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Listener 4176, Small But Perfectly Formed: A Setter’s Blog by Quinapalus

Posted by Listen With Others on 3 March 2012

Like laws and sausages, perhaps most people would rather not know how crosswords are made. But I find other setters’ accounts of how they go about making their puzzles fascinating reading, and I hope other setters and solvers will find something of interest here.

I had been thinking about constructing a three-dimensional puzzle for a while. There are two inherent problems with this idea.

The first problem is that the final grid needs to have at most about two hundred cells (roughly the same as a 14-by-14 square grid), and preferably rather less. That means that even a 6-by-6-by-6 cube is too big. A maximum answer length of 6 letters is not very satisfying for the solver (and writing clues for short words is dull for the setter), and so some trick is needed to fit longer answers in the grid.

I played with having lights entered along non-straight paths, but I couldn’t find a neat way to integrate this with a theme. I tried and failed to find a way to steal—by which I of course mean adapt—the entry method used in Law’s excellent ‘A Three Pipe Problem’ (Listener 3009), one of the first puzzles in the series I ever attempted.

I also experimented with having lights, not necessarily parallel to the axes of the cuboid, running off one side of the grid and reappearing on the other: like a torus, but with one extra dimension. This could be fun, especially if the sides of the cuboid are coprime, say 4, 5 and 7. However, I didn’t fancy the prospect of explaining the entry method (especially the ‘corner cases’) clearly in the preamble. Maybe I’ll keep that idea for another time, or perhaps someone else can ‘adapt’ it.

Finally I settled on the idea of breaking answers into two parts to be entered separately in the grid. With a 4-by-5-by-6 grid I could have six-letter answers entered directly and nine-letter answers broken into four-letter parts and five-letter parts. I could present the grid diagram in four layers, each a 5-by-6 rectangle. Although 120 cells is on the small side for a Listener crossword, it did mean that there was plenty of space to label the layers and still have the diagram fit neatly into a square region as preferred by the vetters.

Then I trawled the Oxford Dictionary of Quotations for something vaguely apt. Often rectangular grids have quotations around the perimeter, so why not do the analogous thing? The King Lear line was a gift, and when the title of the puzzle occurred to me I knew I had a theme. The phrase always makes me smile and think of Morecambe and Wise, but it seems to predate them rather. Simon Cauchi says in LINGUIST List 10.1861

The earliest use I can find of the phrase is in a letter written by Duff Cooper to his future wife Lady Diana Manners in October 1914:

‘‘I really did enjoy Belvoir you know … You must I think have enjoyed it too, with your two stout lovers frowning at one another across the hearth rug, while your small, but perfectly formed one kept the party in a roar.’’

which raises more questions than it answers.

The second problem with a three-dimensional grid is that it is necessary to find a way to deal with triple-checking (a cell being at the intersection of three lights). It seems that even a small amount of triple-checking can make it very hard to find a grid fill. So either I needed to find a way to avoid triple-checking in the first place, or I needed to get some freedom from elsewhere.

Resisting the temptation to have every entry jumbled (which would win a lot of freedom in filling the grid but also the disapproval of many seasoned solvers!), I decided to allow entries to run in either direction. Allowing nine-letter answers to break as 4+5 or 5+4 gave me even more freedom. It was easy enough to tell solvers in which direction the various lights and partial lights run using the clue numbering and by writing ‘(4+5)’ or ‘(5+4)’ instead of (9) after the relevant clues. I didn’t see much merit in withholding this information, and it meant that essentially no ‘cold solving’ was required. Some more freedom came from allowing the quotation to start in an arbitrary perimeter cell.

Would I now have enough freedom to make a satisfactory grid fill possible?

[At this point the story takes a turn of which I’m sure some setters will disapprove. Those of a sensitive disposition might wish to look away now.]

I went over to the computer to find out.

The first job was to decide which six-, five- and four-letter lines through the grid would contain (partial) entries. It was important to keep this number to a minimum to reduce the amount of triple-checking, while nevertheless making sure that there was adequate normal checking. Although there may well be a pure mathematical way to find a good solution to this problem, I took the lazy engineer’s approach and set the question up as a satisfiability problem and got PicoSAT to generate lots of candidates at random. From these I picked a few that looked promising.

From the results it seemed that I was going to have twelve to fourteen six-letter lights. ‘My shape as true’, from the line after the perimeter quotation, is thirteen letters long and fits the title nicely. Could I hide that as a message from the clues, using a gimmick such as ‘Letters Latent’? If I allowed the clues to come in any order (I hoped solvers wouldn’t notice, or at least if they did notice they wouldn’t object too much) it might even give me a bit more freedom in the fill. Using ‘Letters Latent’ also had the advantage of increasing the average answer length.

I fed a few plausible-looking grids into a slightly modified version of Qxw’s grid-fill algorithm, with a specially-constructed dictionary to allow for the possibility of nine-letter words breaking as 4+5 or as 5+4. The first grids I tried proved impossible to fill. This was rather disheartening, but with a bit more perseverance, and a few minor tweaks to the grid-generating process, I eventually got the computer to start making candidate fills.

Many computer-hours later I had a fill that met all the requirements and which used a reasonably interesting and clueable set of words. Then it was a simple job of writing the clues.

I find clue-writing a very slow process. I force myself to go through the lights in order, writing something that I think is at least sound for each word before going on to the next. (Otherwise I might pick off the most interesting words first and be left with the depressing sight of the dross at the end.) Then a few rounds of revision to make some of the less inspired examples a little less bad, followed by sending out invitations to a couple of test solvers. To my relief their reaction was on the whole positive. With their suggested improvements incorporated, I sent the puzzle off to the first vetter and crossed my fingers.

Several exchanges of e-mails and improvements to the puzzle later, it was, to my delight, accepted.

It was pleasing to see some positive feedback shortly after publication on The Site That Must Not Be Named, Let Alone Linked To. I was glad that solving the puzzle had given encouragement to some relative newcomers to the Listener series. The main criticism people had seemed to be that they had found the puzzle a bit on the easy side: I shall see what I can do to remedy that in my next effort!

I would like to thank the test solvers for their generous giving of time and suggestions; the vetters for their work on polishing the preamble and keeping the clues on the straight and narrow; and everyone who sent their comments on the puzzle after publication.

Quinapalus

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