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Multidimensional Crosswords?
Aaron asks: "I write the crossword for the student newspaper at my university (McGill, in Montreal). For the last issue of the year I like to go all-out and do something special. Usually I just make a super-big one, but I had a brainstorm - a crossword is essentially a 2-dimensional matrix where set intersections are judged as valid if they test positive as real words out of a dictionary. Of course, the decision to limit the matrix to 2 dimensions is just pragmatic so if you wanted you could make crosswords of 3 or more dimensions (though a 4-dimension crossword might have to be done in pencil first). Any ideas on how to actually do this?" This would be interesting on a computer, but would be fairly hard to do in print. If you were of a mind to make a 3D crossword puzzle on paper, how would you do it?
If you were of a mind to make a 3D crossword puzzle on paper, how would you do it?
Popup pictures or fold-ins, and until XP SP2 comes out, IE users will have no choice but to solve them.
Ok, no joke, the paper they use for bibles is extraordinarily thin and sturdy, gotta do the pad idea to stack the pages on top of each other instead of on completely discreet full pages to allow the person quick reference across levels. You wouldn't have to add more than even half a dozen layers to the Z axis to make is horribly complicated (even thought the connecting words would of course be limited to that length). Simply print the pad and glue it in...of course the answers would have to be posted similarly...and all of that adds up to an expensive crossword.
0D crossword clues:
Indefinite aricle
Personal pronoun
Dangerous programming language
Not F
Presidential nickname
The latest Slashdot meme.
Forget 3d, it would be too difficult to make and most people wouldn't be able to wrap their tiny little brains around how it works. Make a hexagon-based crossword instead. This gives you 3 directions (vertical, down/left, and up/left), gives you the added complication of 3 possible clues per intersection, and will easily fit on a single page of paper. You'll have to come up with a hexagonal grid, but that's not too difficult. There should be plenty of vector-based hex grids on the web.
I'm a journalism student with some layout experience, so I'm fairly sure I know what I'm talking about here.
It's a neat concept, but kind of silly when you think about it. Print is, by nature, a two-dimensional medium. I've seen two solutions already mentioned here, making the crossword much smaller or spreading it across multiple pages.
The way I envision it, a three-dimensional crossword would have to be shrunk down a lot to be able to fit in the usual space a 2d crossword occupies, which just makes it inefficient. Besides, a 3d crossword isn't going to be much different from a 2d crossword after being flattened for print.
If you were to try and span it out over several pages, you would probably piss your editors off, who likely don't want what is usually a small diversion occupying precious ad space.
vi ~/.emacs
You would have to setup a java app,in order to pull it off.
Just remember your words have to be 3D as well. Each letter would be part of three different words. Even a small cross word will be extremely complex. Even 10x10x10 will be 1000 squares. Now Each word has to intersect with 2 other words at each point. a word like mom would have 6 interconnecting words needed to go with it. And each of those six will have an equally exponential number of words that they interact with.
Have you really thought the depth of this out? it seems a large task to setup.
By the way if you manage to pull it off, send me the link I would love to try it.
i thought once I was found, but it was only a dream.
I was goofing around for a school published magazine. I made a 4D crossword by making a 3D crossword with clues for "Morning", "Afternoon" and "Evening". I solved the display problem by making it very simple, I think about 30 clues for each time point. Then I exploded the crossword 3D model, printing 1 vertical row stretching back in 3D, with pull out text boxes with the clue number. The horizontal clues extruded from the surface, and I worked it out so they didn't occlude clue boxes too much behind, and the "other side" was printed just below.
It's hard to explain, a diagram would make it pretty obvious. There were 3 verticals printed across the page. I couldn't create a 4D crossword you could actually write clues in, so they had to list the answers in a boring list below.
I'm a pretty neat writer so it came out fine, but the photocopies were not perfect. The generation of the clues was an arduous task as I had to do it three times for the different time periods.
Advice for creating the 3d grid initially- lego blocks are your friend. The whole thing took several nights effort, but got quite a laugh, most people thought I was taking the piss. Not sure if anyone actually completed it, but as an intellectual exercise, I enjoyed it.
Meine Schwester ist sehr, sehr reizvoll - Nietzsche
Depending on which interpretation of dimensional you use, a matrix is either always 2 dimensional, or varying the dimension(s) isn't what you want. A tensor is the mathematical object that includes scalars, vectors, matrices, and beyond.
implementation on paper depends on the rules of the game
do you require only simple linear three-d words (e.g. just words on x & y, OR y & z, OR x & z) or are words that function in all three dimensions permitted (i.e. diagonal through the cube)?
if you DISALLOW diagonals, then you could do it (simply) with five (or whatever) crossword grids on a single page, and color code the various dimensions (like 6 down green, 8 across red, etc...)
the obvious difficulty would be that the instructions on how to work it would take up far too much space on the page!
perhaps the short answer is the sad one: since paper is a 2d medium, a 3d crossword puzzle ON PAPER is far more difficult than one would hope, once you take into account the end user
however, there's no reasons you couldn't do it in a medium that alows 3-d modeling, and rotation, and all that good stuff we've come to expect from our little glowing boxes... a web implementation would certainly be fun, and would require FAR less instruction, becuase the 3D nature of the thing would be clearly modeled in the display
it would certainly be fun to see how those solid black boxes work out in the 3d version
This might make it too easy, but at least it won't require unusual spatial reasoning skills just to figure out the clues...
Post a link to slashdot when you're done -- I want to see it!
Am I part of the core demographic for Swedish Fish?
Creating a traditional crossword in a cube, there are a huge number of constraints to be put on each cube, but also a large number of crosswords themselves: The 10^3 crossword requires a stack of ten crosswords of 10x10 each, top to bottom, forward to back, and left to right. That's 30 crossword puzzles you're devising, each one constrained by all the planes not paralleling it.
Perhaps a cube with only the faces showing, so that only the beginnings and ends of words (at the edges and corners) interconnect? That's only six crossword puzzles, and much fewer constraints. The layout could be an unfolded cube, say six puzzles laid out in a latin cross, with perhaps the disconnected edges connected by dashes or another color if your press has it.
Another idea would be to make a much sparser matrix, say twenty words, and drawing only the cubes that contained the letters, like an abstract spatial sculpture or scaffolding. I would put it in a slightly skewed orthogonal perspective, select one face (say, the top), and draw its edges in a heavier or darker line than the other edges. In creating it, I would concentrate on making words intersect like a tree, rather than making sheets of densely packed words.
He was a verray parfit gentil knight.
if your going to do something extravagant, swipe the entire center fold.
i would say that a crossword of normal x,y dimensions would work (though this depends on space and what your norm is... just play with it) the z would be maybe 5 deep (again, playing with this can help.
now. you have the centerfold. start in the bottom left corner place you x,y matrix for z1 (if it were a cube this would be the front side) now, move up and to your right, place your x,y matrix for z2. continure until finished.
you should have a diagonal line of boxes, this leaves the other two corners for hints.
now, on a numbering scheme. lets say for example on the z1 x,y matrix you have a 1 down and a one across AND a one 'spanning' (for lack of a better word). On z2, you also have a one down, a one across, and the previous one spanning.
now, to number these a few ways come to mind. one would be to color code each Z matrix and match the clues to them. another would be to just number the squares normaly for z1 and then normaly on z2, except starting on the ending number for z3.
coming up with the words themselves would blow my mind.
explaining it shouldn't be that hard, and in the space on the corners you could do it.
I would assume that the smaller your dimensions the less mind blowing.
if you do get this working you'll have to hook me up with a link.
face the world with eyes of fire.
Here's one resource, Constructing Isometric Grid Paper, A Computer Aid, but you can buy it at places that sell engineering drawing type supplies. Or at least you used to be able to. I would start at the bottom in the middle and darken in the edges to show which blocks are to be filled in. One problem with this is that you are kind of limited in complexity. If it's too complicated it will be tough to tell what is going on. Even if its pretty simple there are still going to be points at which clues overlap, and that is going to make it hard to understand. I like the idea that someone else had of using hex paper, I think that would be easier to do.
You could draw a cube and see three of its face; would "feel" 3-D to most people, but without the limitations of paper. I gimped a little sketch that explains the idea.
In case you are not aware, Claude Shannon adressed the issue of 3-D crossword puzzles in "The Mathematical Theory of Communication". I quote:
The redundancy of a language is related to the existence of crossword puzzles. If the redundancy is zero any sequence of letters is a reasonable text in the language and any two-dimensional array of letters forms a crossword puzzle. If the redundancy is too high the language imposes too many constraints for large crossword puzzles to be possible. A more detailed analysis shows that if we assume the constraints imposed by the language are of a rather chaotic and random nature, large crossword puzzles are just possible when the redundancy is 50%. If the redundancy is 33%, three-dimensional crossword puzzles should be possible, etc.
Since he also claims that the redundancy of English is 50% (in other places, he claims it is even higher), it appears that the father of information theory has decided that you will not be able to pull off a 3-D crossword puzzle. To me, that sounds like a great reason to try and do it. Not many people sucessfully prove Claude Shannon wrong, even indirectly.
Of course, if you do create a 3-D crossword puzzle, you should call it a 11-D puzzle, and claim that all the other dimensions are curled up very small. If some of the smartest people in the world can get away with that, you should be able to also.
It could be easier...maybe.
Think about solving two clues that intersect on a 2D crossword. You have to find two words that fit the clues that share a common letter at the point where they intersect - right?
One of the things that makes crosswords harder is when there are multiple possible solutions for each clue - and the only way to find which is the right one is by co-solving the two clues. However, it might be that even then there are multiple pairs of words that fit the clues and satisfy the common-letter constraint. In that case, you have to look at another word or words that shares a common letter with one of the two clues. This could lead you off into solving MANY more clues just in order to get those first two words right.
Well, in a 3D crossword (presuming there are locations where THREE clues intersect), there would be fewer sets of THREE words solutions that satisfy the constraints at each intersection than there are TWO word solutions in a 2D crossword.
However, this is definitely a bit of a stretch. I don't think a nicely presented 3D crossword would be much different from a 2D one - the hardest part of hard crosswords is finding answers that fit the clues - and that doesn't change when you go to 3D.
www.sjbaker.org
In crosswords, the "dimensions" don't necessarily have to be orthogonal. It is permissible to create several coplanar vectors (called "directions" instead of "dimensions") that intersect at various angles. For instance you could use squares (two directions), hexagons (three directions), octagons (four directions), and so on. The closest to what you were asking for would be hexagonal shapes with words moving "down", "up-across", and "down-across".
If your three word vectors must be orthogonal, I have seen sparse 3D crosswords drawn in 2D in perspective. They were sparse to allow the reader to solve words that would otherwise be occluded by a dense crossword. A dense orthogonal 3D crossword could be represented in many slices of a traditional 2D crossword.
Michael.
Linux : Mac
This would be interesting on a computer, but would be fairly hard to do in print.
That was my thought too, and there are lots of examples of 3d crosswords online (try Google; for example this). If you have the wherewithal to code it yourself, or if you find a plugin you can use -- I'd say make your puzzle available online, then in the newspaper just put an intriguing screenshot and a link (tinyurl?) that readers can visit to try solving it.
Think outside the box, eh?
There are only 10 types of people: those who understand decimal, those who don't, and, uh, 8 other types I forget.
Wayne White's 3d word art
.
. hmmm
If you write the Daily's crossword, I tip my hat to you. Doing it has saved me from many a boring class (and cleared my head after too long studying). A nice mixture between easy and obscure.
If you do the Trib's, I got nothing. I haven't seriously opened a Trib in a semester.
Cue The Sun...
A 4X4 grid is probably the most common square that is easily and totally filled with answers. In this example, clues x1,x2,x3, and x4 intersect in a valid way with y1,y2,y3, and y4. The next step is to build in a z-level. There are now at least 16 new clues to be written, and if the crossword is to have any difficulty at all, it must be at least 3 deep, as no self-respecting crossword writer uses two-letter words. Building the z-layer is what's really difficult, since as the above author who mentioned the recurrence problem realizes, English doesn't allow for many combinations of valid words that work in 3 dimensions. One begins to be limited to 4-letter palindromes, which in English are quickly exhausted.
The solution, I believe, is to make effective and strategic use of blocker squares. Many of the above authors assumed that a crossword of any size must be filled entirely with answers. This is erroneous, but also makes for a rather boring intellectual exercise.
Some caveats. In standard crosswords, clues for all available dimensions - namely, x and y - are provided for in the Across and Down heading to which we are usually accustomed. A true 3-space crossword would have horizontal and vertical clues for each z-layer. This is a neccesary service for the player, since the possiblity exists that in a puzzle with, for example, only Across, Down, and "Through" headings leaves intersections with no clues. For a crossword to be solvable, it's a good idea for each word to have as many clues as there are dimensional axes.
Lastly, on how to visualize dimensions greater than three: consider a 3 dimensional model of our own universe that you might build at home. Take two toothpicks and align them at right angles, standing vertically, the one lying on a table, and the other standing straight up. Now, take a third toothpick and align it at right angles from its horizontal and vertical brethren. Voila! A three-dimensional universe, albeit with no negative quadrants. Now, take the model you've constructed and place it on a railroad track. The left and right motion is analogous to time, as an object can retain its x,y, and z positions whilst still moving forward and back in another. To imagine more dimensions, just build more tracks, and stack them on top of each other crosswise. Hence, a visualized infinity of range of motion.
Feel free to correct my meanderings.
When I grow up, I'm going to Bovine University!