Problem with the "Zebra Puzzle"

Factual Questions
1

There seems to be something wrong with the Zebra Puzzle as it is formulated here.

Or else I’m reading something wrong.

Some of the rules seem to lead to a contradiction when taken together. Specifically:

  1. The Englishman lives in the red house
  2. The green house is immediately to the right of the ivory house
  3. Kools are smoked in the yellow house
  4. The Norwegian lives in the first house
  5. Kools are smoked in the house next to the house where the horse is kept.
  6. The Norwegian lives next to the blue house

Note that the article clarifies that “right” in rule six means “your right.” In other words, if the ivory house is number 2, then the green house is house 3, and if the ivory house is house 3, then the green house is house 4, and so on.

But what can we derive from the rules I just listed above?

A. The Norweigian is in house number one, by rule 10. (Numbering the houses from my left to my right.)
B. So the blue house is house number 2, by rule 15.
C. This means house number 1 is neither green nor ivory, by rule 6.*
D. Because of B, we also know that house number one is not blue.
E. From A together with rule 2, we know that house number one is not red.
F. From C, D, E, we conclude that house number one is yellow.
G. From F and rule 8, we conclude that the cigarettes smoked in house number 1 are Kools.
H. From rule 12, we know that either the horse is in house 1 and kools in house 2, or else, the horse is in house 5 and kools in house 4.**
I. From H, we can immediately derive that the Kools are in either house 2 or house 4.
J. From G and I, contradiction immediately follows.

So what gives?

*Since the green house is immediately to the right of the ivory one, it follows that house 1 is not green, since house 1 is not to the right of any house. Similarly, it follows that house 1 is not ivory, because the house to the right of house 2 is blue, not green.

**The rule says that the Kools are smoked in “the” house next to the one where the horse is kept. “The” here indicates that there is only one house next to the one where the horse is kept. There are only two houses which have only one house next to them, namely, houses 1 and 5. So the horse is in house 1 or house 5, while the kools are therefore in house 2 or house 4.

-FrL-

2

You’re overthinking it.

Kools ends up being the cigarettes of house 1 and the horse (of course) is the pet of house 2

I edited the wiki entry accordingly.

Side note: if only 2% of the population can solve this, 98% are dumb or just too impatient to wade through the mechanical but not especially challenging process.

3

I’m not done yet, but unless I’m mistaken the Kools have to be in house 1.

Highlight after kools I don’t know how to do a spoiler box.

Woops! Sorry I didn’t see your answer.

4

What the heck is “overthinking” in this context, and why edit the wikipedia entry if I was “overthinking” and not finding a genuine problem in the text? :confused:

I think you’re saying I “overthought” the assumption that says the Kools are in the house next to the house where the horse is kept. But what I think you’re calling “overthinking” is what I would in fact call, simply, “reading.” It is a logic puzzle after all. Things need to be read precisely as they are worded.

Anyway, do others agree with Bryan Eckers that the puzzle has been misformulated, and shouldn’t use the “the” in question?

The ones who can’t solve it just don’t know what that mechanical process is. This has nothing to do with stupdity or impatience.

-FrL-

(While I was typing this, I tried making another correction to the wiki article, and then someone else reverted it to the original “the” version because the article is supposed to present the puzzl in its original published form. Fair enough!)

5

OK, I’m a little stuck.

[spoiler]

Yellow/ Norw/water/ ? /Kools
Blue /Ukranian/Tea/Horse/ ? /
Red/Eng/milk/ ?/?/
Ivory/Spansh/OJ/Dog/L.Strike
Green/Japanese/Coffee/?/Parlament [/spoiler]

6

I used to do these a lot and got pretty good at them, certainly not because I was smart. I’m having trouble with this one. I don’t know if it’s because I’m rusty or in the 98%.

7

Well, “over” in the sense that you’re thinking about this more than I did because it didn’t even occur to me to read the “the” the way you did. I made the edit because you have a point that it could be misinterpreted, but that was without realizing that “original” really did mean “original”. I could get fussy and squeeze a [sic] in there, but… nah.

8

As a minor additional note, I’d like to thank you for starting this thread so I could write a sentence with “the” three times in a row.

9

I think I’ve got it.

[spoiler]

I was thinking fox next to chesterfield meant to the right which screwed me up. So the answer is the Norwegian drinks water and Japanese owns the zebra. If I’m right about the snail [/spoiler]

10

I guess I didn’t read it that way because it didn’t occur to me.

11

Heh :slight_smile:

-FrL-

12

This is interesting.

As soon as I saw these sentences, without thinking about it at all, but rather, simply by reading the sentences, I had the impression that the house with a horse in it must have only one neighbor.

Two people in this thread have said this didn’t even occur to them as a reading.

So now I’m intrigued. I’m really suprised there is a difference of opinion here, but I’m glad to discover it!

What’s the initial, “natural” reading for others?

-FrL-

13

Maybe someone else will come along that read it differently. To be honest, I didn’t read the directions carefully when I started and at first I missed that the houses were in a line. For some reason I picured them in a circle. If I didn’t re-read, I’d have been here all night. :stuck_out_tongue:

Once I got the nationalities and drinks, it got easier. I had to make a little graph and did it about 3-4 times but it wasn’t easy. I had trouble with the Lucky Strikes and OJ and Spain and dog.

I’ll get someone else to take a look and see what they say.

14

Frylock, I didn’t read rules 11 or 12 as you did when I originally solved the problem years ago.

The way I solve these problems is by “brute force” - writing down all the possibilities at each step, indicating “branches” from previous possible solutions with a numbering system. If anyone is interested in the way I do this, it’s included below in the spoiler:

[spoiler] 1. There are five houses.
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 of the ivory house.
7. The Old Gold smoker owns snails.
8. Kools are smoked in the yellow house.
9. Milk is drunk in the middle house.
10. The Norwegian lives in the first house.
11. The man who smokes Chesterfields lives in the house next to the man with the fox.
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 Parliaments.
15. The Norwegian lives next to the blue house.

Who drinks water? Who owns the zebra?

In solutions below, attributes are listed in this order: house number & nationality & colour & smoke & drink & pet

STEP 1
(rules relating to absolute house positions) 1, 9, 10, 15
Rule 1 There are five houses.
and Rule 9 Milk is drunk in the middle house.
and Rule 10 The Norwegian lives in the first house.
and Rule 15 The Norwegian lives next to the blue house.
solution A
1 Norwegian
2 blue
3 milk
4
5

STEP 2 (rules relating to relative house positions) 1, 4, 6, 9, 10, 15
Rule 4 Coffee is drunk in the green house.
and 6 The green house is immediately to the right of the ivory house.
solution A.1
1 Norwegian
2 blue
3 ivory & milk
4 green & coffee
5

solution A.2
1 Norwegian
2 blue
3 milk
4 ivory
5 green & coffee
(from now on try to use rules that are most related to information I already have)

STEP 3 (use color information since I know a lot about colors) 1, 2, 4, 6, 9, 10, 15
Rule 2 The Englishman lives in the red house.
solution A.1
1 Norwegian
2 blue
3 ivory & milk
4 green & coffee
5 Englishman & red

solution A.2
1 Norwegian
2 blue
3 Englishman & red & milk
4 ivory
5 green & coffee
STEP 4 (use color information since I know a lot about colors) 1, 2, 4, 6, 8, 9, 10, 15
Rule 8 Kools are smoked in the yellow house.
solution A.1
1 Norwegian & yellow & Kools
2 blue
3 ivory & milk
4 green & coffee
5 Englishman & red

solution A.2
1 Norwegian & yellow & Kools
2 blue
3 Englishman & red & milk
4 ivory
5 green & coffee
STEP 5 (look for nationalites and drinks) 1, 2, 4, 5, 6, 8, 9, 10, 15
Rule 5 The Ukrainian drinks tea.
solution A.1
1 Norwegian & yellow & Kools
2 Ukrainian & blue & tea
3 ivory & milk
4 green & coffee
5 Englishman & red

solution A.2.1
1 Norwegian & yellow & Kools
2 Ukrainian & blue & tea
3 Englishman & red & milk
4 ivory
5 green & coffee

solution A.2.2
1 Norwegian & yellow & Kools
2 blue
3 Englishman & red & milk
4 Ukrainian & ivory & tea
5 green & coffee
STEP 6 (look for nationalites or drinks) 1, 2, 3, 4, 5, 6, 8, 9, 10, 15
Rule 3 The Spaniard owns the dog.
solution A.1.1
1 Norwegian & yellow & Kools
2 Ukrainian & blue & tea
3 Spaniard & ivory & milk & dog
4 green & coffee
5 Englishman & red

solution A.1.2
1 Norwegian & yellow & Kools
2 Ukrainian & blue & tea
3 ivory & milk
4 Spaniard & green & coffee & dog
5 Englishman & red

solution A.2.1.1
1 Norwegian & yellow & Kools
2 Ukrainian & blue & tea
3 Englishman & red & milk
4 Spaniard & ivory & dog
5 green & coffee

solution A.2.1.2
1 Norwegian & yellow & Kools
2 Ukrainian & blue & tea
3 Englishman & red & milk
4 ivory
5 Spaniard & green & coffee & dog

solution A.2.2.1
1 Norwegian & yellow & Kools
2 Spaniard & blue & dog
3 Englishman & red & milk
4 Ukrainian & ivory & tea
5 green & coffee

solution A.2.2.2
1 Norwegian & yellow & Kools
2 blue
3 Englishman & red & milk
4 Ukrainian & ivory & tea
5 Spaniard & green & coffee & dog
STEP 7 (look for nationalites or drinks) 1, 2, 3, 4, 5, 6, 8, 9, 10, 13, 15
Rule 13 The Lucky Strike smoker drinks orange juice.
solution A.1.1
1 Norwegian & yellow & Kools
2 Ukrainian & blue & tea
3 Spaniard & ivory & milk & dog
4 green & coffee
5 Englishman & red & Lucky Strike & orange juice

solution A.1.2
1 Norwegian & yellow & Kools
2 Ukrainian & blue & tea
3 ivory & milk
4 Spaniard & green & coffee & dog
5 Englishman & red & Lucky Strike & orange juice

solution A.2.1.1
1 Norwegian & yellow & Kools
2 Ukrainian & blue & tea
3 Englishman & red & milk
4 Spaniard & ivory & Lucky Strike & orange juice & dog
5 green & coffee

solution A.2.1.2
1 Norwegian & yellow & Kools
2 Ukrainian & blue & tea
3 Englishman & red & milk
4 ivory & Lucky Strike & orange juice
5 Spaniard & green & coffee & dog

solution A.2.2.1
1 Norwegian & yellow & Kools
2 Spaniard & blue & Lucky Strike & orange juice & dog
3 Englishman & red & milk
4 Ukrainian & ivory & tea
5 green & coffee

solution A.2.2.2
1 Norwegian & yellow & Kools
2 blue & Lucky Strike & orange juice
3 Englishman & red & milk
4 Ukrainian & ivory & tea
5 Spaniard & green & coffee & dog
*** At this point we see that in all the possible solutions the remaining drink (water) belongs to group 1 - we’re halfway there
STEP 8 (look for nationalites or drinks) 1, 2, 3, 4, 5, 6, 8, 9, 10, 13, 14, 15
Rule 14 The Japanese smokes Parliaments.
solution A.1.1
1 Norwegian & yellow & Kools
2 Ukrainian & blue & tea
3 Spaniard & ivory & milk & dog
4 Japanese & green & Parliaments & coffee
5 Englishman & red & Lucky Strike & orange juice

solution A.1.2
1 Norwegian & yellow & Kools
2 Ukrainian & blue & tea
3 Japanese & ivory & Parliaments & milk
4 Spaniard & green & coffee & dog
5 Englishman & red & Lucky Strike & orange juice

solution A.2.1.1
1 Norwegian & yellow & Kools
2 Ukrainian & blue & tea
3 Englishman & red & milk
4 Spaniard & ivory & Lucky Strike & orange juice & dog
5 Japanese & green & Parliaments & coffee

solution A.2.1.2 - eliminated!

solution A.2.2.1
1 Norwegian & yellow & Kools
2 Spaniard & blue & Lucky Strike & orange juice & dog
3 Englishman & red & milk
4 Ukrainian & ivory & tea
5 Japanese & green & Parliaments & coffee

solution A.2.2.2 - eliminated!

STEP 9 (going through rest of rules in order) 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 13, 14, 15
Rule 7 The Old Gold smoker owns snails.
solution A.1.1
1 Norwegian & yellow & Kools
2 Ukrainian & blue & Old Gold & tea & snails
3 Spaniard & ivory & milk & dog
4 Japanese & green & Parliaments & coffee
5 Englishman & red & Lucky Strike & orange juice

solution A.1.2
1 Norwegian & yellow & Kools
2 Ukrainian & blue & Old Gold & tea & snails
3 Japanese & ivory & Parliaments & milk
4 Spaniard & green & coffee & dog
5 Englishman & red & Lucky Strike & orange juice

solution A.2.1.1.1
1 Norwegian & yellow & Kools
2 Ukrainian & blue & Old Gold & tea & snails
3 Englishman & red & milk
4 Spaniard & ivory & Lucky Strike & orange juice & dog
5 Japanese & green & Parliaments & coffee

solution A.2.1.1.2
1 Norwegian & yellow & Kools
2 Ukrainian & blue & tea
3 Englishman & red & Old Gold & milk & snails
4 Spaniard & ivory & Lucky Strike & orange juice & dog
5 Japanese & green & Parliaments & coffee

solution A.2.2.1.1
1 Norwegian & yellow & Kools
2 Spaniard & blue & Lucky Strike & orange juice & dog
3 Englishman & red & Old Gold & milk & snails
4 Ukrainian & ivory & tea
5 Japanese & green & Parliaments & coffee

solution A.2.2.1.2
1 Norwegian & yellow & Kools
2 Spaniard & blue & Lucky Strike & orange juice & dog
3 Englishman & red & milk
4 Ukrainian & ivory & Old Gold & tea & snails
5 Japanese & green & Parliaments & coffee

STEP 10 (going through rest of rules in order) 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15
Rule 11 The man who smokes Chesterfields lives in the house next to the man with the fox.
solution A.1.1
1 Norwegian & yellow & Kools
2 Ukrainian & blue & Old Gold & tea & snails
3 Spaniard & ivory & Chesterfields & milk & dog
4 Japanese & green & Parliaments & coffee & fox
5 Englishman & red & Lucky Strike & orange juice

solution A.1.2
1 Norwegian & yellow & Kools
2 Ukrainian & blue & Old Gold & tea & snails
3 Japanese & ivory & Parliaments & milk
4 Spaniard & green & Chesterfields & coffee & dog
5 Englishman & red & Lucky Strike & orange juice & fox

solution A.2.1.1.1 - eliminated!

solution A.2.1.1.2
1 Norwegian & yellow & Kools & fox
2 Ukrainian & blue & Chesterfields & tea
3 Englishman & red & Old Gold & milk & snails
4 Spaniard & ivory & Lucky Strike & orange juice & dog
5 Japanese & green & Parliaments & coffee

solution A.2.2.1.1
1 Norwegian & yellow & Kools
2 Spaniard & blue & Lucky Strike & orange juice & dog
3 Englishman & red & Old Gold & milk & snails
4 Ukrainian & ivory & Chesterfields & tea
5 Japanese & green & Parliaments & coffee & fox

solution A.2.2.1.2 - eliminated!
STEP 11 (going through rest of rules in order) 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15
Rule 12 Kools are smoked in the house next to the house where the horse is kept.
solution A.1.1 - eliminated!

solution A.1.2 - eliminated!

solution A.2.1.1.2
1 Norwegian & yellow & Kools & fox
2 Ukrainian & blue & Chesterfields & tea & horse
3 Englishman & red & Old Gold & milk & snails
4 Spaniard & ivory & Lucky Strike & orange juice & dog
5 Japanese & green & Parliaments & coffee

solution A.2.2.1.1 - eliminated!
*** Remaining Animal (Zebra) goes with 5 and drink (water) goes with 1[/spoiler]

15

Well, since we’re sharing, here’s my method:

[spoiler]I drew a big square, and divided it into five rows and five columns. Each column stands for a house. Each row stands for a kind–i.e., column one stands for colors, column two stands for nationalities, and so on. Then in each cell, I wrote down five letters, each standing for one of the five items belonging to that cell’s row’s kind. So for example, in the top left cell I wrote “R G B Y I” for the five colors. Same in the second cell from the left on the top. In the first cell of the second row I wrote “E N U S J” for the five nationalities, and so on. Of course, I made sure each of the 25 possible traits has its own unique letter, in order to avoid confusion.

Now I am solving it (I started at work today and stopped when I caught the contradiction–will finish tomorrow) in a way sort of reminiscent of the way you solve a sudoku puzzle. I’m using the 15 clues to cross out letters, and when only one letter is left in a cell, I cross out every other instance of that letter in every other cell. Eventually, I’ll have ‘Z’ and ‘W’ as the only letters occupying their recpective cells, and voila.[/spoiler]

-FrL-

16

I rate this one as pretty easy simply because it is never necessary to use the guess-and-backtrack approach - at all points in working out the solution it is possible to use the clues to place another piece of the puzzle. Here’s a smaller but slightly tougher puzzle (IMO) that I devised:

We hired four soloists to come and play for our concert. All four soloists play different instruments and perform for different orchestras. Unfortunately, they proved a bit of a disappointment, thus:

Fred cost next more than the oboeist
Jo plays for the LSO
Sherri cost next more or less than the player from the Orchestra of the Age of Enlightenment
Simon missed loads of notes out
The trumpeter cost next more than the player from the Boston Pops
The player who was too slow cost the next more than the flautist
The LSO player cost next more or less than the one who played too loud
The Berlin Philharmonic player cost more than the player who was flat
The player who was too loud cost the second most

Who played the viola?

17

Hmm, if I have to use the “guess and backtrack” method, I think of the puzzle as poorly designed.

To me, a really good puzzle is one where you don’t have to guess, but it takes a lot of work to see how to actually do it without guessing.

-FrL-

18

I had to guess too. Malacandra, I’m going to kill you! I have wash to do.
Thanks **Arnold Winkelried **. I’m going to through that later.

**Frylock **, if you enjoy these, there are some online and they sell logic puzzle books. I’ve been hooked on Sudoku and haven’t done these for awhile.
http://www.puzzlersparadise.com/page1034.html

Stupid question but with the Zebra puzzle you were solving for water and zebra. Would there be a way to set up a formula to solve this?

19

Frylock, I’m going to try your method - it seems like it takes less writing than mine.

20

In my experience, some writers will rely on precise language and reward close reading of the clues, but others will not. Figuring out what sort of puzzle writer you have is part of the puzzle.