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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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