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Crossword blog: three-dimensional cryptic crosswords

Alan Connor has his mind fried by Eric Westbrook, who devises 3D crosswords with clues by Guardian setters
Crossword blog: three-dimensional crosswords
One of Eric Westbrook's three-dimensional crosswords

I suppose someone was always going to do it.

Consider Dr Ferdinand Maack, a 19th-century German eccentric who decided that chess was (a) insufficiently difficult and (b) insufficiently like warfare, so added a third dimension and devised "Raumschach", not unlike the tri-dimensional chess they play on the USS Enterprise.

And consider that the same Star Trek game was parodied in the cartoon Futurama, where you can see Professor Farnsworth and Leela playing three-dimensional Scrabble, and that back in the real world, many enthusiasts have patented efforts at a 3D word-based board game.

It shouldn't come as too much of a surprise, then, to learn that our world contains 3D crosswords. Or that the man who devises them is registered blind - I mean, sure. Why not?

Eric Westbrook describes his puzzles as resembling blocks of flats. As you stand in one of the apartments, a word may be spelled out going away from you, to your side, or down through the space vertically below. They are surprisingly easy to get used to. But why does Eric - whose day job is teaching - do it?

Because he's as much of a visionary as Dr Maack. But why else? Well, his puzzles come in the form of a calendar which raises funds for the RNIB Pears Centre in Coventry and Children in Need.

Crossword blog: a three-dimensional crossword by Eric Westbrook

Eric constructs each grid and fills it with words, then hands over the cluing to charitable setters including the Guardian's Arachne, Lavatch, Pasquale, and Rufus as well as Everyman. Araucaria has written an introduction to the 3D crossword website as well as clues, Enigmatist has provided enigmatic support as well as clues and, Eric says, "we may have had the privilege of Taupi's last crossword - he sent the final revisions to his 2010 puzzle the night before he died."

So far so familiar, but what I want to ask is: what's it like being in the middle of an abstract three-dimensional grid fill? "It can be quite a tussle," says Eric. "There's no computer software to construct 3D puzzles. Being registered blind, pencil and paper are not very useful." So he assembles these blocks of flats in his head.

"Day after day, you get close to fitting all the words but you have impossible blanks that even the Urban Dictionary will not solve. If only, you say to youself, a group of dissolute youths in a downtown LA bar had said 'ZXYZZ' just once one afternoon. So then you just have to take down the 3D house brick by brick and build it up differently."

What makes these puzzles harder for setters, though, makes them easier for solvers: since the words cross each other in more ways than usual, you get more quickly to the point where you're working off knowing some of the letters in the answer.

Eric describes the following as "an impossible clue", written by Enigmatist and Jane Teather...

Romans 2 – Venetians 1 (3,5,7,3,5,)

...but one that becomes much easier once you have some of those abundant checking letters (see the bottom of this post).

Embracing this topsy-turvy world, and being nosy, I ask if blindness helps the process of construction.

"In a slightly odd way, yes. It helps not to have distractions so that you can really focus and concentrate. It also encourages you to use your mind in imaginative ways. It's surprising what you can do if you really want to do it. There seems to be no end to what the brain can remember."

The building analogy applies here too. "I bet you could walk around your house blindfolded, no problem. You know it inside out. I walk around three-dimensional grids until I know them inside out and all the letters are in their places. It's not quick - but it's certainly easier than doing a school timetable."

Blind solvers are catered for with various alternatives to the physical calendar: for the 2010 crosswords, the clues were available in audio form, read by some Radio 4 presenters, as well as in size-adjustable word tables and screen-reader-friendly format. "But," adds Eric, "this is not good enough! Where do you put the answers? So we have launched a £1,000 competition for someone to write a program that allows a totally blind solver comfortable access to our puzzles."

Crossword blog: a three-dimensional crossword by Eric Westbrook

Blind or sighted, solving the puzzles can feel like wandering around a real building or playing a multi-platform computer game. You can get pleasurably stuck in the basement, then help yourself up to another level using the elevator of a down clue. When you return to a mainstream two-dimensional crossword, that experience too has an abstract, giddying feel. From lines to flat surfaces to blocks and back again, the obvious question is: has Eric considered a fourth dimension? How about five?

"Yes and yes," says Eric. Of course. Eric describes his experiments in "polydimensional crosswords, which you don't see (how could you?) but you do experience the results. The 'grid' is formed of any number of inter-relating word lists. Relationships between checking letters are dealt with electronically."

"We assume a one-to-one correspondence between checking letters of crossing solutions. But what if they did not correspond one-to-one, but did so by some other pre-determined set of relationships? Then it all works. But not on paper."

My mind starts to imagine a line of cubes, where answers can be read across the corresponding position in each cube as well as away, across and down within each block. But why stop at a line of cubes? Why not a two-dimensional collection? Or a cube of cubes... and so on? Eric, you won't be surprised to hear, has been talking to the good people from CERN about how many dimensions are allowed by quantum mechanics.

For the moment, though, we have our simple 3D crosswords. If you're tempted, there are prizes for solving each of the puzzles in the 2012 calendar, and the first deadline approaches. And the checking letters for "Romans 2 – Venetians 1" are "T_E _L_N_ L_A_I_G _H_ B_I_D".

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Feb 2012