyes to Betty -- i.e.: that Betty thought there could be zero people with blue eyes because she only sees Alice's non-blue eyes. But, after Betty doesn't leave, Alice realizes that Betty also thought that there was at least one person on the island with blue eyes. Since Alice is the only other person, it must be her.
posted by mhum at 8:08 PM on June 23, 2015 [2 favorites]

polymodus: "Logically, if you can set and observe the output once, then you only obtain 1 bit of information, and that's not enough to distinguish between 3 possible configurations of a system. So is this puzzle supposed be a mathematical problem or a trick question, or what? "

It's a trick question. In the abstract, the light bulb only has two states: on or off. The canonical answer relies that on the fact that in practice, you can induce the light bulb into more than two states: on, off, or "off and warm". In blackanvil's solution, the idea is the same except the third state is "burnt out". My solution relies on side-channel information. That is to say, we needn't restrict our observations to only the output end of the system.
posted by mhum at 8:18 PM on June 23, 2015

These people await you clever answer folks, it's a real world problem right here in our laps!
http://ask.metafilter.com/281977/Best-way-to-handle-large-incontinent-dogs
Three dogs, one phantom pooper ,how to solve it.

Or could it could be one of the roommates.
posted by boilermonster at 8:36 PM on June 23, 2015

mhum, I do get how the solution works. And you're right, my silent individual paraphrase was incomplete. Should be "there is at least one blue-eyed islander, and everyone else knows that there is at least one blue-eyed islander." But aren't those still both things that everyone knew before the guru's statement and would know without it? On the other hand, everyone knows that there is at least one brown-eyed islander and that everyone else knows that there is at least one brown-eyed islander, but the brown-eyed islanders can't get off. Why is that?

You find the solution to the puzzle by imagining the counterfactual in which the guru's statement is informative and leveraging the inferences that would disperse through that scenario, but if the guru's statement is only counterfactually informative--that is, is not actually informative--then how does it generate the cascade of inferences, and how, in its absence, do they fail to generate? To put it the other way again, what is the difference, after the guru's statement, between the respective epistemic situations of the blue-eyed and brown-eyed islanders, such that one population can guess its eye color and the other can't?
posted by batfish at 8:39 PM on June 23, 2015

Should be "there is at least one blue-eyed islander, and everyone else knows that there is at least one blue-eyed islander."

Slightly stronger knowledge: Everyone there already knows that everyone else also knows that there is more than one blue-eyed islander. If any of them somehow thought that someone else might believe there could be only one, that might be different.
posted by sfenders at 8:51 PM on June 23, 2015

The question is, and I can't quite figure this out, if the "rules" of the game were exactly the same, just no guru, what would happen? So if the people all just woke up on the island, day 1, would the same thing happen as if the guru spoke? I can't quite get my mind around it, but I think so.
posted by skewed at 9:02 PM on June 23, 2015

Well, sure, and actually all the BLE's know there are at least 99 BLE's and at most 100. All the BRE's plus guru know that there are at least 100 BLE's and at most 101. Furthermore, all the BLE's know that any given BLE knows that there are at least 98 or 99 BLEs and at most 99 or 100. And so on...
But that all goes for BREs too...
posted by batfish at 9:05 PM on June 23, 2015

The common knowledge eye colour puzzle has been done on Mefi and then a different common knowledge puzzle. The first link has a lot of explanations of the puzzle.
posted by jeather at 9:05 PM on June 23, 2015 [2 favorites]

batfish: " To put it the other way again, what is the difference, after the guru's statement, between the respective epistemic situations of the blue-eyed and brown-eyed islanders, such that one population can guess its eye color and the other can't?"

Okay. Let's return to the two blue-eyed scenario of Alice and Betty and add in two more brown-eyed islanders, Charles and David. As I drew out earlier, the key piece of information each islander is working up is the minimum number of blue-eyed islanders there might be based on all available information. For the sake of notation, let's call this the "mincount". And, as alluded to earlier, the key is not just each islander's mincount but their estimate of what every other islander's mincount might be.

So, in the initial set-up of the two blue and two brown scenario, Alice has a mincount of 1. Furthermore, she knows that Betty has a mincount of either 0 or 1 and she knows that Charles and David have mincounts of either 1 or 2. Charles, on the other hand, has a mincount of 2, knows that David has a mincount of either 2 or 3 and that Alice and Betty each have a mincount of either 1 or 2. The higher mincount estimates correspond to the scenario where Alice or Charles might have blue eyes.

Now, when the Guru makes her pronouncement, Charles and David know that no one will depart immediately because they know that everyone has a mincount greater than 0. Alice and Betty know that neither Charles nor David will depart immediately because they know each man's mincount is also greater than 0. However, they don't know whether or not the other woman will leave yet. When Alice realizes that Betty doesn't leave immediately , she updates her view of Betty's mincount and realizes that it was not 0, it was 1 (similarly for Betty). When Alice and Betty get up to leave, Charles and David update their information too. They both understand that Alice and Betty are leaving because each had a mincount of 1 and not 2. And, if the women had a mincount of 1, that means the only blue eyes they saw were each other's and not any of the men's. So, both brown-eyed islanders stay.

The interesting thing here is that right up until the point when all the blue-eyed people leave, each of the brown-eyed people can't rule out the possibility that they themselves might also have blue eyes.
posted by mhum at 9:28 PM on June 23, 2015

skewed: "The question is, and I can't quite figure this out, if the "rules" of the game were exactly the same, just no guru, what would happen? So if the people all just woke up on the island, day 1, would the same thing happen as if the guru spoke? I can't quite get my mind around it, but I think so."

It can't be. Because without the guru setting off the chain reaction of inferences, each islander can't rule out that the possibility that they have purple eyes or something.
posted by mhum at 9:32 PM on June 23, 2015

There are 329 comments here and I've read exactly none of them but the answer to the puzzle as phrased here came to me in about 30 seconds. Heck yes I’m bragging. And I am not remotely as smart as Jo Nesbø, I’m just a random Internet blowhard.
posted by axoplasm at 9:39 PM on June 23, 2015

Well, sure, and actually all the BLE's know there are at least 99 BLE's and at most 100.

Not so important. The argument by induction fails well before you have more than a few. Step 1, "if there's only one blue..." is made irrelevant to the situation just as soon as you have enough blue eyes around that everyone already knows there's more than one.
posted by sfenders at 9:44 PM on June 23, 2015

sfenders: "Step 1, "if there's only one blue..." is made irrelevant to the situation just as soon as you have enough blue eyes around that everyone already knows there's more than one."

But that's the crux of the problem. The added information isn't only that there exists at least one blue-eyed person. The added information is that plus the reactions of the other islanders. Even in the case with only two blue-eyed islanders, each one already knows that there is at least one blue-eyed islander. What they don't know is whether or not the other islander also knows that. And the way each islander gains that added piece of information is by watching the reaction of the other islander.
posted by mhum at 10:02 PM on June 23, 2015

Sorry, of course I meant "as soon as everyone already knows that everyone already knows there's more than one. Not "at least" one, either. I'm not sure how many you need for that, four I think?
posted by sfenders at 10:14 PM on June 23, 2015

Suppose there is only one blue. Then on hearing the guru's statement, that person learns a new piece of information: that there is at least one blue-eyed person.

Suppose there are two. The each already know that there is at least one blue-eyed person because they can each see one. What they learn is that everyone knows that there is at least one blue-eyed person. (This was true before, but they didn't know it.)

Suppose there are three. They all know there is at least one blue-eyed person and that everyone knows that there is at least one blue-eyed person. But it is not true that everyone knows that everyone knows that there is at least one blue-eyed person. Suppose the people are A, B, and C. If A has brown eyes and B and C blue, then B does not know that C knows that there is at least one blue-eyed person. Since A cannot rule out this possibility, A does not know that B know that everyone knows there is at least one blue-eyed person.

Now the guru makes their pronouncement. Everyone knows that there is at least one blue-eyed person because they heard the guru say so (though they had deduced it from their own observations previously). Everyone knows that everyone knows that there is at least one blue-eyed person because they know everyone was there to hear the guru (though, again, they had deduced this previously). Additionally, everyone knows that everyone knows that everyone knows that there is at least one blue-eyed person because they know that everyone who heard the guru saw that everyone else was there to hear the guru. This is new information that they could not deduce without the guru's statement.

You could continue this reasoning. After hearing the guru, everyone knows that everyone knows that everyone knows that everyone knows that there is at least one blue-eyed person. This chain could be continued indefinitely and all the statements would be true. And since everyone is perfectly logical, everyone knows that fact. And everyone knows that everyone knows that fact. And so on in another chain. Which everyone knows. And so on for a meta chain. Which everyone knows. And so on for a meta meta chain. Which everyone knows. And so on for chains with any number of metas. Which everyone knows. And so on, and so on, and so on, for every ordinal. But everyone knows that, too, even though there isn't even a set of all ordinals. I'm pretty sure as soon as any common knowledge is shared, everyone's head explodes.
posted by eruonna at 10:34 PM on June 23, 2015

You could continue this reasoning.

But you stop just before the point at which you can't continue that reasoning. If everyone knows that everyone knows that everyone ad infinitum knows pre-guru that there are at least two blue-eyed people, which is the case when there are 99 of them, then nobody will gain any kind of extra knowledge of anything by the fact that nobody discovered their eye colour on the first day.
posted by sfenders at 10:42 PM on June 23, 2015

Here's why the brown-eyed people and the Guru can't leave:

After the Guru's statement, everyone makes plans to leave, hoping that logic will prove them to be blue-eyed, but the blue-eyed people plan to leave on day 'number of blue-eyed people they can see' while each of the brown-eyed people and the green-eyed Guru - who can see one more blue-eyed person than the blue-eyes can - also plan to go on day 'number of blue-eyed people they can see', which is for them a day late.

So all the blue-eyed people turn out to leave the day before the others were going to. At this point none of the remaining islanders know what colour eyes they have but they know they can't be blue.

I like to think they spend their remaining time on the island inventing some kind of liqueur.
posted by motty at 11:53 PM on June 23, 2015

sfenders: "But you stop just before the point at which you can't continue that reasoning."

Ok, let's do four. An island with only four blue-eyed islanders, Alice, Betty, Carla, and Denise. Before the guru, Alice knows that there are at least three blue-eyed on the island and that Betty, Carla, and Denise all think that there are either at least two or at least three. Right after the guru makes her declaration, Alice chills out. Why does Alice chill? Because, nothing she's observed so far (namely, the presence of three blue-eyed people and the guru's statement that there is at least one blue-eyed person) contradicts the possibility that she has, say, purple eyes. The first boat leaves with no one on it because everyone came to the same conclusion as Alice.

Now, that the first boat has gone, Alice starts to think about what Betty must be thinking. If Betty sees only Carla and Denise with blue eyes, then Alice knows that Betty will be watching to see if Carla and Denise leave on the next boat. If they do, then Betty will know that her (Betty's) own eyes are not blue because Carla and Denise only see each other's blue eyes (and we're back to the situation with two blues and two browns). If they don't, then Betty realizes that she does have blue eyes (because Carla and Denise couldn't be sure enough about their own eye colors to get on the second boat) and will have to get off the island on the third boat. If Betty sees Carla, Denise, and Alice herself with blue eyes, then she's in the same situation as Alice and still can't figure out her own eye color. In either case, Alice still can't say for sure if she herself has blue eyes. So, once again, she hangs back. Because everyone uses the same reasoning, the second boat leaves empty.

After the second boat leaves, Alice thinks again about what Betty is thinking. Alice knows that Betty saw both Carla and Denise not get on the second boat. Using the same reasoning as before, Alice knows that if Betty only sees Carla and Denise with blue eyes, then Betty is getting on the third boat. But, if Betty doesn't get on the third boat, then Betty sees three pairs of blue eyes on the island. Since Alice still doesn't have enough information to tell if her eyes are blue or not, she refrains from the third boat. And, once again, since everyone is thinking the same thing, the third boat leaves empty.

Finally, after the third boat leaves, Alice knows what's up. The only set of facts that would lead to three boats leaving empty is that if Betty sees Carla, Denise, and Alice all with blue eyes. So, Alice has to get on the fourth boat. As does everyone else because they all used this line of reasoning.
posted by mhum at 12:14 AM on June 24, 2015 [2 favorites]

Do they have to wait for 99 boats, if everyone knows that everyone else can see at least 98 people with blue eyes?
posted by misfish at 12:48 AM on June 24, 2015

Alice knows that if Betty only sees Carla and Denise with blue eyes ...

Then Alice didn't already know that everyone knows there are at least two people with blue eyes, and it might take one more. So, five.

Sure, even with an Emily in the picture, Alice would still not know in advance of the guru whether Betty knows that Carla knows that Denise knows that Emily knows that there are any people with blue eyes. You and the previous thread have explained that so thoroughly that even I get it. The hypothesis can be ruled out by the guru's statement. It improves the islanders' arcane meta-knowledge of each other in a peculiar way. It has nothing to do with the subsequent observation that nobody leaves the island, by ferry or otherwise, on the first day.

The lack of immediate departures rules out that already-disproved hypothesis, but not at any one specific point in the chain of assumptions of non-blue-eyedness. Any one of them could be the incorrect one, terminating the logic at an unknown point before it gets back to Alice. The imagined Emily who would have left on the first boat does not exist in reality; that possibility was ruled out for everyone before the guru spoke up. Knowing that everyone knows that everyone knows that everyone knows can not call into question Alice's existing knowledge arrived at through other means that everyone knows that everyone knows.
posted by sfenders at 1:29 AM on June 24, 2015

I believe the answer but do not fully grok the proof. mhum's explanation works for me in the 4-blue case, but I can't quite extrapolate it to 5. One of the things I'm hung up on - if I'm Alice on an island of 5 blue-eyed people, I know that everyone can see at least 3 blue-eyed people, and I also know that everybody else also knows this; why doesn't (everyone know that)^inf there is someone with blue eyes on the island (which as I understand it is the crucial information that the guru brings into being)?
posted by NMcCoy at 3:47 AM on June 24, 2015

I'm still reading the other thread, which is very interesting!

Let's put it this way:

Suppose I am a Blue Eyes on the island as described in the puzzle (not the 4 or 5 person island, e.g.). Then, stated as a proposition, what is the thing that I know subsequent to the Guru's announcement that I did not know before?
posted by batfish at 4:17 AM on June 24, 2015

I'm sometimes a bit confused by the eye color puzzle too, and batfish's question really hits the nail on the head.

Arguably, after the speaker announces the existence of a blue eyed person, everyone now knows that there are either 99 or 100 blue eyed people. The problem is that everyone else already knew something like this: the blue eyed people knew that they might be blue eyed, so there are 99 or 100, and the brown eyed people knew that there were 100 or 101. If you count up from n=1, it seems like a logical progression. Alice didn't know there were any blue eyed people, and then when the speaker speaks, she does. So if n>1, how does it work? On day 2, n=1 means that Alice kills herself. But n=100. So everybody knows no one will kill themselves on days 1-98.

On day 99, each blue eyed person looks around, and they realize that no one has killed themselves. So they all get ready to kill themselves the next day. Meanwhile. the brown eyed people are confident that they're fine on day 99. They wait until day 100; if the 100 blue eyed people they can see kill themselves, they're fine.

If everyone leaves (or kills themselves) on the 100th day, you know there are 99 blue eyed people. If they don't, then you know that you are blue eyed, and so you join them on 101st day.

But here's where I get confused. What did the speaker say that made them start counting days? When n=100, everyone always knew that there were blue eyed people. So the speaker doesn't tell them anything new. Why start count days from the moment he speaks and waiting for everyone to commit suicide?

I think the trouble is when n>2, that is, when there are three or more people. (We get confused because we focus on the transition from n=1 to n>1, that is, we focus on the counting.) Blue eyed or not, the visitor hasn't told me anything I didn't already know. So why do I start iterating days the moment he speaks? Why did I not commit suicide N+1 days after I first realized that there were N other blue eyed persons on the island?
posted by anotherpanacea at 5:44 AM on June 24, 2015 [1 favorite]

why doesn't (everyone know that)^inf there is someone with blue eyes

I'm not sure if they don't "know" something tangible or not really, or if it's just that the guru gives them a new and easier proof for something they did already know, but even though the other thread already has more than enough examples of people doing this, but I'm going to try my own to honour the faint hope that I can convince myself that Alice does actually end up leaving. Five people with blue eyes.

Alice doesn't know her own eye color. For purposes of logic she makes the assumption that it's brown, and only the other 4 have blue eyes. She imagines how any one of the others, Betty for example, would see things then. This hypothetical B (I'm going to call them by letter when not referring to a "real" person) would only see 3 people with blue eyes. For Alice it's unknown whether the real Betty actually sees things like B does. Maybe, as far as Alice knows.

B, relaxing in her comfy armchair in Alice's dream, then imagines a C who would think there could be only 2 people with blue eyes; not A, not B, maybe not herself, but definitely D and E. In B's reckoning, there's a good chance that C corresponds to the Carla that's as real as she is. From Alice's point of view, C cannot actually exist, but there's nothing to prevent her imagining that Betty thinks she does.

Alice then goes on to imagine B considering the possibility of C thinking up a hypothetical D who sees only one blue-eyed person. Everyone other than C and D knows that D can't exist. But to C, it's possible.

Alice, having got the hang of it, continues by having her hypothetical B go on to assume that C, despite being a dream within a dream and definitely not corresponding to anyone who actually exists, is capable of assuming there's a D who then thinks up an E. D would see one person with blue eyes and think she could be the only one. E would see no blue eyes and be surprised by the guru.

This is not vitally important to the people who are actually there, since Alice, Betty, Carla, Denise, Emil, they each knew from the beginning that there was no C in reality. They only proved that there might be someone who thought there was.

They all knew that all the others knew there's no D around. D is the first one who thinks there might be someone leaving on the first boat, and they all know she can't possibly have been there to think that, even as a hypothetical in the pontifications of the other real people in any scenario that each can't easily disprove. So nobody learns anything new about their eyes from this exercise.
posted by sfenders at 6:15 AM on June 24, 2015

There are no mirrors or reflecting surfaces, nothing dumb.

I submit that a society obsessed with eye color but without any reflective surfaces whatsoever is definitely *something dumb* by most standards. But then, that's always the case with these sorts of logic puzzles; they only work in a world that is not our own. Some folks find it a fun place to visit, but who'd want to live there?
posted by kewb at 6:39 AM on June 24, 2015

The solution is obvious as any old tradesman will tell you, you use a buttfor.
posted by humanfont at 8:34 AM on June 24, 2015

The Guru's statement brings no new knowledge by itself. But, the statement, along with subsequent actions or inactions (not leaving on the boat) by everyone is what creates knowledge.

This is easiest to see in the case of two blue-eyed people. Everyone can see a blue-eyed person already. So no new knowledge right?
But, each of the blue-eyed people does not know whether the other blue-eyed person can see another blue-eyed person. So now they wait to see how that other person acts on that information. That's the case for N=2 blue eyed people.

For N=3, everyone can already see 2 or 3 blue-eyed people. If its 2, then the drama above should play itself out after two days. When it doesn't that means N=3.

For N=4, everyone can already see 3 or 4 blue-eyed people. If its 3, then the drama above should play itself out after three days. When it doesn't that means N=4.

For N=100, everyone knows that nobody will leave after 1 night or 2 nights. What they are waiting for is to see if everyone leaves on the 99th night.
posted by vacapinta at 8:47 AM on June 24, 2015

The guru's statement does bring new knowledge; it is knowledge about everyone else's knowledge. Above, sfender argues that when n=5, Alice does not know that (everyone knows that)⁴ there is at least one person with blue eyes because she can imagine a hypothetical world consistent with her observations in which that is not true. After the guru speaks, she does know that because she saw that everyone saw that everyone saw that everyone saw that everyone was there to hear the guru.
posted by eruonna at 9:14 AM on June 24, 2015

I think the guru in the puzzle is unnecessary and something of a red herring — it's the gathering for the guru's pronouncement that provides the common knowledge that kicks off the induction. Before they meet every villager ought to already know how many other villagers have blue eyes. However, they must not have known with certainty that everyone else knows (and that everyone knows that everyone else knows and so on) — otherwise they all would've left long ago. Since the guru's pronouncement provides no new information in itself, the only explanation I find satisfying is that they've never actually been together at the same place and time before.
posted by Wemmick at 9:29 AM on June 24, 2015

> The "leader" solution to the prisoner problem takes on the order of 27 years (100x100=10,000 days)

For fun, I set up a script to run the 100 prisoners under the rules:

Prisoners are selected randomly.
If the lamp is turned off and the prisoner hasn't turned it on yet, they turn on the lamp.
If the lamp is on when the leader visits, he or she turns it off and increments their turnoff count by 1.
When the leader has turned the lamp off for the 99th time, they gamble.

It records both the day the leader gambles and the actual day at all prisoners have visited the room. Running it 10,000 times, I got the averages:

All prisoners visited by day 523.386
Leader gambles on day 9958.021

Graphed in ~6 month increments, it looks like this.

Look at that crevasse between year 4 and year 20. Imagine being the leader sometime in year 10, waiting for the knock and then plodding in chains to the room just to turn off the lamp and add one to the number in your head. Thinking all the while that it's been a decade -- surely all your fellows have visited the room by now! You think about all the lives back home: grown children, aging friends, the world drifting away from all of you. But you all agreed to the plan. Can you really break from it and risk everyone's lives unilaterally? Can you make that decision for 99 other people when the count is only in the 30s?

Of course, at that point it's been safe to gamble for six years.

In 63% of cases, the leader eventually walks into the room to find the lamp unlit. The temptation to gamble right then, in the hot summer of year 13, must be awful. But on average, the count that day is only 49.

For a numerate leader, the puzzle is basically just a 4-year sentence. For an innumerate one, it's torture.
posted by postcommunism at 9:48 AM on June 24, 2015 [6 favorites]

That was awesome postcommunism, thanks.

So basically it takes 4 years to have a 99.99% chance of survival, but 20-40 years for the "real" solution to work? I propose that this riddle should be banned from retelling for all eternity. If the riddle doesn't have an elegant solution that is obviously better than alternatives, it sucks. Unless the real riddle is "the prisoners figure out this scheme, realize it will take way too long, and say fuck it, we'll just wait 4 years, then do it, we don't even need a leader."
posted by skewed at 10:03 AM on June 24, 2015

Whoops, just realized I was counting the total number of times the leader finds the lamp unlit, not just the first. Average day the leader first finds an unlit lamp is 4,158, early Spring of year 11. The average count that day is 41.
posted by postcommunism at 10:20 AM on June 24, 2015

For N=3, everyone can already see 2 or 3 blue-eyed people. If its 2, then the drama above should play itself out after two days. When it doesn't that means N=3.

Sure, that's the standard line. But, this is what happens when you start with n<3. If it's just Alice and Bob, then they never realized that the other one knew there were people with blue eyes. Alice knew that Bob had blue yes, but not that Bob knew that he had blue eyes, and vice versa. When the guru speaks, they each learn something about what the other knows. But I don't think this is enough, or not quite. If n=3, when the guru says, "I see someone who has blue eyes," no one in the crowd gets new information. Each of the blue eyed people thinks: "Yup, you see those two people, and maybe me." But the guru didn't give the blue-eyed people any information they didn't already have, so there's no reason to start counting days right then.

The year before the guru spoke, Alice, Bob, and Charlie already knew that the village contained blue-eyed people, and that this knowledge was common. Alice knew that Bob knew that there was at least one other blue-eyed person (Charlie.) Bob knew that Alice knew that there was at least one other blue-eyed person (Charlie.) Charlie knew that Alice knew that there was at least one other blue-eyed person (Bob). Alice knew that Charlie knew that there was at least one other blue-eyed person (Bob). Bob knew that Charle knew that there was at least one other blue-eyed person (Alice). And Charlie knew that Bob knew that there was at least one other blue-eyed person (Alice).

So all three of them ought properly to have left long ago. Assuming they are logical to start counting when the guru speaks but not the first time they met each other makes them less than perfectly logical, since the guru gave them no new information.
posted by anotherpanacea at 11:05 AM on June 24, 2015

This thread reads like Martin Gardner had a stroke but kept writing his puzzle column.
posted by infinitewindow at 11:40 AM on June 24, 2015 [4 favorites]

You need the guru, even in the 3 person scenario. You're jumping over one layer of abstraction here: each person must consider the possibility that others think that there is only one person on the island with blue eyes, EVEN THOUGH it's obvious to each of them that there are at least two.

Assume A, B and C all definitely have blue eyes. Each knows that the number of blue eyes is either 2 or 3. BUT, each MUST estimate the other's knowledge at either 1 and 2. That's the real mind-bender, I think. Each person has to contemplate the possibility that the others only see 1 pair of blue eyes, even though they can all see two, and all know for a fact that there are either 2 or 3 blue eyes.

So, from A's point of view, if A imagines that A has brown eyes, and B also imagines that B has brown eyes, then B will expect C to leave, BUT ONLY BECAUE OF THE GURU'S STATEMENT. In that scenario, C would hear the Guru, while seeing two brown eyes, and then realize that C is the one with blue eyes. This is a totally imaginary scenario, because C never actually sees two brown eyes. But A has to contemplate B contemplating it, since A doesn't know that B actually sees two blue-eye pairs, A only knows that B sees at least one blue-eye pair. When C doesn't leave, B will realize that B has blue eyes as well. When B realizes she has blue eyes, her estimate becomes 3, at the same point everyone's estimate becomes 3, and they all leave.
posted by skewed at 12:26 PM on June 24, 2015

Alice does not know that Bob knows that Charlie knows that there is at least one person with blue eyes.
posted by eruonna at 12:26 PM on June 24, 2015 [1 favorite]

anotherpanacea: "So all three of them ought properly to have left long ago."

But that can't be the case. Before the guru says anything, everyone's direct experience (which consists only of seeing the other two people's blue eyes and no other information at all) is completely compatible with the their own eyes being brown or purple or any color whatsoever.

since the guru gave them no new information

That's sort of correct in a strict sense. It is true that Alice already knows that there is at least one blue-eyed person on the island, because she can see both Betty and Claire. It is also true that Alice knows that both Betty and Claire know that there is at least one blue-eyed person on the island, because she knows that Betty can see Claire and that Claire can see Betty. The guru's declaration is redundant with these two observations. What Alice doesn't know is whether or not Betty knows that Claire knows that there is at least one blue-eyed person. How could Alice not know this? Well consider two situations:

If Alice has blue eyes, then Betty would be guaranteed to know that Claire also knows that there is at least one blue-eyed person because Betty knows that Claire can see Alice's eyes
If Alice has brown eyes, then Betty herself needs to consider two situations:
1. If Betty has blue eyes, then Claire sees them and knows that there is at least one blue-eyed person
2. If Betty has brown eyes, then Claire only sees brown-eyed people and didn't know that there were any blue-eyed people on the island

Now, as the reader, we know that the true situation is #1 (and that Betty knows that Claire knows that there is at least one blue-eyed person on the island). However, from Alice's point of view, she can't be certain whether she's in situation #1 or #2 and so she can't be certain about what Betty thinks about Claire. Moreover, both we the reader and Alice herself knows that situation #2.2 can't exist because we both know that Betty has blue eyes. But, Alice knows that if she's in situation #2, then Betty can't rule out situation #2.2. In all cases, Alice can't tell which situation she's in yet so, in that sense, the guru didn't provide her with any new information.

However, as soon as the first boat departs with no one on it, Alice re-evaluates what she thinks Betty's mindset might be:

If I, Alice, had blue eyes, then Betty wouldn't be surprised to no one got on that first boat. Everything is consistent so far.
If I, Alice, had brown eyes, then Betty must be thinking something like: "Huh. Why didn't Claire get on that first boat? I know she sees Alice's brown eyes. If I had brown eyes, then Claire would know that the guru was talking about her (Claire) and she'd have to leave. That means Claire must see some blue eyes and those must be mine. Dammit. Now I know my own eye color and I have to leave on the second boat."

Now, at this exact moment, Alice still can't tell whether she's in situation #1 or #2. So, she lets the second boat leave without getting on it. It's really not until she sees that Betty is also not getting on the second boat that Alice finally realizes, "Oh crap. I was in situation #1 all along. I have blue eyes. I have to get on the third boat out of here." And that's that.

There's a further subtlety here. The key is that the guru doesn't just tell everyone that there is at least one blue-eyed person on the island. It's that he tells everyone the information in such a way that everyone knows that everyone else also knows. Imagine a different scenario where the guru whispers to each person individually and in secret that there is at least one blue-eyed person on the island. Well, first, Alice is probably going to feel pretty unimpressed because she'll think "No shit, Sherlock. I can see Betty and Claire's blue eyes so that was a pretty stupid secret." Second, she'll think "I wonder if the guru told Betty or Claire. Even if the guru told Betty and Claire this secret, they'd also think it was a stupid secret because they can see each other's eyes. But I really don't know if the guru told them or not." So, then what happens? No one gets on any boat. Why? Because no one can be certain why any of the boats are leaving empty. They might be leaving empty because the guru didn't tell anyone else this seemingly dumb piece of information. Namely, Alice never gets any evidence to contradict the possibility that the only reason Betty isn't getting on any boat is because Betty still thinks that she (Betty) might have brown or purple or any color eyes because the guru didn't tell her anything at all.
posted by mhum at 12:44 PM on June 24, 2015

mhum, I think I'm pretty satisfied with that answer. I guess my question was: why didn't that happen years ago?

Everyone arrives on the island, and is given their rulebook or whatever. On the first day, at dinner, Alice sees Betty's blue eyes, and sees Betty seeing Claire's blue eyes. Alice knows that Betty knows that Claire has blue eyes, and that Claire knows that Betty has blue eyes. Nobody says anything, but they each think to themselves "Someone on this island has blue eyes."

What's more, everyone's mental model of the other person includes the fact that they believe that "Someone on this island has blue eyes." I take it that the argument is that that mental model doesn't include third party ascriptions: A knows that B knows that there is a blue eyed person, but A doesn't know whether B knows that C knows there is a blue eyed person.

That's the abstraction jump, the meta-knowledge that makes this an induction puzzle in the first place. Everyone has to have n mental models in their head for the successively smaller communities of blue-eyed people, such that n=1 is continuous with n=100.

Anyway, it's weird because I've of course read about this puzzle before, so I always kind of thought I understood it. I think perhaps I've been going through motions on it, or else forgot how each of the moves worked and talked myself into a bad objection. (As usual, the best way to understand something is to teach it or fight about it.) What's that called, when you know something and then forget you know it? Worse, I now have somewhat good reason to believe that I'll forget that I know this in the future....
posted by anotherpanacea at 1:13 PM on June 24, 2015

I still feel like people are just reiterating the logic of the cascade, which isn't the mysterious part. The mysterious part is how the guru's statement sets the cascade in motion without introducing new information.
posted by batfish at 1:40 PM on June 24, 2015

Assume no guru:

A, B and C are each open to the possibility that the other two might think that there is only one blue-eyed person. (A could think that A has brown eyes and think that B thinks that B has brown eyes). In this scenario, A could imagine B thinking that C and no one else has blue eyes.

In that (imagined) scenario, A and B think the only blue-eyed person is C, but C would do nothing. C would view two brown-eyed people, but have no idea about her own eye color. Nobody knows their own eye color, nobody leaves.

But, if the guru says to everyone: "I see blue eyes" then the very fact that C doesn't leave destroys the above scenario. If C views two brown-eyed people and hears that there are blue-eyed people, she would leave. When she doesn't leave, A realizes that the scenario where A is brown, B assumes B is brown and C is blue can't be true.

So, the guru's added information isn't really that someone has blue eyes, it's that nobody is surprised by there being blue eyes. Before the guru, nobody could rule out the surprise scenario.
posted by skewed at 2:03 PM on June 24, 2015

edit to paragraph #2 of the above post:

In that (imagined) scenario, ~~A and B think the only blue-eyed person~~ A could think that B thinks the only blue eyed person is C, but C would do nothing. C would view two brown-eyed people, but have no idea about her own eye color. Nobody knows their own eye color, nobody leaves.
posted by skewed at 2:29 PM on June 24, 2015

Yeah, ok, that's just exactly how it looked to me to begin with (before Skewed put us in the weeds!), but the dress is blue and black again. More or less. Models modeling model-modeling models, and so on...

It truly is a mind-bending puzzle, and when you get into the details you sort of lose faith that everything will stay in appropriate superposition or whatever...

Here's another way to kind of press on that faith. Does the ferry need to come to the island 100 times, or only one time on the 100th day?
posted by batfish at 2:49 PM on June 24, 2015

batfish: "Here's another way to kind of press on that faith. Does the ferry need to come to the island 100 times, or only one time on the 100th day?"

This is a very good question. I'm pretty sure that the ferry actually has to come 99 times and leave empty 99 times before all the blue-eyed people know their own eye color. Then, they leave on the 100th ferry.

Consider the three blue-eyed islander case. Suppose that as the first ferry is pulling into the harbor, it sinks before anyone can get on. Now, Alice knows that neither Betty nor Claire would have gotten on that first ferry. But, Alice doesn't know whether or not Betty might have thought that there was a possibility that Claire could have gotten on that first ferry. So, when the second ferry comes and leaves without a passenger, Alice still doesn't know if Betty thought it was possible for Claire to get on that boat. Only when the third boat comes and Betty still doesn't get on does Alice realize that Betty never had any expectation that Claire would get on the second ferry. So, finally when the fourth ferry comes, Alice (and everyone else) gets on.
posted by mhum at 6:06 PM on June 24, 2015

Right, sorry. To answer your original question, the guru forces everyone to include "someone has blue eyes" in their mental model of the cascade. Before the guru spoke, no matter how many people had blue eyes, they all had a cascade model that was reducible to a dyad, where A and B assumed the other one must not realize that they're the only one with blue eyes. After the guru speaks, no one can include that claim any longer as a part of their mental model of anyone else.

For n=3: A models B modeling C without the knowledge that anyone has blue eyes. Alice believes that Betty believes that Claire could be ignorant of anyone with blue eyes. When the guru speaks, Alice now knows that Betty knows that Claire knows that Claire has blue eyes.

And that makes all the difference.

I still feel like this doesn't work, unless you assume that nobody can see other people seeing things until the Guru calls them up.

It's like ... okay, let's specifically assume n=5, because n<5 falls into that dyad directly. We have five people with blue eyes who meet up, and of course don't talk because they can't communicate. However, they all know that they see four people with blue eyes, meaning there are either four or five blue-eyed people on the island. They also know that each other person sees either three or four blue-eyed people, and so nobody can think that there are less than three blue-eyed people. There is nobody to initiate the cascade, because nobody can ever think that anyone thinks there could be only two blue-eyed people, which is what you need to initiate the cascade whether a Guru pipes up or not.
posted by kafziel at 7:18 PM on June 24, 2015

I agree, I can see how it works for n=3, and how the guru is a necessary component there. But I honestly can't work my head around any population higher than 3 + guru.
posted by skewed at 7:34 PM on June 24, 2015

I can see how it works for n=4. Everyone can see three blue-eyed people, and everyone can think that someone might only see two blue-eyed people, at which the waveform collapses.

Like, Alice, Bob, Carol, Dan. Everyone's blue-eyed. Alice sees all three of Bob, Carol, and Dan have blue eyes, and knows there's either three or four with blue eyes. She also knows that each of them see either two or three people with blue eyes. So, Alice can think that Bob only sees two people with blue eyes, and after the second day when Carol and Dan haven't left as per a dyad, Bob would leave on the third day if Alice wasn't blue-eyed. So after the third day, when they're all there, Alice knows that she must be blue-eyed. That's fine. I get it for four.

But that all hinges on Alice thinking it possible that Bob thinks it possible that there are only two people with blue eyes, because that's the solvable state. With an Elaine in the picture, nobody would ever think that anyone could think there's only two, because everybody knows everyone else can see at least three.
posted by kafziel at 8:45 PM on June 24, 2015

mhum, I'm not so sure. What prompts the question is that I think I was thinking too literally of the Guru's statement as "initiating" the cascade, because that's sort of how the story works. I now tend to think that it's the departure of an empty ferry that does that, or something like that. That is, it's the departure of an empty ferry that prune's away the possibility in a given blue-eyed islander's model that she is not a blue eyes, so that's where the (only) cascade-initiating belief update occurs.

For n blue-eyed-islanders, had any particular one not been a blue eyes (that is, had the possibility "I am not blue-eyed" in her copy of the generalized model been realized), the n-1th ferry would've left with all the blue-eyed islanders on it. It does not leave with all the blue-eyed islanders on it, and ipso facto the other possibility in the model is realized --> she is a blue eyes. The guru's announcement is a condition of the cascade, but what triggers the cascade is the collapsing of a possibility in the generalized model. For n islanders, the collapse triggering the cascade can only occur on the n-1th ferry departure, which is to say that no update in the generalized model occurs between the guru's statement and the departure of the n-1th ferry, so why are the first n-2 ferry trips necessary? Presumably to count up to n-1, but if they all know what they are counting up to, why is it necessary to do so?
posted by batfish at 8:46 PM on June 24, 2015

kafziel: "With an Elaine in the picture, nobody would ever think that anyone could think there's only two, because everybody knows everyone else can see at least three."

Alright. I've already spammed this thread, so screw it. Let's do five. Normally, this problem is demonstrated via recursion -- something like, I know that if I have brown eyes then everyone else would have left on day n-1 but since they didn't, I must have blue eyes so I'll have to leave on day n. But instead, let's work out all the gruesome details. By the time I finish this wall of text, I will probably have written more words in this thread than in my thesis.

For the sake of brevity (ha!), we'll skip ahead a bit and we'll just take it for granted that Alice can't reason out her own eye color after she sees the first three boats leave empty. Now, on day 4, Alice sees the fourth boat leave empty and she sits down to think: "Do I have enough information yet to tell if I have blue eyes or not?"

"Well, let's say I had blue eyes. Then, Betty would have been seeing exactly what I've seen over these past few days and also been stumped as to her own eye color, too. Ok, so the fact that nobody got on any of the last four boats is consistent with the hypothesis that I have blue eyes."

"So, let's switch it up. Let's say I had brown eyes. Then, what would Betty have seen? Well, I know Betty sees Carla, Denise, and Elaine with blue eyes. And, she saw none of them leave on those last four boats. Now, like me, Betty is also perfectly logical and introspective, so she's also been trying to figure out if she has blue eyes or not. Which means that Betty must have, over the course of these past few days, considered the possibility that her own eyes might be brown. What then?

"Well, Betty would have also wondered what Carla was thinking. In this scenario, where I'm imagining that I have brown eyes, and I'm also imagining that Betty is imagining that she also has brown eyes, Betty would have to imagine that Carla sees only Denise and Elaine's blue eyes. So what? Well, if it really were the case that Carla could only see Denise and Elaine's blue eyes (which I, Alice, know to be impossible but the hypothetical Betty that I've imagined does not) then what must she (Carla) have thought when the second boat left empty?

"We need to go deeper. In this Carla's mind -- the one that lives in the hypothetical Betty's mind -- she must have considered whether or not Denise sees either one or two sets of blue eyes. If this Denise saw only one set of blue eyes, then as soon as the first boat left empty, she would know that this Elaine must have been able to also see one other set of blue eyes, Denise's. So, this Denise would have had to leave on the second boat. But, even this hypothetical Carla saw that Denise did not leave on the second boat, so this hypothetical Carla would know that Denise actually saw two sets of blue eyes, Elaine's and Carla's.

"So, this Carla -- who, once again, is a construct within the mind of a hypothetical Betty whom I, Alice, have constructed in my own mind -- would have left on the third boat. But, hypothetical Betty, like real Betty, also saw that Carla did not leave on the third boat. So, hypothetical Betty would have been forced to conclude that (her hypothetical version of) Carla actually saw three sets of blue eyes, including Betty's. So I, Alice, conclude that this hypothetical Betty would have left on the fourth boat once she saw that Carla did not leave on the third boat.

"But now, I remember that the real Betty didn't leave on the fourth boat. Which means that the real Betty never underwent the chain of reasoning that my hypothetical Betty underwent. But, that chain of reasoning definitely would have happened if I had brown eyes. Thus, I am forced to conclude that the real Betty actually sees the same thing that I do -- four other sets of blue eyes between Carla, Denise, Elaine and myself. Now that I know that I must also have blue eyes, I'll be getting on that fifth boat."

So, what the heck just happened here? By the fourth paragraph in Alice's internal monologue, she's constructed a hypothetical Denise living inside the mind of a hypothetical Claire inside the mind of a hypothetical Betty. And somehow, this multiple-level deep Inception-style construct of Denise looking at Elaine's behavior is what the whole edifice is balanced upon.

In fact, working the problem out to this excruciating level of detail has sharpened in my mind what is actually going on. The guru's declaration doesn't actually initiate a chain reaction of inferences. The guru's declaration actually provides a stopping point to a sequence of inferences that each islander has always been creating. It's just that before the guru's declaration, no matter how many boat departures each islander sees, their chain of reasoning always dead-ended with "I can't conclusively determine my own eye color because everything I know and have seen up until now is consistent with me having either blue or brown or green or purple or whatever color eyes." And even though my expositions (including this one) involve working through what each islander sees after a certain number of empty boat departures, that's not actually necessary. As soon as the guru makes her declaration, each islander would be able to start cranking their computer brains through all manner of possibilities and come to the conclusion that if they see the next n boats leave empty (where n is the number of other blue-eyed islanders they see), then they themselves have blue eyes and must leave on the n+1^th boat. They don't need to actually see the boats departing to start hypothesizing. Once they reach this conclusion, then the clock starts and each islander starts counting down the empty boats.
posted by mhum at 12:03 AM on June 25, 2015

Normally, this problem is demonstrated via recursion

The other day, the argument by induction looked like a filthy trick that was probably relying on some chicanery in mixing up of iterations of n and the passage of days. Today it doesn't. Weird.
posted by sfenders at 3:21 AM on June 25, 2015

This was a fun thread. If you actually enjoyed working out the levels of induction with us, you may enjoy the teasers you find reading the Stanford Encyclopedia of Philosopjy entry on Common Knowledge. I did. Especially important is the "is common knowledge attainable" section because it helps show why we don't have to keep going for n=6 and so on.
posted by anotherpanacea at 6:48 AM on June 25, 2015 [1 favorite]

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