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?

Popups

[Micro$will]

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.

3D tic-tac-toe

[svanstrom]

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.

Re:3D tic-tac-toe

[grammar nazi]

The reader would have to think in 3D, but it would be easier. Each letter would be the intersection of 3 words rather than 2 words. You would have one additional clue for each letter, hence it would be easier.

The only hard part would be visualization of a 3D or 4D matrix on a 2D sheet of paper. IMO, crossword enthusists would rather focus on *crossword* skills rather than 3D visualization skills, so higher-D puzzles would fail to catch on.

If you are just interested in creating a challenging crossword puzz

Re:3D tic-tac-toe

[Bob Cat - NYMPHS]

0D crossword clues:

Indefinite aricle
Personal pronoun
Dangerous programming language
Not F
Presidential nickname

Re:3D tic-tac-toe

[Alpha27]

I don't see how the crossword would be easier? It's one thing if you have to compare rows and columns, but to now compare against a 3rd dimension adds a level of compleixity to the crossword game not seen before that the crosswords would take long.

As for putting it on paper, I feel would be a mistake. People would have a very difficult time visualizing the game in 3D if you could find a way to properly display it on 2D. I could only see this being accomplished successfully in an environment suitable for 3D

Re:3D tic-tac-toe

[sbaker]

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-l

Inserted Pad - using "bible" paper

[Capt.Gingi]

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 simila

To make 3D work...

[Ibn al-Hazardous]

...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.

Forget 3d

[UberGeeb]

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.

Don't

[jcenters]

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.

Don't flatten it.

[hummassa]

Perspective view. +45/+45/+45 degrees, right distance, you'll see a lot of cubes, each one is one letter.

Re:Don't

[omega9]

That's right. Fuck creativity, you're all about the money.

Re:Don't

[sweede]

you do know that someone has to pay for the paper to be printed and if its a long run (> 5,000) with more than 4 pages, then it will cost a LOT of money to be printed.

I doubt that the school charges a fee for the paper so they must get funds from yes, evil advertising.

OT: Other Option

[sithkhan]

Well, my alma mater charged each student a fee per credit hour that funded the student paper, in addition to advertising.

Re:Don't

[jcenters]

Oh yeah, it's all about the money baby! That's the only reason we go into journalism, for that big, fat $20,000 salary.

Like the other replier said, newspapers costs a lot of money to print. If it weren't for advertising, we'd either have to charge for it or take it from the University's budget, which would then be taken out of the students' ass.

The reason I'm a journalist is because I want to write. Unless you're a Bob Woodward or a Stephen King, you'll barely make enough to pay the bills in this busin

Interseting but to complex for most people

[peragrin]

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.

Re:Interseting but to complex for most people

[theyenk]

what about if you used time as the 3'rd dimension. So that you would erase parts of words/letters(X) then fill in those spots from other directions. createing new 2D words....so you create different words at different times Could even take it to the next level, where you kept track of all the words you spelt. And that then was then part of another word puzzle. Maybe even just sneak that last part in with the kids word problem that is like that, if ur paper is like mine...could be your hidden level. But a

Re:Interseting but to complex for most people

[mabhatter654]

make the puzzle 3d with "steps" that the puzzle transforms as you step thru time!!! You'd have to have some sort of alpha-blending to "streak" the time direction, but it could be really cool!!

MOD PARENT UP!!

[Gamasta]

Thank you for pointing that out!! I was just looking for this problem among the replies.

I had a similar idea

[SimianOverlord]

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.

2 dimensional matrix?

[5E-0W2]

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.

it depends

[conJunk]

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

make the third dimension small

[pedantic bore]

One way to accomplish this would make the third dimension "small", occupied only by short words. So instead of a 20x20x20 space, you'd only have a 20x20x4 space. Then you could print the four 20x20 layers next to each other on the same page.

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!

Re:make the third dimension small

[HTH NE1]

Indeed, I saw this approach for a 4-dimensional 3x3x3x3 maze once. Travel between adjacent mazes was only possible if the square you were in in one matched the color of the square in an adjacent maze. (A crossword though wouldn't need to deal with color matching, which was just a way to implement the walls of the maze. A crossword would use colored squares only as a pan-dimensional crutch.)

Another problem is the terminology. Down and across is fine for 2-D, but how do you group the clues that span acro

Alternatives

[baruz]

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.

Color and centerfold

[Gleapsite]

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 s

3rd dimension inside each cell

[Sidoine]

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.

4d?

[Arc04]

Could someone explain the concept of 4d shapes and crosswords to me in simple terminology. Thank you :)

Re:4d?

[Zocalo]

First you take a standard, two dimensional, crossword. Then you stack a bunch of other 2D crosswords underneath it so that there are also some clues that run vertically down through two or more of the stacked pages. You now have a 3D crossword. Finally, since the fourth dimension is "time", you change all the clues and answers if the poor bastard doing the crossword can't solve it quickly enough... :)

Re:4d?

[Michael.Forman]

In crosswords, the "dimensions" don't necessarily have to be orthogonal. For instance to do a 3D crossword puzzle, hexagonal boxes will allow one to make words in three directions, "down", "up-across", and "down-across". To make a "4-dimensional" crossword you could stack several slices of these hexagonal structures or even migrate to octagons.

Michael. [michael-forman.com]

Re:4d?

[mabhatter654]

I like the idea of a computer based crossword where the 4th dimension was time. then the "scafolding" would change shape at each "keyframe". Trying to describe it is actually harder than just making a picture! Actually it would be really intuative for crossword gurus... If it's 3D modeled, then you can rotate it for traditional 2-d views...it'd be a cool novelty

Reorder the dimensions

[CaptCanuk]

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 :)

I would probably use Isometric Grid Paper

[jefeweiss]

Here's one resource, Constructing Isometric Grid Paper, A Computer Aid [unleash.com], 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.

Re:I would probably use Isometric Grid Paper

[sweede]

in our drafting class we had to draw isomeric objects on paper, it was NOT fun or easy. a simple 12 point object could have over 3 times as many points in the final image.

Fake 3-D?

[ptaff]

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 [ptaff.ca] that explains the idea.

Simple, just slice the cube

[StatFiend]

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.

Obey Your Father

[dont_think_twice]

In case you are not aware, Claude Shannon adressed the issue of 3-D crossword puzzles in "The Mathematical Theory of Communication" [216.239.51.104]. 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 [superstringtheory.com] can get away with that, you should be able to also.

Re:Obey Your Father

[Dachannien]

It sounds as if Shannon is assuming that crossword puzzles are always fully packed (that is, in a 10x10 grid, every word is 10 letters long), or at least close to it. If you take a crossword puzzle like the normal ones the New York Times or TV Guide publish, then yes, you will likely be overconstrained by the number of consecutive letters that have to fit into the puzzle in 3, instead of 2, directions.

Other crossword puzzle types are more sparsely populated, with words crossing in a fashion more like in S

Re:Obey Your Father

[krysith]

Parent post is quite correct.

Please Mod parent up, Insightful. I used all my mod points yesterday.

Use Coplanar Vectors

[Michael.Forman]

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. [michael-forman.com]

SImple -- just print a link

[jtheory]

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 [bloxword.ca]). 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?

Flashy Crosswords

[jefu]

While the idea of a 3d crossword is intriguing, it seems like it would be very complicated and tough to work out - both for the compiler and the solver. There are some other fun things you could do that would end up with interesting crosswords and still fit nicely in two dimensions.

First there are all the variants on cryptic crosswords. See The Atlantic Monthly [theatlantic.com] 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

something like this

[quiddity]

Wayne White's 3d word art [waxy.org]

McGill Crosswords

[BSDevil]

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.

Do the obvious with slight change...

[NemosomeN]

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.

Paper or No Paper?

[Awenner]

When I thought up the challenge, I never really considered a functioning "on-paper" implementation. It would be just too hard to fill out. That said, sometimes when I'm without a pen I like to scan crosswords and do them mentally, and I trust that those with a higher spacial-reasoning capacity than myself would be able to do the same to a crossword that was never designed to be done otherwise.

A 4X4 grid is probably the most common square that is easily and totally filled with answers. In this example, clu

actual display issues in n-d puzzles

[mattr]

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

Relaxing the Keying Constraint

[Randym]

The technical term for the intersection of 2 words is called "keying". As one poster pointed out, Claude Shannon put the kibosh on *true* 3D crosswords by pointing out the connection between the redundancy of English and the subsequent inability to create 3D crosswords in English. (Although it *is* possible to create *very tiny* true 3D crosswords.)

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