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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.
Just write it like you would a 3D tic-tac-toe... but it's impossible to make it large enough to be like a traditional crossword; using some kind of centerfoldish fold out-solution you sould be able to make it atleast 10x10x10, though.
IMHO that'd be large enough to be interesting, esp. since the reader has to think in 3D to solve it.
perl -e'print$_{$_} for sort%_=`lynx -dump svanstrom.com/t`'
You could always span the z-axis across multiple pages. Of course it would be a bit of a mindfuck to have to flick between pages, but it would be interesting at least.
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.
...I would publish the crossword on multiple pages. It would have to have a rather small side (like 10x10 or maybe 12x12), and have one layer on every page. This kinda assumes that there are 10-12 pages in the paper to begin with (and that you can have the same placement on every page, eg upper-right on odd-numbered pages), or you could have a centerfold with a DIY 3D X-word.
Wouldn't it be hard to construct though? I imagine having software to help with the construction would be nice.
Yes, I am a biological organism. All rumors to the contrary are just that, rumors.
Crossword puzzles are not pragmatically two-dimensional. They are two-dimensional because paper is.
If you really want to do this, write some little 3D app in Java or Flash and put the link in place of the puzzle. The app would have each space represented by a box, and the user could spin and zoom and click on boxes to type in a letter.
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.
You should try to divide each cell in maybe nine sub-cells (3x3) that would be the third dimension. So a word in the 3rd dimension would be written like that :
SLA L** A**
SHD *** ***
OT* *** ***
L**
***
***
If possible, a color code would give the z index for each sub-cell, in order to help visually.
Perspective view. +45/+45/+45 degrees, right distance, you'll see a lot of cubes, each one is one letter.
It's better to be the foot on the boot than the face on the pavement. ~~ tkx Kadin2048
Could someone explain the concept of 4d shapes and crosswords to me in simple terminology. Thank you :)
Give out the grid in the first edition of next year and then give out the clues a few clues "over time" in the following editions.
:)
That should stretch a 2d puzzle into 3d and not make it complicated
---- The geek shall inherit the Earth.
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.
A 3-dimentional matrix, in this case the crossword puzzle, is just a stack of 2 dimensional matrices.
So, just print each slice, as well as a diagram showing how the slices are fit together.
For clarity you should fill in a few example answers so that people can see how responses across each of the dimensions work.
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.
Well, my alma mater charged each student a fee per credit hour that funded the student paper, in addition to advertising.
is it that bad seein a hot chick again? if i see a hot chick walkin down the hall i dont say "repost"
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.
First there are all the variants on cryptic crosswords. See The Atlantic Monthly for some very nice ones (and some very tough ones). If you look around a bit Stephen Sondheim (yup, the guy who writes Broadway Musicals) also published a book of fun (and challenging crosswords).
Then there are cross number puzzles - there are some simple ones, but I'm thinking of one like this . It is fairly small but very fun to solve. (This would probably be of most interest in a school with a distinct science/math orientation.)
I've thought a couple of times about building a crossword that would translate letters into differently colored squares (using only a couple of colors and simple patterns) so that the correctly solved problem would make a picture but ended up trying to find a fun program that would take a completed crossword and an image and find a decent mapping to make the crossword look like the image. (There are some interesting ways to fiddle this idea - the checked lights might only match in shape/color,letters might map to multiple shapes, you might have to determine the mapping of letters to shapes (perhaps matching lines/colors in adjacent squares as clues) ....)
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...
Just make it how you would try it at first, like a perspective drawing (Just a normal xyz plane), but for the added axis, make it intersect the traditional plane of the crossword puzzle with a curve. I hope this is clear enough, but it probably isn't.
I hate grammar Nazi's.
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!
If you are doing a real 3-D crossword, presumably you would visualize say a 10 x 10 x 10 puzzle as a stack of layers, each layer of which has 100 cubes (you have to write a letter into each little cube), obviously if you write 2 dimensionally this means you would want to write on a piece of paper lodged in the bottom of the layer, or maybe floating halfway through the layer. 4-D puzzles are maybe going to give you 4-D letter boxes I guess, which when you project them onto paper will be extremely difficult to make out, not only will they be skewed in shape but maybe invisible depending on the projection angle..
Anyway let:s just talk about 3D crosswords. If it is a cube with a 10x10 crossword on each face you could of course just make a cube that looks like that, and forget the interior. It could be handled as origami, just publish something you need to fold into a cube.
Other amazing origami shapes can allow you to print something on paper or web but require 3D procedures to solve, for example two halves of a word meet up on a mountain fold, etc.
Also there are some hyper-aspects which are really just 3D, but you can make a chinese fortune cookie origami which we used to make as kids, that you can open and close, and lift up tabs to see what is underneath. Possibly making one of these with two or more differently cut sheets of paper could allow you to provide instructions that require the user to lift up the second sheaf under the tab you see when you solve another crossword question.
There are also software methods for visualizing n-dimensions, but probably the easiest would be a straightforward rotatable, zoomable display of a transparent cube. I suppose you will need a lot of black boxes (make them maybe a light green transparent color so you can see through them) but you can still make rows that start and end deep inside the cube.
There is also a well known puzzle, the Rubik's cube you know. Puzzles that require mechanical rotation are another possibility.
Thank you for pointing that out!! I was just looking for this problem among the replies.
reason defies logic
However, if one relaxes the keying constraint, 3D puzzles *are* possible. The way I got around it was by *requiring* the words in my 3D puzzles to have only *2* of the 3 dimensions keyed. Every white cube was in at least 2 words, and *possibly* 3. A word *could* be 3D-keyed but it wasn't required. This made it possible to create a *pseudo*3D puzzle which actually could be solved. Unless you looked very carefully, you would think you were solving an *actual* 3D puzzle.
As to representation: I had 3 directions: Across, Down, Through. So I could rotate the puzzle (it was inside a computer) and display it 3 different ways. Obviously, if the three dimensions were A,D, and T, the total number of 2D crosswords contained in the 3D puzzle was A+D+T. (A D*T + D A*T + T A*D.)
The creation difficulty of the puzzle was figured by adding up the keying score for every white cube and dividing by the number of white cubes in the puzzle. If the average score was at or near 3, the puzzle was virtually impossible to create. 2.5 was about the limit to be able to create decent "3D" crosswords; that is, half of the white boxes had a score of 3 and half had a score of 2. That was still pretty hard though. 2.3 ones (of 3 white cubes, 2 were 2Dkeyed and 1 was 3D keyed) were -- comparatively -- easy.
A useful algorithm I developed was called "slabs". Little 2D slabs (X*Y*1) were connected at the corners to other 2D slabs; the corner cube where the connection was made was the only 3Dkeyed piece then. The results looked more like 3D diagramless puzzles than traditional crosswords.
DNA is a Turing machine. You, however, being dynamic and emergent, are not.
and find a bunch, including:
. ht ml
. ht ml
http://www.drking.plus.com/hexagons/words/hexxw
http://www.drking.plus.com/hexagons/words/index