There seems to be something wrong with the Zebra Puzzle as it is formulated at the wikipedia article linked to above. Here’s the link again.
Or else I’m reading something wrong.
[spoiler]Some of the rules seem to lead to a contradiction when taken together. Specifically:
- The Englishman lives in the red house
- The green house is immediately to the right of the ivory house
- Kools are smoked in the yellow house
- The Norwegian lives in the first house
- Kools are smoked in the house next to the house where the horse is kept.
- 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.[/spoiler]
-Kris