There are five houses, each of a different color and inhabited by men of different nationalities, with...

[ Editor: the two solutions below are for variants of the puzzle whose
clue lists are not in the collected material.  In the one Nick Barnes
solves, the cigarettes are tobaccos (spun cut, rough cut, flake,
mixture, medium; abbreviated r, f, m, x in his tables).  In Doctor
Rob's, they are flowers (geraniums, roses, marigolds, lilies,
gardenias), and his clue numbers run one higher than Brown's. ]

In article <D6uFD1.MG0@info.uucp> take7333@mach1.wlu.ca (Kazutaka
Takemura u) writes:

   WHO OWNS THE ZEBRA?

The Norwegian drinks water, and the Japanese owns the zebra.

Trivially, without combining rules, one comes up with this table of
possibilities for the houses:

1               2               3               4               5
Norwegian       UJ              ESJ             SUJ             ESUJ
yellow          blue            ri              ig              rg
water           to              milk            cto             cto
fz              horse           dsfz            dsfz            dsfz
spun cut        rfx             rmx             rfmx            rfmx

Now consider where the Englishman lives.  If he lives in house 5 with a
red door, house 3 is ivory and house 4 is green with coffee.  So the
tea-drinking Ukrainian must live in house 2.  That leaves the
Englishman to drink the orange juice and smoke flake.  But since the
Spaniard has a dog and not snails, he does not smoke medium cut.
Neither does the Japanese.  So nobody smokes medium cut.

Therefore the Englishman must live in house 3, which trivially gives
this table:

1               2               3               4               5
Norwegian       UJ              English         SUJ             SJ
yellow          blue            red             ivory           green
water           to              milk            to              coffee
fz              horse           sfz             dsfz            dsfz
spun cut        rfx             mx              rfmx            rmx

Since orange juice is not drunk by the Ukrainian or by the Japanese, it
must be drunk by the Spaniard, so the Japanese must live in house 5,
the Ukrainian in 2, and the Spaniard in 4.  Then the Spaniard smokes
flake so the Ukranian must smoke mixture and the Englishman smokes
medium and keeps snails.  The fox must be in house 1, and the Spaniard
has the dog, leaving the Japanese with the zebra:

1               2               3               4               5
Norwegian       Ukrainian       English         Spaniard        Japanese
yellow          blue            red             ivory           green
water           tea             milk            orange juice    coffee
fox             horse           snails          dog             zebra
spun cut        mixture         medium          flake           rough cut

-- Nick Barnes <nickb@harlequin.co.uk>

----------

I first saw this problem in 1962 in a magazine called _International_
_Life_.  It is probably older than that.

Who Owns the Zebra?

Of course one could just enumerate the 5^5 = 3125 different possible
answers, and scratch off all of those which didn't fit the clues, but
this is the hard way.  With a little logic, the correct answer can be
deduced.

[ Editor: with five attributes each permuted among five houses there
are (5!)^5 = 24,883,200,000 possible assignments, not 5^5 = 3125. ]

The kind of logic used goes like this:

Number the houses from left to right as 1, 2, 3, 4, and 5.

By No.2, the English person lives in the red house.  This implies that
the English person does not live in the green, ivory, yellow, or blue
house, and that the Spaniard, Ukrainian, Norwegian, and Japanese do not
live in the red house.  Thus this one clue gives us nine facts.

By No.3, the Spaniard owns the dog.  Again, this tells us nine facts:
the Spaniard does not own the snails, fox, horse, or zebra, and the dog
owner is not English, Ukrainian, Norwegian, nor Japanese.  It also
implies that the person who lives in the red house is not the dog
owner, a tenth fact.

By No.4, coffee is drunk in the green house.  Again, this tells us nine
facts: coffee is not drunk in the red, ivory, yellow, or blue house,
and tea, milk, orange juice, and water are not drunk in the green
house.  It also implies that the coffee drinker is not English.

By No.5, the Ukrainian drinks tea.  Again, this tells us the usual nine
facts: the tea drinker is not English, Spanish, Norwegian, or Japanese,
and the Ukrainian does not drink coffee, milk, orange juice, or water.
Also the tea drinker is not the dog owner, nor does he live in the red
house.

We'll hold off on No.6 for a bit.

By No.7, the geranium grower owns snails.  Thus the geranium grower
does not own the dog, fox, horse, or zebra, and the snail owner does
not grow roses, marigolds, lilies, or gardenias.  Thus the geranium
owner is not the Spaniard.

By No.8, the rose grower lives in the yellow house.  Thus the rose
grower does not live in the red, green, ivory, or blue houses, and the
person living in the yellow house does not grow geraniums, marigolds,
lilies, or gardenias.  This implies that person living in the yellow
house does not own snails.  Furthermore the rose grower does not drink
coffee.

By No.9, milk is drunk in house 3.  Thus milk is not drunk in houses 1,
2, 4, or 5, and neither coffee, tea, orange juice, or water is drunk in
house 3.

By No. 10, the Norwegian lives in house 1.  The Norwegian does not live
in houses 2, 3, 4, or 5, and the resident of house 1 is not English,
Spanish, Ukrainian, or Japanese.  This implies that house 1 is not red,
the resident of house 1 does not own the dog nor drink tea.

We'll hold off on No.11 and No.12, too.

By No.13, the lily-grower drinks orange juice.  Thus the lily-grower
does not drink coffee, tea, milk, or water, and orange juice is not
drunk by the growers of geraniums, roses, marigolds, or gardenias.
Then the lily-grower cannot be Ukrainian, live in house 3, or live in
the green house.  Furthermore the drinker of orange juice cannot own
snails, live in the yellow house, live in the green house, live in
house 3, or be Ukrainian.

By No.14, the Japanese grows gardenias.  Thus the Japanese does not
grow geraniums, roses, marigolds, or lilies, and the gardenia-grower is
not English, Spanish, Ukrainian, or Norwegian.  We can deduce that the
gardenia-grower does not drink tea, own the dog, live in the red house,
or live in house 1, and further that the Japanese does not live in the
yellow house, own snails, or drink orange juice.

By No.15, the blue house must be number 2.  Thus the blue house is not
numbers 1, 3, 4, nor 5, and house 2 is not red, green, ivory, or
yellow.  Then milk is not drunk in the blue house, and house 2 is not
owned by the English person, nor is coffee drunk there, nor are roses
or marigolds grown there.

Now we must deal with No.6, No.11, and No.12, which deal with the
position of houses.

One of the things implied by No.6 is that the green house is not number
1, and the ivory house is not number 5.  This implies that coffee is
not drunk in house 1.  In fact, there are two possibilities: the green
house could be number 4 (and ivory number 3) or number 5 (and ivory
number 4).  Let us take them in order:

Case 1:  The green house is number 4 and the ivory house is number 3.
Then the red house is number 5 (the only possibility left), and so the
yellow house is number 1.  This allows us to deduce that the Norwegian
lives in the yellow house, the Englishman in house 5 (by elimination),
roses are grown in house 1, coffee is drunk in house 4, the Norwegian
grows roses, tea is drunk in the blue house (by elimination), the
Ukrainian lives in the blue house, the water-drinker grows roses (by
elimination), the Japanese drinks coffee (by elimination), the Spaniard
drinks milk (by elimination), the English person drinks orange juice
(by elimination), tea is drunk in house 2 (by elimination), orange
juice is drunk in house 5, water is drunk in house 1 (by elimination),
orange juice is drunk in the red house, water is drunk in the yellow
house (by elimination), the English person grows lilies, the Spaniard
grows marigolds (by elimination), the Ukrainian grows marigolds (by
elimination), lilies are grown by the owner of house 5 (which is red),
the Ukrainian owns snails (by elimination), marigolds are grown by the
dog owner (by elimination), the milk drinker owns the dog, the Spaniard
lives in house 3 (which is ivory), and so on!

[ Editor: "the Ukrainian grows marigolds" evidently should be "the
Ukrainian grows geraniums", since the Spaniard grows the marigolds and
the Ukrainian is then said to own the snails (clue 7). ]

Not quite all of the remaining assignments can be made in this way.

Now we have to check No.11:  The marigold grower (the Spaniard living
in house 3, which is ivory, the dog-owner, milk drinker) has to live
next to the fox owner.  The fox owner can't be in house 2, so must be
in house 4.  This implies many further facts.

Now we have to check No.12: Roses are grown house 1, so the horse must
be in house 2, which is a contradiction, since snails are kept there.
(Certainly there is a shorter way to see this contradiction!)

Case 2:  The green house is number 5 and the ivory house is number 4.
Then the yellow house is number 1 (by elimination) and the red house is
number 3 (by elimination).  This implies that the English person lives
in house 3, the English person drinks milk, the Norwegian lives in the
yellow house, the Norwegian lives in house 1, the Norwegian grows
roses, roses are grown at house 1, coffee is drunk in house 5, the
Japanese drinks coffee (by elimination), water is drunk in the yellow
house (by elimination), water is drunk in house 1, the Norwegian drinks
water, the Spaniard drinks orange juice (by elimination), the Spaniard
grows lilies (by elimination), the Japanese lives in the green house,
and so on.

Now we check No.11: The house with marigolds can be either 3 or 4, so
the house with the fox can be 2 or 4, or 3 or 5, respectively, but not
1.

Now we check No.12: The roses are grown in house 1, so the horse has to
be in house 2.  This implies by elimination that the zebra is in house
1, and the dog in house 4, the fox in house 5, and the snails in house
3.

[ Editor: the table below has the marigolds in house 2, the fox in
house 1 and the zebra in house 5, contrary to the two paragraphs
above. ]

The rest now follows.  The results are:

House   Color     Nationality   Animal    Beverage    Flower
1       Yellow    Norwegian     Fox       Water       Roses
2       Blue      Ukrainian     Horse     Tea         Marigolds
3       Red       English       Snails    Milk        Geraniums
4       Ivory     Spaniard      Dog       O.J.        Lilies
5       Green     Japanese      Zebra     Coffee      Gardenias

So the Norwegian drinks water, and the Japanese owns the Zebra.

-- Doctor Rob, The Math Forum (http://mathforum.org/dr.math/), August
   1997