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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?
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.
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 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
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.
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.
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
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...