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?

Comments

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.

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.

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: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-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.

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, 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.