# The Zebra Puzzle



## Feo Takahari (Jun 16, 2013)

It took me two and a half hours to solve this, and I want to inflict it on others.

This puzzle comes from Life Magazine in the '60s. There are five adjacent houses, each of a different color, whose occupants are each of a different nationality, own a different animal, drink a different beverage, and smoke a different brand. These are your clues:

The Englishman lives in the red house.
The Spaniard owns the dog.
Coffee is drunk in the green house.
The Ukrainian drinks tea.
The green house is immediately to the right of the ivory house.
The Old Gold smoker owns snails.
Kools are smoked in the yellow house.
Milk is drunk in the middle house.
The Norwegian lives in the first house.
The man who smokes Chesterfields lives in a house next to the man with the fox.
Kools are smoked in a house next to the house where the horse is kept.
The Lucky Strike smoker drinks orange juice.
The Japanese man smokes Parliaments.
The Norwegian lives next to the blue house.

Who owns the zebra?

(The fifth drink is water. Some versions include a clue involving it, but you can find the answer without it.)

P.S. If you get the answer, please post it in spoilertext, not in plain text.

P.P.S. If you can beat my time, I've got a bonus challenge . . .


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## Chilari (Jun 16, 2013)

Oh I did this one another time. I struggled with it for like 2 hours, then something clicked and it all fell into place, and I'd solved it 5 minutes later. Gonna have a go at the other one and let you know.


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## Devor (Jun 16, 2013)

I did it in under forty-five minutes.  This is what I got.



Spoiler: Answer



The Englishmen, in the the last house, which is red, drinks orange juice, smokes Lucky Strike cigarettes, and owns a Zebra.



It took me one if-this, then-that statement, after I had filled in seven of 25 boxes.

((edit))

Apparently I'm wrong.  Not sure where I screwed up the if-then-statement, but I knew I should've tried both ways.


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## Legendary Sidekick (Jun 16, 2013)

5 min!



Spoiler: what I was doing during those 5 minuntes






Feo Takahari said:


> It took me two and a half hours to solve this, and I want to inflict it on others.
> 
> This puzzle comes from Life Magazine in the '60s. There are five adjacent houses, each of a different color, whose occupants are each of a different nationality, own a different animal, drink a different beverage, and smoke a different brand. These are your clues:
> 
> ...



Admittedly, my notes are incomplete. But the house order was right, and I had all the info in my head on the Japanese guy.

I rely on intuition a lot for these things, so I may not really have bragging rights.


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## Penpilot (Jun 16, 2013)

Took me over an hour but here's what I came up with. Had to use a spread sheet to organize my thoughts.



Spoiler: Answer



Norwigian-----Yellow-----Fox-----Kools-----Water
Ukranian------ Blue-------Horse---Chesterf--Tea	
English---------Red-------Snails---Old Gold--Milk	
Spaniard-------Ivory------Dog-----Lucky	-----OJ	
Japanese------Green------Zebra---Paliments-Coffee	

So It's the Japanese guy who owns the zebra. Is that right?


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## Feo Takahari (Jun 16, 2013)

Penpilot, you've got it.

(I admit, solving it in one hour makes me feel a little slow in comparison. I don't really understand the five-minute solution, though, so I'm not sure how to count it.)


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## Nihal (Jun 16, 2013)

I used to solve these puzzles when I was a child! I drew to keep track of the connections, took 45min.

I didn't follow LS's logic too, I don't understand what he used to determine the last three houses colors.


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## Legendary Sidekick (Jun 16, 2013)

@Penpilot, you rock!

@Feo, I won't hold it against you if you think it as a lucky guess. I don't know if I can adequately explain intuition. I just started analyzing the different clues by getting the obvious out of the way (like where one of the animals was) and used colors to mark which clues went with which house. I figured out the house order quickly (~1-2 min), which helped. I stopped using color codes shortly after I had the houses figured out, and shortly afterward, I found there was one guy I knew everything about except which pet. I couldn't shake the feeling it must be him. It seemed to easy to get the info on that guy, but not have any animal clue for him.

After the 5th minute, I just looked for a wiki. I wasn't surprised to to see house order and info on the right guy as I had it, but I probably wouldn't have been able to figure everything about the other guys as Pen Pilot did.


EDIT-

@Nihal, the closest thing to logic I can offer is I had to prepare dinner, so I only intended to see how far I could get in 10 minutes or less. I stopped when I knew who owned the zebra—or more to the point, I knew everything about the guy who owned the zebra except that he owned a zebra—and the next couple clues just made it more likely I was right. As I said within the spoiler tags, I probably don't deserve bragging rights, since I didn't spreadsheet/draw everything out as you and Penpilot did. No offense taken if you think I just guessed and got lucky.



Spoiler: how I figured houses within a minute



first is yellow, blue is next to; green is to the right of ivory; therefore only the red house can be the middle house. I didn't mark the middle house line in red when I realized that - instead, I just typed house colors from L to R as seen in spoiler.


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## Nihal (Jun 16, 2013)

Legendary Sidekick said:


> @Nihal, the closest thing to logic I can offer is I had to prepare dinner, so I only intended to see how far I could get in 10 minutes or less. I stopped when I knew who owned the zebra—or more to the point, I knew everything about the guy who owned the zebra except that he owned a zebra—and the next couple clues just made it more likely I was right. As I said within the spoiler tags, I probably don't deserve bragging rights, since I didn't spreadsheet/draw everything out as you and Penpilot did. No offense taken if you think I just guessed and got lucky.
> 
> 
> 
> ...



Some random text so the spoiler tag's content won't show in the activity stream. ~~



Spoiler: Here is the thing



Ah ha! It's stated the green is the one to the right of the ivory, but the problem lies in never being stated that the green is the last one, being necessary to solve some other variables of this puzzle before assuming it *is*. It could be Yellow, Blue, Ivory, Green (still at the right of the ivory), Red.


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## Legendary Sidekick (Jun 16, 2013)

True… amazing how a hasty assumption can speed things up. Like I said, I really don't deserve bragging rights, I was just excited that I stumbled onto the answer since I would've had to stop anyway. I did keep going and found clues only confirmed my assumption, and finally saw it was past 6:00 and I had to start the grill.

Out of curiosity, did you have a good intuition about who the zebra owner was before you solved every single piece of the puzzle? I can't imagine I'm the only one who did—I'm just the only one who had to step away from the computer.


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## Penpilot (Jun 16, 2013)

Feo Takahari said:


> Penpilot, you've got it.
> 
> (I admit, solving it in one hour makes me feel a little slow in comparison. I don't really understand the five-minute solution, though, so I'm not sure how to count it.)



Don't feel that way. In university, I took courses (linear algebra and linear programming) were everything was geared towards solving problems like this, so it's more of being familiar with how to organize your thoughts rather than real smarts. I know there's an elegant way to break down the problem into a algebraic equations and solve, but it's been so long I couldn't remember the approach, so I did a brute force deduction. 

I needed the first half hour to find a way to organize my thoughts. First it was sticky notes and paper, then the spreadsheet.  What I did was read through the facts, and under the headings of ethnicity, I wrote down everything that was obvious about that person. Then using the headings of color of house, I wrote down everything that was obvious about each house.

After doing those two things, I tried merging those two fact tables as best as I could until nothing was obvious any more. When I was done that, I went through the facts and figured out what each house couldn't be. For example if you knew the house/person drank something other than milk, then that house/person couldn't be the middle house. And you knew the Ivory house couldn't be the last house, etc. I kept going through the list and eliminating options for each house until one thing could only belonged to a certain house/person. 

To tell you the truth I almost gave up a couple of times, and I can see myself taking way longer if I didn't stumble into the right way to organize my thoughts.

As for LS, No, you rock. Awesome is what awesome does.  Sounds like you got a great set of deduction skills. I know for a fact it's hard for me to make those deductive leaps. It's why I tend to do things with brute force, so I didn't even venture a guess before starting the gears grinding.


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## Legendary Sidekick (Jun 16, 2013)

Well… that, or I count on intuition more than I should.

In grad school, we all took Meyers-Briggs Personality tests and, after we were all finished, the professor asked us what _his_ Myers-Briggs result was. I was the only one in the class that guessed ESTP, and I insisted I was correct. The teacher asked me why I thought so. I said I didn't think so, I _knew_ so because every time he described the different personalities, he always made the ones that applied to himself sound better. He asked what I was, and I said INFJ (his opposite). He told the class that INFJs rely on intuition and stubbornly stick to those intuitions.

I was right about the professor, but unlike this puzzle, the clues he unwittingly gave me were completely obvious.

That said, he's probably right about his criticism in the sense that, had I been wrong about the house order, I would have misread the additional clues. I retraced my steps based on Nihal's PM and, long story short, can see how Devor came up with his solution. I'd like to say it was the drinks that confirmed I nailed it, but… yeah, I would've had the middle-man drinking OJ had I put his house in the wrong place.


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## Ophiucha (Jun 16, 2013)

It took me about fifteen minutes.



Spoiler: puzzle ponderings



For me, the hardest part was sussing out who smoked which brand. Once that fell into place the rest of the puzzle solved itself, really. (I got as far as having the colours right and two of the countries - England and Norway. It took me a while to move everything around to get the cigarettes right, but I got it after rereading the Old Gold and Chesterfields lines - since that eliminated most of the options regarding the animals, only one thing could fit for each given Spain's requirement.) 

Also, because I have a crippling inability to remember my left from my right, I actually switched up Green and Ivory.  I still managed to get the right answer (just by the luck of the animal-based clues), but this is why I don't do logic problems.


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## Legendary Sidekick (Jun 17, 2013)

For the bonus puzzle, I came up with this within seconds. But I'm not sure how much better a solution you can have because of that third God…



Spoiler: imperfect solution to gods puzzle



…by "third" I mean the Random god.

My question would be "Did you just lie to me?" repeated three times.

True would say "no", "no", "no."

False would say "yes", "no", "no." — Yes is false the first time, since he hadn't yet spoken to me.

I don't know what the hell Random would say, but the whole point is no matter what I ask his answers are random. On top of that, their language is unknown, so I can't tell "yes" from "no." So the best solution I could see was to ask questions that would force True and False to answer differently. True answers that same three times, False's first answer is different from the other two. There's a 50% chance that Random won't match either pattern. There are eight combinations, but yes-yes-yes and no-yes-yes can't be distinguished from the True or False replies. Therefore, there's a 1-in-6 chance that I'd pick the Random god _and_ he'd accidentally fool me into thinking he's True or False. Or… there's a 2-in-3 chance I'd pick either True or False, but I'd walk away knowing there's a 25% chance I'd been talking to Random.

So anyway that—the question, not the explanation—is what I came up with immediately after reading, or within a few seconds. Seeing how it's the hardest logic puzzle in the world, I figured that was a pretty good answer, and with all the time in the world, I'd never figure a better one. Since Random's answers can't be controlled, the three-question limit makes it—as far as I can see—impossible to come up with a perfect solution.

I'm not sure if I misunderstood, but I thought the puzzle worked so you only talk to one of the gods and ask three questions to that one. If I can ask all three three questions, I'm much more likely to learn yes from no after speaking to two of the gods, then I can just straight up ask the last god who's who, knowing that the third one is either Random or who I think he is. If two gods gave the same alternating pattern, I'd know that I had already talked to Random, so I'd know yes from no after the first question to the third god.


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## Feo Takahari (Jun 17, 2013)

Legendary Sidekick said:


> For the bonus puzzle, I came up with this within seconds. But I'm not sure how much better a solution you can have because of that third God…
> 
> 
> 
> ...



You're misunderstanding--you ask one question of each god.

(I included that basically as a joke. I looked up the solution, and it's absolutely bizarre. Even an honest god might be confused into lying by such convoluted questions.)


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## Legendary Sidekick (Jun 17, 2013)

Random text for those who want to give the bonus a try...



Spoiler: decorum



Oh... well, if I'm allowed to repeat the question, my solution works (since it's only one question, not three). Otherwise, I can't see how that puzzle can be solved. (Gotta see students in 2 min, so I can't look this up until much later.)

No matter what you ask, True and False need to have different answers, and Random can always copy one of their answers. Because you don't know what the word means or who you're talking to, Random would match one of the answers and you'd have no way of knowing which god his answer matched.

If the question can be repeated, True's answer to my question would never change, False's answer to my question would change once ever, and only Random would (eventually) change his answer when asked more than twice. So either I solved it, or I'm having trouble believing this can be solved at all. (Two possible answers and three gods???)

Can you link the solution? I'd like to check it out at lunch. But I'm suspicous, as you mentioned that a god could be tricked into lying, which means the so-called solution is imperfect.


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## Devor (Jun 17, 2013)

You get three different questions, but only one for each god.  So presumably, you need to ask the second and third gods about the first god's answer.

So at a guess, it's something like:

God 1:  "Are you lying to me?"  Liar:  No (because he is).  Truthteller:  No (because he's not).  Random:  Yes or No.  If yes, you've IDed him (well, once you've figured out yes and no).
God 2:  "Did he just lie to me?"  (Ohh geeze, now I'd have to make a chart...)
God 3:  How about him?  Did he just lie to me? (now the chart is huge)

Then you'd test their answers against the chart and figure it out.  But I'm not even going to try and test that theory.

((edit))

Ohh geeze, I looked it up and the published answer gets complicated.


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## Legendary Sidekick (Jun 17, 2013)

Okay, I looked at the Wiki, and I'm not buying the first solution that I looked at. Those who don't mind seeing the answer, please tell me where I'm going wrong.



Spoiler: the love of everything that's good and decent






			
				Some Guy on the Wiki said:
			
		

> Q1: Ask god B, "If I asked you 'Is A Random?', would you say _ja_?". If B answers _ja_, either B is Random (and is answering randomly), or B is not Random and the answer indicates that A is indeed Random. Either way, C is not Random. If B answers _da_, either B is Random (and is answering randomly), or B is not Random and the answer indicates that A is not Random. Either way, you know the identity of a god who is not Random.


I want to believe but… no, you don't know who's not Random!

My take on it:

I think this solution is a cop-out, because the asker is in effect defining _ja_ as yes. But there's only a 50% chance it's yes in the language of the gods, and I don't see why the gods would redefine words in their language because a nosey mortal implicitly demanded it. I expect the gods to use their own language, meaning True and False would have identical answers, and you can't know which answer you've heard from Q1.
If B says _ja,_ C can be Random. If A is True and B is False, you're asking if False would say yes if A is Random. He would say yes because that's the false response. So even if, like me, you run with an assumption that has a 50% chance of being wrong and happen to guess correctly, you still learn nothing.

Here are all the possible answers to Q1:


ja = ja is yes, A is Random, B is True, C is False (B says "ja," as in "Yes, I would say 'yes.'")
ja = ja is yes, A is True, B is False, C is Random (As in "Yes, I would say 'yes' because the truth is 'no.'")
ja = ja is yes, A is True, B is Random, C is False
ja = ja is yes, A is False, B is Random, C is True
ja = ja is no, A is Random, B is True, C is False (As in "No, I wouldn't say 'no', I'd say 'yes.'")
ja = ja is no, A is True, B is False, C is Random (As in "No, I wouldn't say 'no', I'd say 'yes,' sucker.")
ja = ja is no, A is True, B is Random, C is False
ja = ja is no, A is False, B is Random, C is True
da = da is yes, A is False, B is True, C is Random (As in "Yes, I would say 'no.'")
da = da is yes, A is Random, B is False, C is True (As in "Yes, I would say 'no,' moron.")
da = da is yes, A is True, B is Random, C is False
da = da is yes, A is False, B is Random, C is True
da = da is no, A is False, B is True, C is Random (As in "No, I wouldn't say 'yes', I'd say 'no.'")
da = da is no, A is Random, B is False, C is True (As in "No, I wouldn't say 'yes', I'd say 'no,' *[CENSORED]*!")
da = da is no, A is True, B is Random, C is False
da = da is no, A is False, B is Random, C is True

Am I wrong here, or does this Q1 tell you nothing?



EDIT - The answer's not a cop-out. My own answer list shows that True would say _ja_ if A is Random regardless of what _ja_ means. But I still disagree that if B says _ja,_ C is not Random.


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## Devor (Jun 17, 2013)

I don't know if I need caffeine or alcohol to understand that list, but I'm sure I need help of some kind.


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