Wikipedia:Reference desk/Archives/Mathematics/2010 August 23

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August 23

Logic puzzles

Complete grid, without copyright problems

Hi. I recently came across some logic puzzles in my textbook. I don't have the book with me now, but I'll try to describe them. They are the kind where there are 4 cats, each with his own toy, sleeping space, age, and name. Then you get some clues like "Rocky doesn't like the 10 year old cat" or "The cat that sleeps on the floor doesn't play with the rubber mouse", and others. Then you have to match the cat to the sleeping spot to the age to the toy (the things like name/age/sleeping spot/toy change between problems of this kind, of course). I'm told there's an algebraic way to solve this kind of problem, but how? 76.228.196.92 (talk) 01:02, 23 August 2010 (UTC)

You can often make a list of the relations and then use a resolution-like procedure to look for a satisfying assignment. 67.122.209.167 (talk) 02:02, 23 August 2010 (UTC)

See Logic puzzle#Logic grid puzzles and Logic-Grid Brain Teasers. -- 114.128.212.28 (talk) 06:17, 23 August 2010 (UTC)

I'm sorry that no one else has responded, as I was hoping someone would provide a link to instructions on using the grid. I've run across these a few times on standardized tests, and each time I've improvised a solution, taking more time than I feel is appropriate. I've not known how the typical small grids are supposed to help; with the one illustrating Logic puzzle#Logic grid puzzles, I know what to do when told that Nikolas doesn't like champagne, but not if told that the person who likes feta doesn't like champagne. -- ToE^T 12:06, 24 August 2010 (UTC)

You could try [1] which has tutorials on how to use the grid and how to solve it. --Salix (talk): 12:37, 24 August 2010 (UTC)

Thanks Salix. Interestingly, it uses the very same grid that appears in our article. Despite the instructions saying, "The grid allows you to cross-reference every possible option in every category.", I still don't see what to do with that truncated grid if told that the person who likes feta doesn't like champagne. The first full puzzle it offered me included not a truncated grid, but a full block triangular grid with n(n-1)/2 blocks (for n attributes), giving nC2 blocks. There I understand what to do! -- ToE^T 17:01, 24 August 2010 (UTC)

Looks like the grid has been truncated for display purposes. The real grid would have three large box on the top row, two on the second and one in a third row. This would give space to add the feta/champagne info. You need the full grid to be able to solve the puzzle. It might be an idea to change the picture, and there is a chance it might be a copyright violation.--Salix (talk): 18:59, 24 August 2010 (UTC)

Hmm. I've seen truncated grids before (containing n-1 blocks so that all attributes are shown, but not all correlations) that I thought were intended for use, but perhaps they too were only for illustration. Regarding the copyright issue of the image, the uploader has properly revealed the source for all three puzzle images they have uploaded, but also claims to be the copyright holder. The three websites are related, so it is possible that the uploader runs the sites. As the uploader has not been active in a year and a half, is the proper action to contact the site? -- 1.47.203.216 (talk) 00:40, 25 August 2010 (UTC)

I've now made a complete grid which is all my own work so no copyright problems. A slight simpler 4x4 puzzle.--Salix (talk): 09:10, 25 August 2010 (UTC)

That looks really good. Thanks. -- ToE^T 12:05, 25 August 2010 (UTC)

The Cantor Cube

Hi, I try to understand the Cantor cube and something is missing. If I understand correctly, it is a topological group. Does anybody know what is the topology defined on it? I mean, It's said that it is the product topology. But what is the topology defined on each coordinate. I mean, Suppose that our space is $\{0,1\}^{\mathbb {N} }$, then do we take the discrete topology on $\{0,1\}$? and if we do, isn't the product topology simply the discrete topology? Which seems not logical to me because then it would be more or less like saying almost nothing on this group would't it? Can someone maybe describe the open sets? Thanks! Topologia clalit (talk) 06:57, 23 August 2010 (UTC)

No, the product topology is not the discrete topology. The box topology would be the discrete topology. The product topology is different because the rectangles that serve as basic open sets must have all but finitely many factors equal to the whole space. --Trovatore (talk) 06:59, 23 August 2010 (UTC)

I hope I get what you mean.. Do you mean that an open set is determind by a finite number of coordinates? for example, is the set $\{(a_{1},a_{2},a_{3},...):a_{1}=1\}$ open in $\{0,1\}^{\mathbb {N} }$? —Preceding unsigned comment added by Topologia clalit (talk • contribs) 09:45, 23 August 2010 (UTC) Topologia clalit (talk) 09:47, 23 August 2010 (UTC)

Right. --Trovatore (talk) 09:50, 23 August 2010 (UTC)

Thanks! Topologia clalit (talk) 10:16, 23 August 2010 (UTC)

An open set is a union of sets of that kind. Michael Hardy (talk) 02:05, 25 August 2010 (UTC)

PhD in Math

Hi guys. Apologies for my previous bad behaviour. I've understood what I've done wrong and put my word that it won't happen again. I'll be a nice bloke from now on ...

My question is about a PhD in math. I'm looking to get a PhD in math. I've just completed my undergrad. and I'm looking to do a PhD somewhere in the States. But I've heard about the so-called qualifying exams the no.1 nightmare for math PhD students. I've heard that they're notoriously hard, very time constrained, and you like need to know everything imaginable in a number of very unrelated fields in math.

So how are these qualifying exams really? What sorts of topics do they cover? I've seen a couple from some pretty top tier places, and they look pretty hard to me so how are they in general? Feel free to comment even if you haven't particpited in one cause they're probably similar things in Aus, UK and other countries. My question is like: Which University has the easiest quals.? How do I strike a balance between good university and easy wuals? And lastly, how do I choose a university where the quals. don't require so much math background. Thanks guys ... —Preceding unsigned comment added by 110.20.55.3 (talk) 08:17, 23 August 2010 (UTC) , 23 August 2010 (UTC)

Qualifying exams at a good research university are not easy, but they're probably the easiest phase of your PhD studies. The hard part is the original research. The quals are there to make sure you have enough background to be successful at research. Having the background is usually a necessary condition, but not at all sufficient.

So basically I think you should forget looking for a school with easy quals. Look for one with potential advisors who do stuff you think is interesting. It's not going to advantage you much if you sail through the qualifying exams, but then can't find anyone who can guide you into a productive line of research. --Trovatore (talk) 08:32, 23 August 2010 (UTC)

Thanks for the inspiring answer Trevor! Much appreciated mate. But I'm still kind of scratching my head with the quals. Yeah I definitely agree I should go where there're lots of good mathematicians who like the same things I like. But what are the quals. exactly? What kind of animals are they? :) I mean an example: [2]. And UChicago requires you know this much math! [3]. It's seems to much for an average guy like me. But I've heard if I don't go to these places (or similar top tier places) for my phD I'll never get jobs anywhere unless my thesis is spectacular, because the guys who offer jobs look at where you've got PhD from: two guys with the same quality thesis, one from Harvard, one from some country village university, even if they've done similarly spectacular work, the Harvard guy will get the thumbs up. Is this true in the math community? I see you've got a PhD so you'll probably be an expert on these matters. How have you found it when it comes to getting jobs? —Preceding unsigned comment added by 110.20.55.3 (talk) 08:45, 23 August 2010 (UTC)

The job market in academic math is hard. No sugar-coating that. If an academic job is your aim, you need to understand that you have set yourself a difficult goal. To me that means, if you get into a place like Chicago (with sufficient support to live on), go there and work as hard as you need to. (I'm not saying I always did that; it's what I should have done. :-)

As to how hiring committees work, I've really never been on that side of it, so I can't say how they judge based on the quality of the school, but a school with a good name will certainly not hurt, and the better school might get better work out of you in the first place. Also, and I hesitate to mention this because there's an argument for not thinking too much about your safety net, if you don't make it all the way through, a Master's from Chicago is better than a Master's from a no-name. And if you do get the PhD but don't get a tenure-track job, you'll get more interviews in industry if your PhD says Chicago on it. --Trovatore (talk) 08:58, 23 August 2010 (UTC)

(Edit Conflict) I would say that the qualifying exams offered at Harvard are by far the easiest among many similar ranked universities. Here "easy" is the measure of the "difficulty" of the exams. Clearly you need to have a relatively broad background in mathematics to be able to answer these questions but trust me, once you have that background the exams will look far, far easier. There is no need to panic just yet if you have recently completed your undergraduate education. In fact, typically the first two years in graduate school is spent to prepare for these qualifying exams so you will have plenty of time to learn the necessary background material. (Some students who already have most of the required background generally sit the exam earlier - but this is not mandatory and generally with some universities you can take the qualifying exam multiple times.)

I am not sure what you mean by "country village university" but I can assure you that if your PhD thesis is of a very high quality, it should not matter from where you have obtained your PhD. (But of course, as Trovatore (his name is not "Trevor"!) mentioned, you should look for universities where there are people with similar interests to yours.) In any case, doing your PhD at Harvard (for example) will not have any value unless it is of a high quality.

And please do not be under the impression that Harvard and Chicago are the only places for mathematics! There are so many other places with excellent mathematicians and you should consider your options carefully. In particular, there are certain areas in mathematics in which you might wish to pursue a PhD, for which Harvard is not the best place. However, if you are interested in topology/geometry or representation theory I would strongly recommend Harvard. PST 09:08, 23 August 2010 (UTC)

(edit conflict) In addition to what Trovatore said, you should keep in mind that grad schools at the PhD level generally want their students to do well. I can't speak to math directly, but my experience in physics was the following. Quals consisted of four parts, two 3-hour written exams and two 1.5-hour oral exams. Each part was scored independently, and any part could be repeated up to three times. Only about 25% of students passed all four parts on the first try. Hence nearly everyone repeated at least one exam, and many people repeated more than one. After the first not passing grade, the department generally required students to take supplemental coursework in the area(s) they were weak. (The department wants to help you pass, even though the whole process can feel like torture.) In most cases (perhaps 80%), the second attempt was successful. In part this was because the faculty are more lenient on second attempts. A borderline effort the first time tends to fail, but a similar effort the second or third time will tend to pass. In the few cases where individuals did fail round two, a significant fraction decided not to continue trying to get a PhD. By the time someone has taken the quals at least twice they have already had a significant amount of coursework and an opportunity to consider research specialties and career prospects. I suspect that many of the people who left after a second failed qual had reached the conclusion that they wouldn't be competitive in an academic marketplace and decided they were better off spending their time elsewhere. In general though, don't despair. The entire process is a giant pain in the ass, but most people will make it through, and the department wants to help their students succeed. Dragons flight (talk) 09:12, 23 August 2010 (UTC)

One thing you should do before you pick one is make sure that "most people" do indeed make it through in the program. This was not the case where I did my PhD, and doesn't make for a great environment. Staecker (talk) 14:15, 23 August 2010 (UTC)

Looking at those exam questions from Harvard, I have to agree with PST. They aren't that hard at all. Once you know the definitions of the objects then you are almost at a solution. Although, it makes me wonder about the point of them. If you have just finished a postgraduate course with many lectures on many subjects then you will easily pass those exams; especially if you can repeat multiple times! But how many research fellows have all of that material at their finger tips? How many people, after ten years of specialised research, could pass those exams without studying again? They want to check that you're a Jack of all trades when, indeed, you may be master of none. I understand that they need a way to filter their candidates, but this doesn't seem to be an ideal way of doing. Take as a hypothetical example, which I know is extreme, a candidate may have an insane topological intuition and may have published 10 papers. But because they have concentrated soley on topology, they will never pass the Qualification Exams and they will never be accepted to do a PhD. — Fly by Night (talk) 15:00, 23 August 2010 (UTC)

There was a (true) story I once heard of a mathematician - she specialized in von Neumann algebras but when her advisor gave her a paper on the cohomology of the Lie algebra of vector fields on a manifold, she could not read it because she did not know what "cohomology" was, what a "Lie algebra" was, what a "vector field" was, or what a "manifold" was!

Harvard wants to make sure that this does not happen to students. Not everyone who does a PhD at Harvard goes on to research multiple areas of mathematics, of course, but there are a select few students who do benefit from these qualifying exams. It is also true that intuitions from other branches of mathematics are sometimes very helpful when one does research - of course, as Fly by Night says, Harvard primarily tests whether you know the definitions. (For example, if you know what an Artinian ring is, how can one not be able to prove that it has finitely many maximal ideals?!)

I agree with you Fly by Night - I have known some very, very specialized researchers who have done excellent work in their fields while having only a very narrow knowledge. But there are some areas which are highly connected to the qualifying exam topics. The topics that one is required to know for the general Harvard qualifying exams are algebra, algebraic geometry, algebraic topology, complex analysis, differential geometry, and real analysis. (More information can be found here.) In actual fact, if one researches number theory, algebraic geometry, or PDE's one may need each and every one of these topics at one's fingertips. And many people tend to go into one of these three areas. (Although many do not as well.)

Also bear in mind that what goes on in Harvard is "secret" to the "outside world". One does not need to "directly" pass these qualifying exams. For example, if you are able to pass a course in say, differential geometry, and obtain a satisfactory grade, you may be excused from sitting the qualifying exam in differential geometry. And of course, this is Harvard! They expect hard work from you in your first two years of graduate study (this is time when one prepares for the qualifying exams), but even harder work from you after this during your original research. But on the whole I agree with you Fly by Night - ultimately most people see these qualifying exams as an annoyance and unless one actually wants to dish out the books and study them on one's own, one will never be able to get an appreciation of other branches of mathematics. Qualifying exams force one to learn - but that is no where near as effective as learning out of one's own interest. PST 23:09, 23 August 2010 (UTC)

PST, when you said "There is no need to panic just yet if you have recently completed your undergraduate education. In fact, typically the first two years in graduate school is spent to prepare for these qualifying exams so you will have plenty of time to learn the necessary background material" Do you mean you take the quals after 3years in grad school? I thought these quals are meant for undergrads trying to apply for a phd position. Please tell me I thought wrong... I don't understand how life works after undergraduate can someone explain it to me?Money is tight (talk) 02:51, 24 August 2010 (UTC)

What I meant was that a student is typically expected to pass the qualifying exams within the first two years of graduate school. (I should have been more clear.) This is, of course, for a top graduate schools such as Harvard or Chicago. Other schools may give additional time to a student to pass the qualifying exams.

If you are an undergraduate student, in which year are you currently? There are so many pathways one can take after undergraduate studies so it is difficult to give a "hard and fast rule" as to how life works after undergraduate. If you plan to go to graduate school, you typically would have to apply to several graduate schools. Once you get into a good graduate school (which hopefully you should!) you would then have to pass certain requirements to do a PhD. One requirement is, of course, the qualifying exam - as I said, if you have a broad background in mathematics already, you should usually be allowed to sit the qualifying exams as soon as you enter graduate schools. (And you should not worry about passing - there is usually no stigma associated to taking the qualifying exams several times.) Another requirement is that you should be able to read, to a reasonable extent, mathematics in one or two of several other languages. (German, French, Russian and Italian, for example, are the standard choices.) There are other requirements as well - for example, teaching requirements. Perhaps you should read about it yourself since I could go on for several pages about this ... One link for Harvard's requirements is this. But you should research other schools as well.

One point that I should elaborate on is your application to graduate schools. There are so many points one could talk about, but the most important factors are: good grades, the GRE (Graduate Records Examination) mathematics subject test, the general GRE, letters of recommendation, a strong statement of intent etc. (Some of these factors are more of a formality that a practical requirement if you ask me. You can do quality research in mathematics without being able to get a strong score on the general GRE. But rules are rules - I do not make them; I state them!) The most important thing (or, one of the most important things) that graduate schools want to see is that you have attempted to take "hard mathematics courses". Usually applicants to top graduate schools are serious - they have everything: good scores, good grades etc. The best way to separate the "good from the bad" is to see what courses they have taken. E.g., if you take a 4th year course while still in your second year, that would be very useful for your application. (Provided you get a good grade!) Ideally, you should be taking graduate level courses in your 4th year at the latest. Also try to take a variety of courses from several different areas of mathematics - that shows graduate schools that you have a "back-up plan" in case something went wrong with doing the area of mathematics you originally wanted to do.

Hope that helps! PST 03:47, 24 August 2010 (UTC)

It's worth noting that this is how the American system works. It's not the same in the UK. I imagine it's different in the rest of Europe too. Not to mention Russia and Asia; although I don't really know about the last two. — Fly by Night (talk) 19:16, 25 August 2010 (UTC)

Convex subnetwork?

Let "network" mean "undirected weighted graph with positive edge weights". Given such a network N, is there a specific term for a subnetwork S in N such that for any two vertices in S, the distance between them in S is equal to the distance between them in N? This of course meaning that it is not beneficial to leave S when trying to travel between the vertices, it seems both reasonable and quite natural to call S a "convex subnetwork", but I haven't found any references. Maybe I'm searching for the wrong thing, or maybe the concept is so unfruitful that it's not in use? 85.226.207.22 (talk) 15:24, 23 August 2010 (UTC)

"Isometric subgraph" seems to be fairly standard. Algebraist 17:26, 23 August 2010 (UTC)

Ah, thanks. To be sure, I mostly find uses related to unweighted graphs, but the concept above certainly is a natural generalization of that (an unweighted graph is just a weighted graphs with all weights 1, right?), so it seems fine to use the same term. 85.226.206.72 (talk) 05:46, 26 August 2010 (UTC)

Magicicada lovers...

Ok, I'm not entirely sure how to pose this question: I'm writing a science fantasy story - it's a strange love triangle: three characters, two are in love, the third wants to murder the man so he can have the woman. But this is the thing: they're populations of magicicadas, or creatures inspired by them - usually living beneath the ground, rising at set intervals, at which times they can interact. What I guess I would like from you guys is a set of three numbers - the periods at which the three characters rise from the ground - that brings about an interesting interaction between the three characters. So let's say the hero male rises after the passage of every M number of years, the female after F number of years, the villain every V years - it'd be nice if V works out so it touches M before it touches F, because the villain wants to kill the male before he gets to the female; but maybe the male and the female have worked it out so they can join forces to destroy the villain at some point....

Sorry - floundering here - told you I was having trouble posing the question. I'm hoping someone might find the question fun enough to play with...

Thanks for your forebearance.

Adambrowne666 (talk) 20:25, 23 August 2010 (UTC)

The cicadas choose (or evolve) a large prime number so that they don't interact with their predators, of course. You presumably want regular interactions, so why not choose the first three prime numbers: say M = 2 ; F = 3 ; V = 5. This will give an interaction between M & F after 6 years for the romance, between M & V after 10 years for possible killing, M & F again after 12 years if M survives, V & F after 15 years for V to claim F, but leaves a twist after 18 years when a surviving M can meet F again, but another chance for V to kill M after 20 years, another romantic reunion between M & F after 24 years, and a final denouement after 30 years when they will all meet. How complex is your plot? Dbfirs 21:32, 23 August 2010 (UTC)

Good answer well expressed, thank you. Although primes are great, and I hate to seem an ingrate, they've been a bit overdone in sf - does anything else recommend itself? Still, I like the plot you've set out; it's a nice satisfying backbone - but it could go more baroque - longer, weirder - I'm open to imaginary numbers, square root of negative-one, that sort of thing... Adambrowne666 (talk) 11:37, 24 August 2010 (UTC)

Coprimes would be slightly less obvious than primes. 93.95.251.162 (talk) 15:34, 24 August 2010 (UTC) Martin.

Well you could use Quaternions, but they are not used for counting years in the real world! Dbfirs 07:41, 25 August 2010 (UTC)

Ooh. I like quaternions. I don't understand the first thing about the first thing about them. How confident are you with them? Could you give me a sequence like the one you did for primes? Or on second thoughts, maybe not... Reading articles like this one make me realise how little I know about maths. Stuff they were doing 300 years ago is completely opaque to me. Completely. How about just imaginary numbers then? Could you maybe help me work out a sequence? I could credit you if/when the story's published (just about everything I write ends up being published in semi-pro magazines).... Thanks for the coprimes suggestion too, Martin. Adambrowne666 (talk) 05:29, 26 August 2010 (UTC)

We do have an article on Imaginary time, but my imagination fails me on how to bring this into a story that uses real time as perceived by normal people in the real world. I can't see how to map time that flows in two (or more) dimensions into the real world. Does anyone else have any ideas? Perhaps we should ask Stephen Hawking!

Ah, but remember, this isn't 'real time as perceived by normal people in the real world' - this is an ultraweird sf story. If you can come up with a sequence as you did with the primes, I reckon I can get it to work in the context, which only touches but lightly on the real. I say go for it! Hit me with something bizarre!

Puzzles

Do all puzzles need logic for their solution? Is there some subset of puzzles depending on some other method for solution? The question arises from the WP Category:Puzzles that lists a subcategory of Logic puzzles, which by implication suggests that there are puzzles solved by some other means. 196.30.31.182 (talk) 20:47, 23 August 2010 (UTC)

Puzzles that can be solved by the systematic application of an algorithm are often called logical puzzles. Other puzzles rely mainly on prior knowledge for their solution, and yet others require "lateral thinking". Many puzzles require a combination of methods. Dbfirs 20:55, 23 August 2010 (UTC)

Could you give examples of each? —Preceding unsigned comment added by Androstachys (talk • contribs)

Hi anon 196.30.31.182, it happens that there was a mildly interesting chat related to this at Category talk:Logic puzzles, Talk:String girdling Earth and Category Talk:Puzzles, where the previous contributor (Androstachys) insists that the string puzzle belongs in the category Logic Puzzles because matematics, and therefore logic is needed to solve it, and beacause mathematics and logic "are virtually synonymous", whereas to me it is clear that this is a mathematics puzzle or a geometry puzzle at most, and by no means a logic puzzle. DVdm (talk) 06:59, 24 August 2010 (UTC)

If you read my contributions with more care you'll see that I feel that no puzzle can be solved without using logic, which is why I think that the category Logic puzzles is belabouring the point. Subcategorising Puzzles into Logic puzzles I think "is looking for a bright-line distinction that simply does not exist". I was hoping to keep you out of this discussion in order to get some unbiased opinions about the matter. Androstachys (talk) 12:58, 24 August 2010 (UTC)

Ha, you were hoping to keep me out of this discussion. I thought this was a genuine question by an anonymous user. Sorry for having blown your cover, and of course for having disturbed the 'discussion' with my biased opinions. DVdm (talk) 13:30, 24 August 2010 (UTC)

It seems to me that 196.30.31.182/Androstachys is looking for a bright-line distinction that simply does not exist. In its most restrictive sense, the term logic puzzle refers to a partricular type of puzzle in which logical deductions are made from a set of given statements. Other types of puzzle, such as sudoku, can also be solved using logic and so could be loosely described as "logic puzzles" too - this seems to be the sense in which the term is used in Category:Logic puzzles. However, a crossword is clearly not a logic puzzle (in either sense), as it requires lateral thinking ratrher than logic; crosswords and similar puzzles are grouped in the category Category:Word puzzles. Gandalf61 (talk) 09:19, 24 August 2010 (UTC)

I think most crossword puzzlers would take issue with the idea that they do not use logic in their solutions. Perhaps I have a broader view of logic that feels that lateral thinking, like any other form of thinking, decidedly involves logic. Androstachys (talk) 13:03, 24 August 2010 (UTC)

Nonsense. To take a famous example, there is no process of logical deduction (in the accepted sense of the word) that can take you from the clue "Gegs (9,4)" to its solution. The majority of cryptic crossword clues are language-dependent, using puns, homophones, anagrams and abbreviations. Logic puzzles, on the other hand, are largely language-independent and are easily translated form one language to another. Your definition of "logic" as "any form of thinking" is absurd - for example, where is the logic behind the thought "I like bananas" ? In particular, our article on lateral thinking defines its as "reasoning that is not immediately obvious and about ideas that may not be obtainable by using only traditional step-by-step logic.". Gandalf61 (talk) 13:30, 24 August 2010 (UTC)

It seems to me that the problem is that Androstachys interprets the term "logic puzzle" as a puzzle whose solution, among other things, also needs logic, whereas the usual meaning is that it is a puzzle which can be solved using only logic. This is not helped by the fact that typically this "logic" needs to be interpreted in a very broad sense encompassing at least combinatorics, hence a "combinatorial puzzle" or "mathematical puzzle" would be a more appropriate description.—Emil J. 13:51, 24 August 2010 (UTC)

That is why I feel that the word "only" should be added to the category description of [[Category:Logic puzzles]] again. See Category talk:Logic puzzles. Thanks for this 3rd opinion. DVdm (talk) 14:00, 24 August 2010 (UTC)

The claim that logic is required to solve all puzzles is flawed. Consider a jigsaw puzzle. You can randomly try to place the jigsaw pieces on a table until you see the proper picture. No logic was required. Logic would help, but it is not required. Consider a common knot-puzzle (where you have to undo some knot of string/metal). You can just wiggle the thing around until, eventually, they come apart. No logic needed, but logic would help. Consider a crossword puzzle. You can write random words into the boxes. Then, see if those words match the clues. If not, erase and try again. No logic required. When it comes to a logic puzzle, it is possible to give an answer without using logic, but logic is required to check the answer. In the jigsaw puzzle, checking the solution simply requires looking at the picture. In the knot-puzzle, count how many separate parts there are. If there are two, you are done. In the crossword puzzle, you must check every answer in the puzzle against every clue. If the answer doesn't match the clue, try again. This is language, not logic. For a logic puzzle, you must form a logical proof to show your answer is correct. -- kainaw™ 14:02, 24 August 2010 (UTC)

I absolutely reject the counter-argument: Everything in existence may be defined with math and all of math may be defined with logic, so everything is logic, so all puzzles are logic puzzles. -- kainaw™ 14:03, 24 August 2010 (UTC)

Solving a jigsaw puzzle is not a job that you could easily give to a robot. Fitting the pieces together calls for judgement and reasoning. If the robot worked randomly it would - eventually - come up with the solution, just as a computer putting words together at random would eventually come up with "War and Peace" and not know when it had done so. Any reasoning or thinking of necessity involves logic or a rational approach. Androstachys (talk) 16:31, 24 August 2010 (UTC)

If it were pure logic, Eternity II puzzle would have been solved. Kittybrewster ☎ 16:50, 24 August 2010 (UTC)

What sort of logic is that? All logical problems or puzzles capable of solution would have been solved by now? There are very many unsolved and insoluble problems in maths and physics. Ouch, my stomach hurts...

My Chambers' defines logic as "the science and art of reasoning correctly" and the Oxford "...the application of science or the art of reasoning...". Some Wikipedians obviously have different views on the meaning of logic. Androstachys (talk) 19:01, 24 August 2010 (UTC)

Either I wasn't clear or you ignored my point... A logic puzzle requires logic to check the solution. What logic is required to look at a jigsaw puzzle and say, "Yep, that looks right"? -- kainaw™ 23:59, 24 August 2010 (UTC)

The same logic that will tell you that the Eternity puzzle has been solved - the jigsaw puzzle is just a simpler version. Androstachys (talk) 07:06, 25 August 2010 (UTC)

Yes, perhaps I should have written (in my original reply) that a "logic puzzle" is one that can be solved by the systematic application of an algorithm that is not just "trial and error". Perhaps there is no clear distinction? Alfred Jules Ayer and Edward de Bono were friends, but stopped discussing anything related to logic because they couldn't even begin to agree. Ayre insisted on digging deeper and deeper, whilst de Bono kept looking for new places to dig. Dbfirs 07:20, 26 August 2010 (UTC)