williams@kirk.DEC (John Williams 223-3402) (08/03/84)
SYMBOLOGY AND THE STUDY OF PROBLEMS
Here is a problem which was presented to me in net.puzzle.
First I will solve the problem and then describe a proposed method of
solving it artificially.
Newsgroups: net.puzzle
Path: decwrl!decvax!ittvax!dcdwest!sdcsvax!sdcrdcf!hplabs!tektronix!teklds!azure!harriett
Subject: WHO OWN'S THE ZEBRA
Posted: Mon Jul 30 13:14:07 1984
<I think someone said this goes to the line eater??>
The following is a brainteaser I got a long time ago. Many have tried
and failed, many have guessed. It is possible to solve alone or in a group.
If you really want to give yourself a brain hernia, try to solve it in you
head without writing anything down (It can be done, that is the way I solved
it the first time I tried it, it took about 15 to 20 hours over a three day
period!!!!!!)
I will give the answers in net.puzzles ONLY in about a week or so as I get
your answers. Mail all questions and answers to tekmdp!harriett. I'll post
any questions that get asked a number of times. Have Funnnnn ............
WHO OWNS THE ZEBRA .................
ON A CITY STREET, STRANGER ACCOSTS STRANGER WITH A XEROXED SHEET OF PAPER
AND THE QUESTION: "HAVE YOU SEEN THIS?". IN UNIVERSITY DORMITORIES THE
PROBLEM IS TACKED TO DOORS, MUCH AFTER THE MANNOR OF MARTIN LUTHER.
IN SUBURBAN HOUSEHOLDS THE RING OF THE TELEPHONE IS LIKLEY TO HEARLD
A VOICE THAT ASKS 'IS IT THE NORWEGIAN?'
THE CAUSE OF THE EXCITEMENT IS THE BRAINTEASER BELOW. IT'S HARD, BUT
CAN BE SOLVED BY USING DEDUCTION, ANAYLSIS, AND A LOT OF PERSISTENCE.
1. THERE ARE FIVE HOUSES, EACH OF A DIFFERENT COLOR AND INHABITED BY
MEN OF DIFFERENT NATIONALITIES, WITH DIFFERENT PETS, DRINKS, AND
CIGARETTES.
2. THE ENGLISHMAN LIVES IN THE RED HOUSE
3. THE SPANIARD OWNS THE DOG.
4. COFFEE IS DRUNK IN THE GREEN HOUSE
5. THE UKRAINIAN DRINKS TEA.
6. THE GREEN HOUSE IS IMMEDIATELY TO THE RIGHT (YOUR RIGHT) OF THE
IVORY HOUSE.
7. THE OLD GOLD SMOKER OWNS SNAILS.
8. KOOLS ARE BEING SMOKED IN THE YELLOW HOUSE.
9. MILK IS DRUNK IN THE MIDDLE HOUSE.
10. THE NORWEGIAN LIVES IN THE FIRST HOUSE ON THE LEFT.
11. THE CHESTERFIELD SMOKER LIVES NEXT TO THE FOX OWNER.
12. KOOLS ARE SMOKED IN THE HOUSE NEXT TO THE HOUSE WHERE THE HORSE IS KEPT.
13. THE LUCKY STRIKE SMOKER DRINKS ORANGE JUICE.
14. THE JAPANESE SMOKES PARLAIMENTS.
15. THE NORWEGIAN LIVES NEXT TO THE BLUE HOUSE.
NOW ...........
WHO DRINKS WATER?
AND ...........
WHO OWNS THE ZEBRA?
GOOD LUCK!
................ put that in your .bin and smoke it!!!!!
Harriette L. Lilly
Tektronix MDP Marketing
Technical Support
Beaverton ORG.
tekmdp!harriett
The answer to the five house problem is not so straight forward.
The first step to take was to solve the orientation of the houses.
The second house to the left was blue, being next to the norwegian on the
far left. The norwegian could not be red, that belonging to the englishman.
The norwegian could not be ivory, because of it's relative orientation to
green, nor could it be green leaving the second house from the left ivory.
The norwegian owned the yellow house. The middle house could not be green,
for the middle house drank milk, and not coffee, nor could it be ivory,
making the second house green, so it was red. The green and ivory fell into
place at this point.
YELLOW BLUE RED GREEN IVORY
Norwegian English
Horse
Milk Coffee
Kools
The next step was to resolve who had what cigarettes.
The norwegian had the kools, which were in the yellow house, and the japanese
had the parliaments. Neither the ukrainian nor the englishman could have the
lucky strikes because they had a different drink than orange juice. This
meant that the old golds and the chesterfields were mutually inclusive to
the ukrainian and the englishman leaving the spaniard having the lucky
strikes.
The next step was to solve who had what drinks.
The ukrainian had the tea, the englishman had the milk, and the spaniard
had the orange juice. This meant that the water and coffee were mutually
inclusive to the norwegian and the japanese. Since the norwegian's house
was yellow, he could not have the coffee. Therefore, the japanese had the
coffee and the NORWEGIAN HAD THE WATER.
The next step was to solve who lived where.
The norwegian lived in the yellow house, the englishman lived in the red
house, and because the japanese drank coffee, the japanese lived in the
green house. This meant that the blue and the ivory houses were mutually
inclusive to the ukranian and the spaniard. Since the blue house had a
horse, and the spaniard had a dog, this meant that the ukrainian owned
the blue house and the spaniard owned the ivory house.
The next step was to solve who had what cigarettes previously incomplete.
The old gold and the chesterfields belonged mutually inclusively to the
ukrainian and the englishman. Since the ukrainian lived in the blue and
had the horse, and the man with the snails also had the old golds, the
ukrainian had the chesterfields and the englishman had the old golds.
The next step was to solve who had what animals.
The ukrainian had the horse, the englishman had the snails, and the
spaniard had the dog. This meant that the fox and zebra belonged mutually
inclusively to the norwegian and japanese. Since the japanese did not live
next to the ukrainian, who had the chesterfields, he could not have the
fox. Therefore, the norwegian had the fox and the JAPANESE OWNED THE ZEBRA.
YELLOW BLUE RED GREEN IVORY
Norwegian Ukrainian English Japanese Spaniard
Fox Horse Snails Zebra Dog
Water Tea Milk Coffee Juice
Kools Chesterfields Old Golds Parliaments Lucky Strikes
This one definitely had a few wrinkles.
John Williams Digital Equipment Corperation
It appears to me as though the key to solving this problem was to
discover mutually inclusive sets of symbols, in this case, pairs.
Given:
a = x or y
b = x or y
a <> b <> c
c = x or y or z
Then:
c = z
This could be utilized by first defining sets ( or lists, for you lisp fans ),
of the various categories, owners, pets, drinks, etc., and a basic initial
condition. That is, each symbol has with it a list of possible connections.
The englishman is exclusively connected to the color red, whereas the japanese
is connected to all colors. The norwegian is connected to the left most house,
etc. The process is accomplished by rotating the context, that is, looking
for inclusive sets in convoluting categories, eliminating possible connections
until a stable state is achieved.
When I solved the problem, or should I say, when I wrote down the answer,
I naturally chose the most direct context switches for analysis. I do
not believe that this is nessesary. It would only mean that in an artificial
analysis, there would be contexts where analysis would not perform any
reductions. The choice of context was on my part, intuitive, and for a
finite problem, would only mean an increase in the amount of time required
to solve the problem, or prove it couldn't be solved.
I think a program like this would be an interesting study of problem
reduction. The formation of symbols in this program would be an even
more interesting problem.
< puzzled? >
(DEC E-NET) KIRK::WILLIAMS
(UUCP) {decvax, ucbvax, allegra}!decwrl!dec-rhea!dec-kirk!williams
(ARPA) williams%kirk.DEC@decwrl.ARPA
williams%kirk.DEC@Purdue-Merlin.ARPAestate@abnjh.UUCP (D.R.Pierce) (08/07/84)
I hate to be the one to tell you this, and I think it's only fair to
post it on the net to avoid driving anyone crazy. One of the conditions
originally set forth for the puzzle was that the green house be immediatly
to the right of the ivory house. Your posting shows the green house
on the left of the ivory house (an obvious mistake, but I couldn't resist
posting this article anyway !). This puzzle only took one hour to complete
("honest boss ! I did it during my lunch break !"). I would be curious
to know how long it would take a program to run it (or for that matter
how long it would take to develop a successfull algorithm). :-)
(Visions From The Orcrest Stone)
Carl D.
I swear to God boss, I posted it during my coffee break!
Boss, what are you doing with that typewriter ?!!!steve@hpfloat.UUCP (steve) (08/15/84)
.
If you are serious about writing a program to solve puzzles like this,
you might take a look at
Weston, Paul E., "To Uncover; To Deduce; To Conclude",
Computer Studies in the Humanities and Verbal Behavior _3_ (2) 77-89
(1970).
This article uses the 'Smith, Jones, Robinson' puzzle as its example, but
the original motivation for it was 'The Five Houses' (the puzzle in the
base note).
.............................
{hplabs,ihnp4}!hpfcla!steve-t Stephen Taylor