Listen With Others

 
[eXtent is a collaboration between eXternal and Serpent, each of whom contributes [below]. Ed.]
 
 
[eXternal] Serpent agreed to collaborate on a puzzle with me in 2016. I had an idea for a theme, but I couldn’t work out how to implement it successfully as a puzzle. The puzzle we eventually produced turned out to be quite complex and we decided to submit it to The Listener, using the pseudonym eXtent. It remained in the queue for some time.

I had a conversation with Roger Phillips at last year’s Listener dinner in Paris (March 2018) regarding that puzzle, which had come up for vetting. Roger had some reservations about it, so I offered to withdraw it and supply a replacement. We talked a little about his chrysanthemum-themed puzzle and he mentioned that he would welcome more puzzles using non-standard grids. That conversation was the inspiration which would lead to Doing the Rounds.

Back in England, I let Serpent know what had happened and he was happy for me to suggest an alternative puzzle. To look for potential ‘grids’, I simply did a Google Images search for something like ‘geometric patterns’ or similar. I found the design of ‘The Flower Of Life’ pattern, which seemed to offer possibilities for a fill with cross-checking of entries. Once I realised that the twelve letters of FLOWER OF LIFE could be entered in the 12 cells of an inner circle, I was certain there was potential for a puzzle. I identified that entries could run in straight lines through the lenticular cells and that these could be checked by using the rings of six cells around each circle as entries. The inner cells of the circle could contain 12-letter words, providing cross-checking from overlapping circles, the rings of 6-letter entries and the straight entries.

I printed a few copies of the design to try some manual grid-fills, just to get an idea as to whether it looked possible to completely fill the design in the way that I had envisaged. Pretty much straight away, I knew that the 12-letter answers would need to be entered as jumbles, as a grid-fill with clockwise/anti-clockwise entries would be impossible. However, a central clockwise entry for FLOWER OF LIFE looked appealing and would provide a base from which solvers could work outwards towards the edges of the grid. I thought that the solver would need to fill in the framework from the straight entries and six-letter rings, thereby providing six checking letters for each of the twelve-letter jumbles. I proceeded with a manual grid-fill on this basis, using QAT to offer alternatives for the 12-letter jumbles as I worked outwards. It went surprisingly well and I became more confident that a fill would be possible. I filled about half the grid manually, but knew that we’d need help from a computer to get beyond that stage. Unfortunately, I had no idea how to replicate the design in Qxw (which is the application that I and Serpent always use). Fortunately, I knew Serpent is more adept at this sort of thing than I am, so I contacted him with the proposed puzzle.
 
 
[Serpent] I was very enthusiastic about the grid design and set to work with Qxw. I first had to represent the Flower of Life (FoL) grid in such a way that I could use Qxw, which involved associating each cell in the FoL grid with a number. These numbers were then used to index the cells in a standard rectangular grid. (I was pleasantly surprised to discover the FoL grid contained 144 cells.) The next stage was to define the ‘entries’ in the Qxw grid. Obviously none of the rows and columns (or subdivisions thereof) defined entries in the FoL grid, so I had to encode all the entries in the FoL grid using Qxw’s free light facility.

That, however, was not the end of the story. eXternal pointed out that some 12-letter entries contained two unchecked cells. Given that these entries had to be entered jumbled, I also had to ensure the grid-fill was unambiguous. The inclusion of more free lights (one for each pair of unchecked cells) and the use of a dictionary containing all 26 strings of repeated pairs of letters ensured that the 12-letter entries could be entered without ambiguity (although see below).

eXternal and I try, as far as is feasible, to use relatively familiar words as entries in our puzzles. To this end, I use a fairly restricted dictionary when first attempting to find a grid-fill. However, the constraints imposed on the grid and the existence of so many 12-letter words meant that no fill was possible using entries from this dictionary. The next step was to use my restricted dictionary for shorter entries and a much larger dictionary for the 12-letter words. Still no fill was possible, although Qxw did at least think about it for much longer before deciding! Thereafter it was a matter of confirming that a fill existed and then trying to limit the number of obscurities, especially in the shorter entries because these were to be defined using a single word. (It turned out that there were several entries that we were unable to define with a single word. Reluctantly, we extended the hidden definitions to two words for some entries.) Nevertheless, eXternal and I were very happy with the grid-fill and set to work on the clues. We were ready to submit the puzzle by early May 2018.
 
 
[eXternal] I heard from Roger in January that the puzzle had been accepted for publication. The main changes were to rotate the grid for a better fit on the page, addition of numbers for ease of reference and some tweaks to preamble and clues. Roger also identified that the fill was ambiguous, if the solver did not follow the premise that unchecked cells within the same circle should both contain the same letter. He changed our original entry of MENSTRUATION to METATHEORIES to avoid this.

Feedback from solvers was very positive on the whole. Solvers seemed to appreciate the novel design and gained a great deal of satisfaction from the fill, albeit with a lot of effort!

And finally, thanks to our test-solvers: David, Norman and Paul (Apt).