Problem with the "Zebra Puzzle"

[Omphaloskeptic]

@Caridwen

I had to guess too. Malacandra, I’m going to kill you! I have wash to do.

Is anyone else imagining a long, bloody pause between the second and third sentences? …Malacandra, I hope you’re OK!

[DrDeth]

Does anyone else suspect the why of the free product placement for cancer sticks? :dubious:

[Pleonast]

@Frylock

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

I took Frylock’s approach as well (before reading any spoilers). I think with the popularity of sudoku, many more people will be able to solve these sorts of puzzles.

[Caridwen]

@Malacandra

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?

I’m not sure I understand what you mean by next more?

[Gangster_Octopus]

Frylock,

I also interpreted the word “the” the way you did. Unfortunately I did not get a chance to finish the problem.

[Antinor01]

I skipped past most of this thread to avoid being spoiled and have only read the puzzle in Wikipedia. Can someone who knows the answer tell me if I have this right?

My solution is, house 1=yellow,norwegian,fox,water,kools. House 2=Blue,ukrainian,horse,tea,chesterfields. House 3=red,englishman,snails,milk,old golds. House 4=ivory,spanish,dog,orange juice,lucky strikes. house 5=green,japan,zebra,coffee,parliments.

[Arnold_Winkelried]

@Antinor01

I skipped past most of this thread to avoid being spoiled and have only read the puzzle in Wikipedia. Can someone who knows the answer tell me if I have this right?

Give yourself a high five!

[Antinor01]

@Arnold Winkelried

Give yourself a high five!

Cool. I love these kinds of puzzles.

[Biffy_the_Elephant_Shrew]

I actually misread line 12 at first because the repetition of the word “house” and the echo of that word in the word “horse” fooled my eye into thinking it said “the house next to the house next to the house”…that is, either two houses down or the same house. Once I re-read it correctly, I did not for a moment assume that there was only one house next to the horse house.

[Caridwen]

@Antinor01

I skipped past most of this thread to avoid being spoiled and have only read the puzzle in Wikipedia. Can someone who knows the answer tell me if I have this right?

My solution is, house 1=yellow,norwegian,fox,water,kools. House 2=Blue,ukrainian,horse,tea,chesterfields. House 3=red,englishman,snails,milk,old golds. House 4=ivory,spanish,dog,orange juice,lucky strikes. house 5=green,japan,zebra,coffee,parliments.

Your like me! I printed it out so I wouldn’t be tempted to go back and look.

[zagloba]

The real reason only 2% solve this correctly is98% of people assume that someone must own a zebra and drink water. However, the puzzle never says this. All you can deduce is that there is an unknown pet and an unknown beverage.

[Frylock]

@zagloba

The real reason only 2% solve this correctly is98% of people assume that someone must own a zebra and drink water. However, the puzzle never says this. All you can deduce is that there is an unknown pet and an unknown beverage.

I’m not sure whether you were joking, but

[spoiler]If we are not to assume that the unknown pet and beverage are a zebra and water, then there is no way to solve the puzzle at all. The puzzle asks where the zebra and water are. If I do not assume they are in one of the five houses, then I have no basis on which to offer any answer other than “I don’t know.” “I don’t know” is not a correct answer to any question*–it is a refusal (justified or not) to answer the question. Since we are being presented with what is being called a puzzle, and since puzzles are supposed to have solutions, and since there is no solution unless one of the houses has a zebra in it and one has water in it, we may conclude that one of the houses is supposed to have a zebra in it and one is supposed to have water in it.

*Well, one could be smart and come up with questions like “Do you know the square root of 18,356?” :)[/spoiler]

-FrL-

[zagloba]

Frylock

The New York Express leaves Chicago for New York at 10:00 a.m. traveling 85 mph. The Midwest Flyer leaves New York for Chicago at noon. At what time do they meet?

Seems to me that it’s as important to know the limits of your knowledge and be explicit about your assumptions as it is to come up with an answer.

[Frylock]

@zagloba

Frylock

The New York Express leaves Chicago for New York at 10:00 a.m. traveling 85 mph. The Midwest Flyer leaves New York for Chicago at noon. At what time do they meet?

I don’t know.

Seems to me that it’s as important to know the limits of your knowledge and be explicit about your assumptions as it is to come up with an answer.

I agree. What I said in my post agrees quite well with what you’ve said here. Sometimes, instead of giving an answer, you should say “I don’t know.”

What’s your point again?

If the question you asked about trains and whatnot is supposed to constitute a puzzle of some kind, then it is a poorly designed puzzle, as I can easily demonstrate by showing that it does not provide sufficient information for a solution. Furthermore, there is no plausible reading of your intended meaning which yields a well-designed puzzle. So it’s irredeemable as a puzzle. I believe this was your intention.

Look what happened: I read your question, tried to interpret it in a way which yields a unique solution, and found no way to do so. As a result, I said “I don’t know” is the appropriate response. No answer can be given to the question you asked.

With the Zebra puzzle, this is not the case. We find a clear, very plausible interpretation* which yields a unique solution. As I know it is the puzzle maker’s intent that there be a unique solution, I assume the interpretation I’ve given it is the intended one.

-FRL-

*Why would the puzzlemaker be talking about water and zebras unless he intended us to understand that the water and the zebra are in one of the houses? Why would it just happen to be the case that five of every category are mentioned in the clues, except for the category of drinks and the category of pets, where only four are mentioned? This would be an amzing coincidence unless we are supposed to understand water and zebra to be the fifth members of these categories. Is it interesting, challenging, and possible to solve the puzzle on the assumption that zebra and water belong in the houses? Yes. This is evidence that this is the intended puzzle, and furthermore, even if it turns out, strangely, that this is not the intended puzzle, nevertheless the puzzle plus those assumptions makes for a good puzzle in itself, so why not solve it? Is it an interesting and challenging puzzle with a unique solution on the assumption that “zebra” and “water” do not belong in the houses? No. This means that on this assumption, the puzzle is a bad one. Who wants to deal with a bad puzzle? Why would we ascribe a bad puzzle to the puzzlemaker when there is a much better puzzle we have good reasons to ascribe to her?

And so on.

[Frylock]

So I solved the puzzle, by the way, butToward the end I had to do some pretty complicated hypothetical reasoning. I had to do something like “Okay, if the coffee is here, then the orange juice is there, and that means… and that means… and that means… and that means… and that means… but the coffee being where it is means… which means… which means… which leads to a contradiction, so the coffee is there, and the orange juice is here.” I had to do this for a couple of different categories before I could zero in on the Zebra. (I suspect I could have just eliminated possible Zebra locations one by one more easily. Maybe I’ll try again tomorrow and see if that does it.) I find it more satisfying when I’ve “mechanically” solved things down to a point where I don’t have to engage in such long hypothetical chains, but I could find no way to do so. Is it likely that I missed something, or is such a chain of reasoning inevitable in this puzzle? If the latter, I’ll chalk it up to good practice at keeping chains of assumptions lined up in my head–though really, I see the whole point of logic games to be finding ways to organize information so as not to have to do this, yet not to have to take forever writing things down as well.

-FrL-

[zagloba]

Well, my response was meant to be tongue in cheek. I also confess to playing a bit with your response that “‘I don’t know’ is not a correct answer to any question*–it is a refusal (justified or not) to answer the question.” – not infrequently, “I don’t know” is the best answer to a question. I guess I’m really just observing that our perception of the intent of the communicator plays into our understanding of what they’re saying. Of course, the first time I saw this puzzle, I went ahead and solved it making the same assumptions that you did and that almost anyone else would. As you noted, we fill in information that isn’t really there because from it’s form we assume that the puzzle is meant to have a solution or that it would at least be more fun if that is what was intended.

Sometimes a puzzle like the Zebra puzzle is presented in interviews for software engineers with the purpose of seeing whether candidates spot the implicit assumption that goes into making it a real puzzle instead of a trick question. Of course, if in an interview I only said “there’s no answer because it doesn’t say anyone owns a zebra” and refused to consider it as a real puzzle, the interviewer would most likely suspect I was being a smartass, just as you did.

[Frylock]

@zagloba

Well, my response was meant to be tongue in cheek. I also confess to playing a bit with your response that “‘I don’t know’ is not a correct answer to any question*–it is a refusal (justified or not) to answer the question.” – not infrequently, “I don’t know” is the best answer to a question. I guess I’m really just observing that our perception of the intent of the communicator plays into our understanding of what they’re saying. Of course, the first time I saw this puzzle, I went ahead and solved it making the same assumptions that you did and that almost anyone else would. As you noted, we fill in information that isn’t really there because from it’s form we assume that the puzzle is meant to have a solution or that it would at least be more fun if that is what was intended.

Sometimes a puzzle like the Zebra puzzle is presented in interviews for software engineers with the purpose of seeing whether candidates spot the implicit assumption that goes into making it a real puzzle instead of a trick question. Of course, if in an interview I only said “there’s no answer because it doesn’t say anyone owns a zebra” and refused to consider it as a real puzzle, the interviewer would most likely suspect I was being a smartass, just as you did.

Heh.

Anyway, it looks like I’ve just been over-explaining your own point to you, so now I’ll bow out.

-FrL-

(Though I’d still say there’s a difference between a “response” to a question and an “answer” to it.)

[ErinPuff]

@Malacandra

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?

Jo, who’s from the LSO, cost the most, and played too slowly?

[Malacandra]

@Caridwen

I’m not sure I understand what you mean by next more?

Sort them in order of cost from lowest to highest, A-B-C-D. C cost next more than B. (C cost more, but not next more, than A.)

@Frylock

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.

Well, each to his own taste. I used that approach originally with the zebra puzzle and it took me some time to hit upon a proof that didn’t entail assert/backtrack at any stage. And the musicians puzzle doesn’t rely solely on assert/backtrack - it’s just that there comes a point where you have to resort to it. With the right solution, you need do so only once.