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Who Owns the Fish? (Einstein's Problem)

Date: 07/18/2002 at 10:52:39
From: Xena
Subject: problem solving

There are 5 houses sitting next to each other, each with a different 
color, occupied by 5 guys, each from a different country, 
and with a favorite drink, cigarette, and pet.  Here are the facts:

The British occupies the red house.
The Swedish owns a dog.
The Danish drinks tea.
The green house is on the left of the white house.
The owner of the green house drinks coffee. 
The person who smokes "Pall Mall" owns a bird.
The owner of the yellow house smokes "Dunhill".
The owner of the middle house drinks milk.
The Norwegian occupies the 1st house.
The person who smokes "Blend" lives next door to the person who owns 
a cat.
The person who owns a horse live next door to the person who 
smokes "Dunhill".
The person who smokes "Blue Master" drinks beer.
The German smokes "Prince".
The Norwegian lives next door to the blue house.
The person who smokes "Blend" lives next door to the person who drinks 
water.

The question is: Who owns the fish?


Date: 07/18/2002 at 13:34:56
From: Doctor Ian
Subject: Re: problem solving

Hi Xena,

This is a famous problem, attributed to Albert Einstein.  If you 
just want to find out the answer, you can go here:

    http://www.davar.net/MATH/PROBLEMS/EINSTEIN.HTM 

If you'd like to find the answer yourself (it's actually pretty 
fun once you get into it, so I recommend finding the answer 
instead of just looking it up), you'll have to set up some 
systematic way to eliminate the possibilities. 

For example, you might list the houses, along with the possible 
owners, and information about the owners, e.g., 

  House 1     House 2     House 3     House 4     House 5
  ----------  ----------  ----------  ----------  ----------
  Brit        Brit        Brit        Brit        Brit
  Swede       Swede       Swede       Swede       Swede
  Dane        Dane        Dane        Dane        Dane
  Norwegian   Norwegian   Norwegian   Norwegian   Norwegian
  German      German      German      German      German

  Red         Red         Red         Red         Red
  White       White       White       White       White
  Yellow      Yellow      Yellow      Yellow      Yellow
  Green       Green       Green       Green       Green
  Blue        Blue        Blue        Blue        Blue

  Pall Mall   Pall Mall   Pall Mall   Pall Mall   Pall Mall
  Dunhill     Dunhill     Dunhill     Dunhill     Dunhill
  Blend       Blend       Blend       Blend       Blend
  Blue Master Blue Master Blue Master Blue Master Blue Master
  Prince      Prince      Prince      Prince      Prince

Then you use the clues to eliminate possibilities, until only one 
possibility is left. For example, the Norwegian occupies the 
first house.  That means that no one else can be in the house, 
and the Norwegian can't be in any other houses:

  House 1     House 2     House 3     House 4     House 5
  ----------  ----------  ----------  ----------  ----------
              Brit        Brit        Brit        Brit
              Swede       Swede       Swede       Swede
              Dane        Dane        Dane        Dane
  NORWEGIAN   
              German      German      German      German

  Red         Red         Red         Red         Red
  White       White       White       White       White
  Yellow      Yellow      Yellow      Yellow      Yellow
  Green       Green       Green       Green       Green
  Blue        Blue        Blue        Blue        Blue

  Pall Mall   Pall Mall   Pall Mall   Pall Mall   Pall Mall
  Dunhill     Dunhill     Dunhill     Dunhill     Dunhill
  Blend       Blend       Blend       Blend       Blend
  Blue Master Blue Master Blue Master Blue Master Blue Master
  Prince      Prince      Prince      Prince      Prince

Another clue says that the Norwegian lives next door to the blue 
house.  This means the second house has to be blue, and no other 
house can be blue:

  House 1     House 2     House 3     House 4     House 5
  ----------  ----------  ----------  ----------  ----------
              Brit        Brit        Brit        Brit
              Swede       Swede       Swede       Swede
              Dane        Dane        Dane        Dane
  NORWEGIAN   
              German      German      German      German

  Red                     Red         Red         Red
  White                   White       White       White
  Yellow                  Yellow      Yellow      Yellow
  Green                   Green       Green       Green
              BLUE  

  Pall Mall   Pall Mall   Pall Mall   Pall Mall   Pall Mall
  Dunhill     Dunhill     Dunhill     Dunhill     Dunhill
  Blend       Blend       Blend       Blend       Blend
  Blue Master Blue Master Blue Master Blue Master Blue Master
  Prince      Prince      Prince      Prince      Prince

Another clue tells us that the Brit lives in the red house.  This 
means he can't be in the blue house.  And the German smokes 
Prince, so that can't be smoked by the Norwegian:

  House 1     House 2     House 3     House 4     House 5
  ----------  ----------  ----------  ----------  ----------
                          Brit        Brit        Brit
              Swede       Swede       Swede       Swede
              Dane        Dane        Dane        Dane
  NORWEGIAN   
              German      German      German      German

  Red                     Red         Red         Red
  White                   White       White       White
  Yellow                  Yellow      Yellow      Yellow
  Green                   Green       Green       Green
              BLUE  

  Pall Mall   Pall Mall   Pall Mall   Pall Mall   Pall Mall
  Dunhill     Dunhill     Dunhill     Dunhill     Dunhill
  Blend       Blend       Blend       Blend       Blend
  Blue Master Blue Master Blue Master Blue Master Blue Master
              Prince      Prince      Prince      Prince

I haven't included the drinks or the pets, but clues for those 
would work the same way.  

Note that you'll probably have to revisit some of the clues 
several times.  A clue that seems to give you no information at 
first might prove to be useful later on, after the possibilities 
have been narrowed down.

For example, the first clue, that the Brit lives in the red 
house, wasn't useful until we knew that he didn't live in the 
first house.

Also, you need to use ALL of the information given to you by each 
clue.  For example,the clue

  1. The Brit lives in a red house

tells you all of the following:

  (1) If you know that the Brit lives in a house, 
      then the house must be red.

  (2) If you know that a house is red, 
      then the Brit must live in it.

  (3) If you know that a house isn't red, 
      then the Brit can't live in it,

  (4) If you know that the Brit doesn't live in a house,
      then the house can't be red. 

Just to make sure that the technique I'm suggesting actually 
works, I went ahead and solved the puzzle.  Here are the clues 
that I used, in the order that I used them:

   9. The Norwegian lives in the first house.
  14. The Norwegian lives next to the blue house.
   8. The man living in the house right in the center drinks milk.
   1. The Brit lives in a red house.
   4. The green house is on the left of the white house 
      (next to it).
   5. The green house owner drinks coffee.
   4. The green house is on the left of the white house 
     (next to it).
   1. The Brit lives in a red house.
   7. The owner of the yellow house smokes Dunhill.
   3. The Dane drinks tea.
   2. The Swede keeps dogs as pets.
   6. The person who smokes Pall Mall rears birds.
  11. The man who keeps horses lives next to the man who 
      smokes Dunhill.
  15. The man who smokes blend has a neighbor who drinks water.
   1. The Brit lives in a red house.
   3. The Dane drinks tea.
   2. The Swede keeps dogs as pets.
   6. The person who smokes Pall Mall rears birds.
  12. The owner who smokes Blue Master drinks beer.
  13. The German smokes Prince.
   2. The Swede keeps dogs as pets.
  12. The owner who smokes Blue Master drinks beer.
  15. The man who smokes blend has a neighbor who drinks water.
  13. The German smokes Prince.
   3. The Dane drinks tea.
   2. The Swede keeps dogs as pets.
   6. The person who smokes Pall Mall rears birds.
  10. The man who smokes blend lives next to the one who 
      keeps cats.

Note that I used many of the clues more than once.  Sometimes 
this is because they yielded extra information the second time 
around; sometimes it may have been because I didn't notice 
something the first time I applied a particular clue.  For this 
reason, just trying to use the list above may not work for you. 
You're going to have to come up with your own. 

In any case, I can tell you with confidence that the puzzle can 
be solved by this method (i.e., using a table like the one 
above), with some patience, some care, and about 30-60 minutes. 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/ 
Associated Topics:
High School Logic
High School Puzzles

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