# Who has the fish?August 4, 2005 3:22 PM   Subscribe

Who has the fish? Einstein logic puzzle. If I can do it, you guys can.
posted by swift (53 comments total) 1 user marked this as a favorite

Used as an example of how to solve logic puzzles using spreadsheet optimization.
posted by jasper411 at 3:30 PM on August 4, 2005

Note II: Of course, you never know, we might have been smart enough to shuffle the variables a bit so that the answer you find from Googling previous posts of the puzzle might be wrong in a way that allows us to know of your laziness and treachery. Not that we'd ever make such knowledge public or anything.

Hmm... And how do we know that the 'shuffling' didn't destroy the problem? Unless they are only replacing labels, this problem could be unsolveable.
posted by delmoi at 3:47 PM on August 4, 2005

Erm, okay. All of the constraints are the same as they are on the website jasper411 linked to, however the order has changed. I have no idea why they would have changed the order, but thats all they did.
posted by delmoi at 3:54 PM on August 4, 2005

um. This is Who owns the Zebra for which there are 880 direct hits by google. It is old. Someone told me they solved it in highschool in 1969.
posted by MonkeySaltedNuts at 4:15 PM on August 4, 2005

But . . . it's a fish.
posted by swift at 4:18 PM on August 4, 2005

Technically, 100 percent of people are able to solve the problem, as the solution is found through logic alone. Ninety-eight percent of them just can't be arsed, as our friends across the pond might say.
posted by jenovus at 4:25 PM on August 4, 2005

These two articles plus things I've heard in person lead me to believe that the Zebra Puzzle was published in Readers Digest around 1968. It has often appeared as an example of constraint satisfaction problems. (374 hits)

It is a shame that somebody had to rename it to "who has a fish" and call it the "Einstein Problem".
posted by MonkeySaltedNuts at 4:44 PM on August 4, 2005

hints:

Those are not "hints". The problem would be unsolvable without them.
posted by dreamsign at 4:50 PM on August 4, 2005

Think outside of the pants box, kids - quonsar has the fish.
posted by goodnewsfortheinsane at 4:52 PM on August 4, 2005

Was I meant to do it in my head? I used pen & paper, does that make me a cheat? (Obfuscated answer: whare ma?)
posted by The Monkey at 4:58 PM on August 4, 2005

I suspect that Einstein's 98% claim (if it isn't apocryphal) bespoke a time in which potential puzzle-solvers would not know to make charts with circles and x's and to propagate those circles and x's across the other circles and x's.

2% would probably be a reasonable number for the percentage of people who could come up with an equivalent puzzle-solving system on their own. Maybe that's high, then.
posted by nobody at 5:26 PM on August 4, 2005

wow, it's a puzzle made by EINSTEIN? It must be HARD!!!
posted by jeffj at 5:29 PM on August 4, 2005

Gee thanks guys. Now I don't feel special for solving it at all! (Spent about an hour in Notepad making charts!)
posted by knave at 5:33 PM on August 4, 2005

(It occurred to me that the solution might be different if you assume house #1 is on the right and house #5 on the left. The only two clues that reference directionality are:

10. Norwegian is in the 1st house.

and

4. The green house is to the left of the white house.

So the question is whether shifting the meaning of clue #10 would end up interfering at all with the ordering in clue #4, and whether that changes the answer or makes the whole puzzle fall apart with contradiction and incompatibility. If someone else tries this out, then I won't have to do it tomorrow.)

posted by nobody at 5:37 PM on August 4, 2005

nobody, without trying, I'm assuming it will fall apart if you try putting house #1 on the right instead of left. In the English speaking world, we count left to right. :)
posted by knave at 5:42 PM on August 4, 2005

Because we all know Einstein had nothing better to do with his time that cook up entirely ordinary logic puzzles like we did back in Slightly-Advanced-Kids Class, and perform enough tests with random samples of the population in order to know that 98% of people couldn'twouldn't solve it.

In other words, Einstein did no such thing, and I don't have to Google the solution (probably at Snopes) to figure *that* one out.
posted by JHarris at 5:59 PM on August 4, 2005

Used as an example of how to solve logic puzzles using spreadsheet optimization.

Huh. Wasn't even thinking that way, but my eventual solution (which seems to be correct, though I tend to suck at these) is indeed laid out like a spreadsheet. Neat. Maybe all that tedious mucking about in excel that my job has required from time to time has been good for my brain after all.
posted by PinkStainlessTail at 6:29 PM on August 4, 2005

As if I need MetaFilter to provide jarring reminders of the grimmest portion of the Law School Admission Test (LSAT). Really, I would have expected Einstein to make better use of his time.
posted by sindark at 6:34 PM on August 4, 2005

I'm still trying to come to terms with the knowledge that Reader's Digest used to print logic problems.
posted by box at 6:36 PM on August 4, 2005

I used a text-editor and lots of +this -that to solve it. It reminded me of an abstract Sudoku puzzle.
posted by Stuart_R at 6:44 PM on August 4, 2005

Who is this Einsteen kid, I'm gonna kick hi9s butt!!11!!!!!
posted by snsranch at 6:47 PM on August 4, 2005

By adept use of Google I was quickly able to determine that all the fish are belong to us.
posted by johngumbo at 6:48 PM on August 4, 2005

snsranch i hakc u
posted by jenovus at 6:51 PM on August 4, 2005

2ez.
posted by woil at 6:52 PM on August 4, 2005

This was easy. After 3 beers it took me 10-15 minutes to work it out on paper. I like doing these things, though - anyone know any better puzzles of this type?
posted by bashos_frog at 7:05 PM on August 4, 2005

As if I need MetaFilter to provide jarring reminders of the grimmest portion of the Law School Admission Test (LSAT). Really, I would have expected Einstein to make better use of his time.

If I remember correctly, there were a whole lot of these on the GRE, but I don't know about the LSAT.

(Of course there were a lot of these on the GRE. It was my highest scoring section and NONE of the grad schools I was looking at considered the score in admissions.
posted by kamikazegopher at 7:18 PM on August 4, 2005

Colonel Mustard, in the conservatory, with the lead pipe.

bashos_frog: Check your local bookstore for Dell Puzzles or other similar puzzle books. It's pretty easy to find big compilations of similar logic puzzles.
posted by sellout at 7:29 PM on August 4, 2005

It occurred to me that the solution might be different if you assume house #1 is on the right and house #5 on the left.

Nobody, unless I botched it up, it doesn't matter which end is "first."

Anyone care to verify?
posted by unperplex at 7:30 PM on August 4, 2005

The green house is on the left of the white house. If you reverse the house order you have to reverse this as well, right?
posted by swift at 7:35 PM on August 4, 2005

If you reverse the house order you have to reverse this as well, right?

No, the wording of the clues doesn't need to change, and you can pick either side as "the first house." (assuming my solution is right).

I was worried about clarifying that point, as it might be construed as an additional hint. But anyone clever enough to use that tidbit of information to aid in solving the puzzle could probably solve it in 10 seconds anyhow.
posted by unperplex at 7:48 PM on August 4, 2005

I remember doing problems like this in elementary school. Not with 14 constraints, but about five.

Anyway, as someone mentioned it's a CSP: Constraint Satisfaction problem. The algorithm to solve these is pretty straight forward, so if you can do 5 you can do 14.

Not that there would be any point in doing so.
posted by delmoi at 7:51 PM on August 4, 2005

Thanks, that was fun to solve.
posted by lundman at 7:58 PM on August 4, 2005

So would anyone care to explain how one systematically solves this sort of puzzle, or provide a link to someone who does? I successfully worked it out on a piece of scrap paper, but didn't employ any real methodology -- just started from what was known and went step by step to deduce more information. I did the LSAT section the same way, never having been Kaplan-trained or anything. (And didn't end up going to law school, but that had nothing to do with my LSAT score.) But I'm curious to find out how one is *supposed* to attack these.
posted by TonyRobots at 8:04 PM on August 4, 2005

My boyfriend teaches "Math for Survival" at an art school, and they do problems like this all the time. I'm still not sure why this is a survival issue, it's not like the fish will eat you if you get it wrong. Although that would certainly be motivation.
posted by ruby.aftermath at 8:08 PM on August 4, 2005

I'm curious to find out how one is *supposed* to attack these.

Any way that works, really, and for the LSATs it's any way you can get to work FAST. For puzzles like this, I usually draw a little picture and make little boxes with all my restrictions.

So you've got five "boxes", restricted by order, and each is filled with a five-segment box: color, nationality, drink, pet, cigar. Into each of these smaller squares goes a positive or negative asset [eg. must have tea, can't have dogs] which you can represent as little pictures/glyphs/letters. You have to be able to distinguish between MUST, MIGHT and CAN'T in assigning these attributes. You put as much as you know for sure into these boxes, both positive and negative. When you are done filling them in, see if you can draw any secondary deductions. For LSATs, this is usually where the answers lie. This is often something like "Oh Mr. Pink can't have the ferret because the ferret is next to the flamingo and Mr. Green is allergic to flamingos and lives next door....

When you have things that can move around "X is next to Y" you can write that on a rule list, that you can use for checking against your guesses, again pictorially.

XY/YX [x is next to y, on either side]
X _ _ Y [x is three doors down from Y]
X-Y [x is to the left of y]

Any time you are trying out a possible answer, you have to go down this list of conditionals and make sure they're met. Assuming the problem has a solution, this usuallyy draws it out. Sometimes you have to try a set of solutions to figure out what is impossible and, Sherlock Holmes style, the only non-impossible solution is the right one.
posted by jessamyn at 8:45 PM on August 4, 2005

Little slips of paper make it pretty easy to solve, except you have to spend all that time making little slips of paper. If you write the rule numbers on the referenced slips, or even the rules in shorthand, you can keep track of what constraints have to be satisfied.

What I wasn't certain of was whether "on the left of" meant the immediate left or any slot to the left. Would it be cheating to reveal whether one or both conditions were true in the solution?
posted by tss at 8:48 PM on August 4, 2005

TonyRobots, a google search for "logic problem grid solving" gave this as the first result.

And if you click the "interactive grid" button on this page you'll get to try it out without searching for graph paper or rulers.

You can see that how complicated one of these puzzles is has less to do with the number of constraints and more to do with the number of variables and how well-chosen the constraints are to avoid redundancy and delay a solution.

The "next to" clues made the "Who has the fish" puzzle more interesting.

A question: If unperplex is correct, do you think it was by design that a right-to-left house ordering doesn't interfere? It would be so easy for it to have done so -- if the original constraints had described a solution different by only one variable. . .
posted by nobody at 8:52 PM on August 4, 2005

On preview, jessamyn's method sounds like more fun.
posted by nobody at 8:54 PM on August 4, 2005

It is a most elusive fish. Oh fishy fishy, fish.
posted by davelog at 8:56 PM on August 4, 2005

I should clarify. Each slip is a property (e.g. "Yellow" or "Coffee"). The slips are arranged in a 5x5 table, where the columns are the house positions and the rows are the property types (nationality, house color, and so on).

Rules like 8 correspond to absolute, fixed entries in the table, so go ahead and stick those right in. Most of the other rules are only relative relations. They "clump" the slips together into fixed blobs: rule 1 means that the "British" and "Red" slips are forever linked. (Note that two "clumped" pieces can still have gaps between them!) The tricky ones are the ones like 11, since "next" could mean on the left or the right. There are two possible configurations for that clump.

Anyway, once you've got your slips clumped up according to the rules, you have to fit the shaped clumps together like in Tetris. The clumps with different possible configurations make this a little harder, but even in Tetris you have to rotate the pieces around, which is roughly the same thing.
posted by tss at 8:57 PM on August 4, 2005

(tss' method sounds like even more fun.)

The page I linked to doesn't quite do the grid method justice. A lot of the logic gets automated by the grid, without necessarily needing any further reference to the restraints.

Take this image, representing progress halfway through a more simple puzzle:

A dot (or checkmark or star or circle or whatever, indicating a known connection) in one section of the grid will generate more information in the other sections.

For instance, here the dot matching George to Erichsen (indicating a known connection) will translate the X (indicating a known non-connection) between Erichsen and Ash at the bottom into an X between George and Ash on the right (because if George is Erichsen, then anything true about one is true about the other). Placing that George/Ash X immediately lets you place a dot/star/checkmark one space below it matching Ash with Harvey (because there were no other available options for Ash in the upper right section of the grid).

There are a number of other sorts of commutations/translations, but it's more interesting to puzzle them out the first time you try it than to be told in boring, boring paragraphs of didactic, didactic prose.
posted by nobody at 9:19 PM on August 4, 2005

Speaking of Sherlock...
posted by mikeweeney at 9:52 PM on August 4, 2005

Yep, definately law-school-esque. I think I got it the first time through though, so apparantly the LSAT cramming helped for something.
posted by craven_morhead at 12:06 AM on August 5, 2005

if I looking for fish
him name is hopkin green fish
I Lost my fish
29-3228
Love, Terry
P.S. I'll find my fish
Who took my fish
Who found my fish
2012 15th AVE. S
posted by obiwanwasabi at 12:23 AM on August 5, 2005

I say the monty python version is more confounding.
posted by flagellum at 1:08 AM on August 5, 2005

Took me 3 minutes.

There is a very simple way to solve these things amost instantly. Just draw one 5x5 grid for house numbers across the top then characteristics along the side. Draw each relationship on a piece of paper as two nodes... the distance between the nodes should match the grid you've done. Cut them out... slot them in. A few nodes have fixed locations, some are relative, the rest just fit according to available spaces. It's almost totally visual and only takes a few seconds once you've cut out your pieces. It amounts to the same logic above but is totally obvious once you see it in front of you.

Perhaps Einstien assumed everyone would solve the puzzle his way...
posted by missbossy at 2:24 AM on August 5, 2005

Missbossy, I sort of understand your approach, but not really. Are your "nodes" different lenghths, or what? Is it any different then just checking the box, other than the ability to move things as needed?

Me, I guessed based on blind luck... hey, 20% odds aren't bad....

I was wrong.
posted by sdrawkcab at 6:25 AM on August 5, 2005

This is a joke, right? Like Delmoi and others, I was doing problems like this from grade 4 onwards.
posted by dirtynumbangelboy at 9:21 AM on August 5, 2005

This probably ranks as an "easy" logic game on the LSAT. (BTW, kamikazegopher, the GRE no longer has logic games, they replaced that section with an essay portion).
Anyway, it took me about 5 minutes to do. The spreadsheets and multiple pieces of paper methods seem to me to add excessive work to this problem.

I used one sheet of paper and just drew a few diagrams. Top of the page: 5 boxes, arranged horizontally, with 5 lines, to represent each house w/ slots for the entities that go in. Under that, a list of all the entities by category (color, pet, etc). Then a list of all the rules in shorthand, plus any rules that can be deduced from them; for example: Blends smoker next door to cats also means Blends smoker doesn't have cats. Then start plugging in entities according to the rules & deductions and crossing them off as they are eliminated. The set-up takes maybe 3 -4 minutes, depending on how quickly you read and write, but then plugging in everything takes maybe 2 min max.

And yeah, no way Einstein wrote this thing. As Snopes pointed out in a myth about a student embarrasing his teacher, Einstein's name just gets attached to anything in order to make it seem "really brilliant."
posted by papakwanz at 10:12 AM on August 5, 2005

Yeah, I remember when you could buy puzzle books stuffed with these kind of problems. Once you get a grid drawn out, it falls into place pretty quickly. Still pretty good fun, though... Sudoku leaves me cold however: it's the same principle reduced to a grid of full of digits.
posted by smiffy at 12:32 PM on August 5, 2005

sindark, that's funny, this is exactly why I loved taking the LSAT. "Hey, I'd do these for fun."

The "green house is left of the white house" is a terrible clue. If you assume it means "next door" then the puzzle is pretty easy; each constraint leads naturally to another. Otherwise, it's a bit maddening, not to mention allowing multiple solutions.

The "first house" garbage is actually easier to deal with, because it's clearly garbage.

Arrghh, nothing spoils a good logic puzzle better than sloppy instructions. Lazy, imprecise "logician" -- no cookie for you!
posted by bjrubble at 6:07 PM on August 5, 2005

Thanks for the link. I really enjoyed doing the puzzle.
posted by zia at 9:37 PM on August 5, 2005

bjrubble: it's actually "The green house is on the left of the white house" Still vague, but a little easier to interpret as immediately to the left.
As for "first house" I don't think it's a bad clue. It's an English language puzzle, so obviously it's going to go by English language conventions, meaning 1-5 goes left-right.

In fact, I'm trying to work it out interpreting the green-white rule in a more loose manner, and it doesn't work. If the Green house is immediately to the left of the white, they have to go...

(SPOILER)

In slots 4 & 5. That's critical to solving the puzzle. If you assume that Green can be anywhere to the left of White, then ...

(Another SPOILER)
Green has to be in 1, but White can go in 3, 4, or 5. You don't have enough info to make enough deductions and actually solve it.
posted by papakwanz at 10:21 AM on August 6, 2005

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