Whose Fish? (logic puzzle)
Yesterday I stumbled across this logic puzzle.
What always drives me crazy about stuff like this is that no one ever discusses the answer. I’ve never liked the implied wink wink smarty-pants attitude (see here). I want to know how someone arrives at the answer. What fascinates me is thinking, not trivia or secrets.
Here’s how I found the answer.
I don’t recall ever seeing this puzzle before and did not google it until I’d proven the results to myself. The puzzle is difficult, but I’ve posted answer at the end of the post, so you’ve been warned. The three little dots (∴) is the “therefore” symbol.
First I set up a 6×5 matrix of attributes then started highlighting and crossing out relevant details.
Then I got stuck.
Intuitively, I knew it all came down the Norwegian. This because we know he has only one neighbor. Everyone else can have one or two neighbors. Eventually, it came down to coffee (consumed and in clue 5).
The Puzzle:
There are five houses in a row in different colors. In each house lives a person with a different nationality. The five owners drink a different drink, smoke a different brand of cigar and keep a different pet, one of which is a Walleye Pike.
Who owns the fish?
The 15 clues:
- The Brit lives in the red house.
- The Swede keeps dogs as pets.
- The Dane drinks tea.
- The green house is on the left of the white house.
- The green house owner drinks coffee.
- The person who smokes Pall Malls keeps birds.
- The owner of the yellow house smokes Dunhills.
- The man living in the house right in the center drinks milk.
- The man who smokes Blends lives next to the one who keeps cats.
- The Norwegian lives in the first house.
- The man who keeps horses lives next to the one who smokes Dunhills.
- The owner who smokes Bluemasters drinks beer.
- The German smokes Princes.
- The Norwegian lives next to the blue house.
- The man who smokes Blends has a neighbor who drinks water.
The end of this puzzle will have five units, each with 6 attributes: {address, house color, nationality, drink, pet and smokes}
The data seems to break down into two types: Definitive data, that which defines an attribute directly within one unit. And relational data, which defines an attribute relative to another unit. Relational data often acts as a negating definition as well, showing what isn’t in a unit by describing what’s nearby.
Now stepping through the clues, definitive data related to nationality first:
- 1. The Brit lives in the red house.
- Brit == red
- 2. The Swede keeps dogs as pets.
- Swede == dogs
- 3. The Dane drinks tea.
- Dane == tea
- 10. The Norwegian lives in the first house.
- Norwegian == 1st house
- 13. The German smokes Princes.
- German == Princes
Next comes the secondary definitions. These can be used to reveal data which eliminates possible units based on what is already known:
- 5. The green house owner drinks coffee.
- Coffee == Green ∴
Brit != coffee
Dane != Green
- 6. The person who smokes Pall Malls keeps birds.
- Pall Malls == birds ∴
German != birds
Swede != Pall Malls
- 7. The owner of the yellow house smokes Dunhills.
- Yellow == Dunhills ∴
German != Yellow
Brit != dunhills
- 8. The man living in the house right in the center drinks milk.
- Milk == 3rd House ∴
Norwegian != milk
Dane != 3rd House
- 12. The owner who smokes Bluemasters drinks beer.
- Bluemasters = beer ∴
German != beer
Dane != Bluemasters
| Third | Fourth | Fifth | ||
| Red | ||||
| Brit | ||||
| Beer | Milk | Water | ||
| Birds | Cats | Fish | Horses | |
| Blends | Bluemasters | Pall Malls |
| Second | Third | Fourth | Fifth | |
| Blue | Green | White | Yellow | |
| Swede | ||||
| Beer | Coffee | Milk | Water | |
| Dogs | ||||
| Blends | Bluemasters | Dunhills |
| Second | Fourth | Fifth | ||
| Blue | White | Yellow | ||
| Dane | ||||
| Beer | Coffee | Milk | Tea | Water |
| Birds | Cats | Fish | Horses | |
| Blends | Dunhills | Pall Malls |
| First | ||||
| Green | White | Yellow | ||
| Norwegian | ||||
| Beer | Coffee | Milk | Water | |
| Birds | Cats | Fish | Horses | |
| Blends | Bluemasters | Dunhills | Pall Malls |
| Second | Third | Fourth | Fifth | |
| Blue | Green | White | ||
| German | ||||
| Coffee | Milk | Water | ||
| Cats | Fish | Horses | ||
| Princes |
Many of the relational data clues reveal additional information about what a unit doesn’t have:
- 4. The green house is on the left of the white house.
- Green = White’s address - 1
- 9. The man who smokes Blends lives next to the one who keeps cats.
- Blends = Cat’s address ± 1 ∴
Blends != cats
- 11. The man who keeps horses lives next to the one who smokes Dunhills.
- Horses = Dunhills’ address ± 1 ∴
Dunhills != horses
Horses != Yellow
- 14. The Norwegian lives next to the blue house.
- Blue = 2nd house ∴
Brit != 2nd house
Norwegian != Blue
- 15. The man who smokes Blends has a neighbor who drinks water.
- Blends = Water’s address ± 1 ∴
Blends != water
The fourteenth clue is one of the most important. Since we know the Norwegian lives in the 1st house (clue 10), we know that the blue house is number 2. Number 4 is a tricky one, there is no reason to believe that the green house is the first house, all we know is that the white house is on it’s left. Also, clues 9 and 15 could be referring to one or two neighbors.
It’s interesting that the clues sort out into three quintuplets.
Here’s where it starts to get really hard. All that is known for certain is what was defined in questions 1-3, 10 and 13. There remain three or four unknowns for each unit. What I’m looking for is the first link in a causality chain. Of course it’s probably not so much a chain as a loop, so looking for an end is futile. How about an onramp?
After several minutes of staring, and re-reading the clues, I got the chills (really!)
WARNING: THE ANSWER IS REVEALED BELOW
The green house drinks coffee. The center house drinks milk. So the center house is not green. But the Green house is on the left of the white house. Since we know the second house is blue, we then know that the first house is not green either. So the only place the green house can be is fourth, making the 5th white. Now is the first yellow, or is the first red?
The elimination steps above provide the answer. We know the Norwegian is in the first house, and the Brit is in the Red house. That means the Brit is in the red house in the middle, drinking milk, and the Norwegian’s house is yellow and he smokes Dunhills.
Whoa, more chills.
At this point, the whole things starts to fall together.
Clue 11 puts horses in the blue house.
Clue 3 means the Dane is not in the green house
Clue 15 puts Blends in the second house, and, with clue 9, water and cats in the first house.
etc. etc.
The Answer
Here’s the final breakdown:
| First | Second | Third | Fourth | Fifth |
| Yellow | Blue | Red | Green | White |
| Norwegian | Dane | Brit | German | Swede |
| Water | Tea | Milk | Coffee | Beer |
| Cats | Horses | Birds | FISH | Dogs |
| Dunhills | Blends | Pall Malls | Princes | Bluemasters |
The German has the fish and drinks coffee in the green house, which is fourth on the block.
That was fun.
I hate puzzles.
Update: Here’s a programmatic solution to “Einstein’s Riddle” and another walkthrough by James Yates.
I don’t think it’s particularly fair to go posting the answers to this puzzle. coudal.com is running a competition for this puzzle, with some pretty good prizes on offer, and you’ve just made it a whole lot easier for idiots to cheat. Some people will have spent a long time working on the answer, and you’ve just negated all those people’s efforts. Very considerate of you.
Hi! Im very impressed with how you got the answer. However, I figured it out within seconds after reading the riddle. I knew it was the German because Einstein was German. I tell jokes about Polish people because I myself am Polish! lol I will now leave you with a quote from Albert as a response to the other comment: “The secret to creativity is knowing how to hide your sources. “
Dear anonanonanon,
This is not a new puzzle and the answers to this are all over Google.
As for this posting, the answer is at the very end, there is a warning about it at the beginning and someone would have to scroll about four full screens to get to the paragraph where I start to put it together. Out of deference to your not entirely polite request, I’ve added a large warning header before that paragraph. Still, I doubt anyone looking for a quick answer would wade through my excessive canoodling.
Congratulations on your answer; I arrived at the same one.
However, you define clue number 4 in a very convenient way. Just because the house in on the left, it does not have to be on the “immediate” left. So, the 1st house could be green and the 3rd house can be white. This makes House 4 yellow and House 5 red. After finishing the table this way, you come to the conclusion that the fish could belong to either the German or the Dane. Here is my 2nd table:
Notice also, the cat and fish can be interchanged. This is because Blends is inbetween the two. Also notice, that the green hosue in on the left of the white. In fact, all 15 clues work out perfectly in this example also.
So this puzzle has two answers, or I am making a huge mistake somewhere.
- Alex
Wow. Yeah, that does appear to work as well, at least i wasn’t able to disprove it easily. You’re right that the language of the fourth clue is sloppy and would literallly mean that the green house is anywhere from 1 to 4 houses left of the white house. I was fairly certain of my answer, but I think your interpretation of clue 4 is completely valid.
it could also be:
House1 House2 House3 House4 House5
German Swade Brit Dane Norwegian
Green White Red Blue Yellow
Prince Bluemaster Pallmall Blends Dunhil
Coffee Beer Milk Tea Water
FISH Dog Bird horse Cat
This answer also works:
House 1| House 2 |House 3 |House 4 |House 5
German | Swade |Brit | Dane |Norwegian
Green | White |Red |Blue |Yellow
Prince |Bluemaster|Pallmall|Blends |Dunhil
Coffee |Beer |Milk |Tea |Water
FISH |Dog |Bird |horse |Cat
And there was me thinking that the Dane was a dog kept by the swede, which was being grown in the green house with all the other vegetables. I feel silly now!
If we are going to get picky and it appears we are, clue # 15 is a little sloppy as well. Neighbor; One who lives near or next to another. Does not specifically mean next to as it is stated in clues # 9, 11, and 14. If one is to use this rational the whole puzzle becomes a mess. If you want to get into all the possibilities of the puzzle you have more time than I. I think that using the most “obvious” conclusions the answer is clearly the German, with coffee breath, smoking a prince, standing in front of the green house, wearing an “I love fish” shirt.
If you like these logic puzzles then you might want to try Sudoku puzzles that have become this year’s puzzle fad in UK newspapers. The times puts its ones online everyday (see here).
The aim is to ensure that every box contains the numbers 1 though 9, and that every horizontal and vertical line contains 1 through 9. The puzzles rely on the same logical gymnastics as the fish puzzle, but without the narrative element. They come in varying difficulties - the easiest only needing basic logic and the hardest requiring you to work through mutliple contingent possibilities.
kieran
I also hate puzzles, but I did it just to prove to myself that I understand it conceptually and knew that it wasn’t so hard. And I succeeded. But puzzles are just work, as far as I’m concerned. :*)
Correction: “…understood…”
p.s. Oh, not that I’m against work. As a graphic designer, I have to solve problems and puzzles all day long. And I don’t mind solving *those* puzzles. It just means I don’t like doing puzzles when I’m not in the office. :*)
What a great puzzle, if we get it are we in menze? I actually used Microsoft Excel to help with the graphing and coloring. The hardest challenge for myself was not getting the clues intertwined with each other. A true brain teaser and an enjoyable one.
Guess I’m a little late to the party- I’ve had the original puzzle bookmarked for like a month now until I actually had time to sit down and figure it out. I worked out the solution pretty much the same way as you did. One point to note though… It never specifes whether the Norwegian’s house (”the first house”) is the left-most or the right-most house. So if you are ordering them from first (Norwegian) to last, it could be either “Norwegian, Dane, Brit, German, Swede” or “Norwegian, Dane, Brit, Swede, German”. Given the way the puzzle is set up, it turns out that it doesn’t really matter what order the last two houses are in…
I have to agree with the second poster, though. I suspected from the start that it was the German, but still had to go through the steps to prove it to myself. I was kinda surprised that he wasn’t a beer drinker, though.
we cheated. NARF NARF.
twas good twsa good.
sooooo. ich bin ein berliner. YABADABADOO!
WERE ONLY YOUNG!! EWRE NOT THAT SMART! but we did alot, all by ourselves. twas good twas good. okay, byebye nowwww
In holland we like fish! why where there no dutchman in this puzzle!haha
Now serious it was a really hard puzzle because ive just last night when out drink to much and to less sleep in the morning I saw that a friend of my posted this puzzle in my mailbox so..i went on it the same way as you did and in between 30 minutes a had the correct answer but thats because it is sooo logical peoplezzz! see ya
At guy who posted before me: Dude some of us check our answers with this joe maller…
Thanks so much!
hi, i got given this puzzle at skool and thought i would have a go but come no where near close enough to solve it!!! it actually said down the bottom of the puzzle only 98% of people in the world have figured out the answer. and i think its great that u gave us the answer……hehehehe it doesnt make me think, and i dont like to think.
oh yeh, its me again, speaking of logic i thought that the person who drank milk was the cat!!! and that the cat and dog couldnt live next door to each other coz they fite anyway i now get the term “logic” lol
I used a slightly different approach but got the same answer (the German has the Fish). However, I have the houses ina different order. Goes like this
Colors: Green-Blue-White-Yellow-Red
Nationalities: Norw-Ger-Swede-Dane-Brit
Pets: Birds-Fish-Dogs-Cats-Horses
Drinks:Coffee-Water-Milk-Tea-Beer
Smokes:PM-Prince-Blends-Dun-Blue
The main difference is that the Blends guy has a neighborm with cats and a neighbor with water. You have them as the SAME neighbor, which is not disallowed. I had them as different neighbors, one on one side, one on the other. Took me about 30 minutes.
My grade nine math teacher is makin us do this problem and its so hard
My boyfriend challenged me with this riddle that had been sitting on his desk for weeks… It only took two lunch breaks at work and a ton of scratch paper (since I apparently wasn’t brillant enough to utlize Excel), but I figured it out. Answer: The German has the fish and drinks coffee in the green house, which is fourth on the block.
“Im a freakin’ genius!!!”
hi! thanks for posting the answer, i needed to make sure that i was right when i solved it. however, there’s something that is bugging me. You said, “But the Green house is on the left of the white house. Since we know the second house is blue, we then know that the first house is not green either.” Ok excuse my ignorance but why can’t the first house be green? I came to the two choices, whether to have the first house be yellow (the correct solution) and whether to have the first house be green (wrong) and i chose the first one. so please email me why if you have the time. thank you!
The beauty of this puzzle, and in math in general, is that “The first house” is never truely defined. We assume that the first house is on the left, more in part by the sociological aspect of syntax; We read from left to right, so, far left must be the beginning, ergo, house #1 is on the far left.
In fact, all the symbols offered in this logic puzzle could be interchanged with any other symbols and we would still arrive at the same product! And yet it’s our generally accepted conventions- (green=the color green)(fish= a fish) that has us all arriveing at the same answer! How intresting!
I can’t believe I actually solved this. I’ve never been able to figure out a sudoku puzzle…this was so maddening. Once you get it organized on paper it does come together. So we are in the 2% , are we?? LOL
First of all, this is a great puzzle. Comes together well and considering its a logic puzzle, it only has one logical solution. The fact that everyone is splitting hairs goes against the fact that it is logical. Also, generally accepted conventions are different then logic, and given that the generally accepted convention of first being on the left could be changed, it doesnt follow logic if it is. Symbols in this cannot be interchanged, they can be interpreted as they are intended by the maker of this LOGIC puzzle. If one is too look at this in detail, he/she will realize that the writer of this wrote it so that there is one logical solution, one solution that is correct, this one solution is the one that the writer based this problem off of, but when analyzed more in depth the creator made sure that as long as some sort of logic was followed, while it may not have been his/her own, the correct answer was still reachable. The fact that there is one answer that makes more logical sense is what im sure the statistic that “98% of people could not figure this out” is referring too. Sure, many people can figure out the answer, but only 2% of people reach it with perfect logic while others split hairs and cut corners in order to reach the answer.
Alex at 2:51pm on Sunday, August 7th, 2005,
It can’t be that way, because it says that the Norwegian lives in the first house and near the blue house.
I understand I am way tooooooo late, but I just saw this.
Yay! I feel super smart right now, as I managed to solve the puzzle.
However, I wanted to know whether it really only is 2% of the population who can solve it. Personally, I felt it was just time and patience that was required; I’m sure everyone could derive the answer if you spent long enough on it!
The real answer to the question is, who said anything about a fish? There is no fact that indicates that the 5th pet is a fish, the answer to the puzzle is that you can’t truly answer who owns a fish. You can determine who owns the 5th pet, but is it a fish? How can you be sure?
[a walleye pike is a fish. -- joe]
dude your an idiot! We had three people in my house who figured out this puzzle seperately in about 20 to 30 minutes. Your explanation seems to just have a bunch of flowery language directed at talking over people. It’s simple, process of elimination & and a little mind muscle.
I did this problem at school and the answer to the riddle is…
There is no answer.
When Einstein said that only 2% of the population could answer this he ment it. If you look closer at each clue, not one of them says anything about a fish at all.
The probability of a fish being in the German’s house is as likely as a zebra being in the house. The fish would have to be part of the clues in order to fit into a catagory. That’s why this riddle can be answered in less than 1 minute.
[a walleye pike is still a fish. -- joe]
The question clearly states “The five owners drink a different drink, smoke a different brand of cigar and keep a different pet, one of which is a Walleye Pike.”
I don’t know about those who say the questions don’t mention a fish & blah blah. The questions states clearly that one of the pets is a fish, so that means the unmentioned pet is a walleye fish….
Read the whole question people
Hey! it can be the german, or dane who smokes blend .. look at my solution.
http://img301.imageshack.us/img301/2218/soler7.jpg
Oh he meant DAnnish by “Dan” and british by “Brit” which messes up my solution..working on a new one
I finished this in 67 minutes, on one piece of paper, and I’m still in grade school…
mmmm… i started this and then realized that with the challenges at work (dont want to be caught do puzzles)the pressure to keep mentioned job the bills compressing the panic you could feel i came to this conclusion that over and above the fact that only a small % of people have access to computers in the world (yes starving Ethipians, war ridden countries etc)even less actually get emails regarding puzzles as they have strict emailing policies etc the 2% are people who to the rest of us 98% dont even blink on the need to know you scale ask your self this and its a hard puzzle to figure out when last did you do something life changing for someone else!! privileged little geeks with less brains than sense! wake up your life is passing you by and you dont even know it!! for the rest who had this as a project this lesson will teach you nothing valuable in Africa you use your hands and manual labour is daily privilege you interact with people and learn from thier lessons hope you will realize your purpose as to help others this helping yourself.
a thing to consider: einstein says the green house is on the left of the white, BUT not necessary on the immediate left, it could be couple houses down. therefore i got a different answer that is completely possible. the dane has the fish.
I graphed it out with five boxes representing the houses. Then I wrote inside the boxes each of the five facts as I logically derived them. Above each box I wrote what could *not* be in the box logically, with a little “X” next to it. Below each box I put in parentheses with a little question mark next to it, what *could likely* be in that box.
Then I read through the clues over and over, refining the graph until all the variables were accounted for except the one missing pet entry. It took me about 2-3 hours.
Steve S.