Some months later I decided it was, so I watched the scene in question a few times and made sure I fully understood the plot and characters involved. I also read up on the film itself and discovered the link with Battleship Potemkin, of which I was previously unaware. Obviously the grid would have to have a staircase represented in some manner, and my first idea was that both films should be involved with the solver having to make the correct choice after resolving some ambiguity. Eventually I decided this wouldn’t work, partly because it was too complicated but also because I wanted to mirror as closely as possible the preamble to One-Taker which required a ‘15-letter film title’, though I still wanted to reference Battleship Potemkin in some way.

A bit of doodling on a blank grid gave me the 3-D idea for the staircase which would require some drawing instructions. ‘EN’ was demanded by One-Taker’s preamble (‘with the star of the film represented by two clashing letters’), and double-letter cells also seemed a useful entry method for the baby and pram (conveniently the same length); using single squares for each letter would make the pram too big. This would need to fall down the steps, so clashes in the original positions and double letters in the final positions might work.

Around this point I started to consider the other three main characters from the scene (George Stone, Bowtie and the bookkeeper) and noticed the coincidence of ‘one’ and ‘two’ appearing in ‘Stone’ and ‘Bowtie’ (albeit backwards in the latter). Given the title (which was currently ‘Two-taker’), this was too good not to use, so ‘Stone’ and ‘Bowtie’ would appear as full names (given by overlong answers and multiple clashes), allowing the critical dialogue (“One…”, “Two!”) to be represented. The bookkeeper would have to be ‘WP’ (Walter Payne).

At some stage I remembered that at least one foreign (Indian?) word in Chambers was defined as ‘untouchables’, and a search yielded Burakumin, Dalit and Harijan (all in Chambers and Bradford’s). Although my original idea was to embed one of these in the grid somehow, I noticed that ‘Burakumin’ and ‘Battleship Potemkin’ shared quite a few letters, and that those in the second but not the first, TTLESHPPOTEI, were surprisingly close to ‘Eliot Ness’. After a lot of letter-juggling, I included ‘Eisenstein’ and ‘Russian’ to produce the long anagram to ‘Eliot Ness’, ‘he hunts Al Capone’, ‘Nitti’, ‘Burakumin’, ‘best spies’; this last phrase was perhaps a little forced but it was the best I could do. I decided that the letters involved would map to the clues in some fashion, although 47 was a slightly awkward number. I’d also noticed that ‘Eliot Ness’ anagrammed to ‘Stone lies’, which he does at the foot of the staircase, and again that was too fortunate to ignore.

Now for the grid, at which point I realised how hard it would be to have ‘The Untouchables’ portrayed symmetrically. I considered a big grid with 15 columns (maybe 15×12) and ‘The Untouchables’ on the top row, but this might have been a bit excessive, so I decided that dropping the ‘The’ might be preferable and aimed for a more standard 12×12, although I knew that with 47 clues the average answer length would be shorter than is ideal. Having noted that ‘Untouchables’ and ‘Union Station’ both began with ‘U’ and were twelve letters I decided to try those in the first row and column, although I never thought that would be feasible; it would also make symmetry extremely difficult to achieve.

To my surprise, my first few efforts at putting something in the grid weren’t as hopeless as I’d expected, so I persevered. After many hours’ effort I finally came up with something I was fairly happy with. The grid was symmetrical apart from the two missing bars in the first row and column, and though the average answer length was, as expected, quite low (though still over 5) I felt the amount of checking made up for this to some extent.

Next came the question of how to include the messages. Using misprints was my first intention, with the correct letters yielding one message (‘Eliot Ness’, etc) and the incorrect letters the other (the drawing instructions for the staircase). After some thought it occurred to me that I could change the title to ‘Take Two’, a more natural phrase anyway, and use that thematically in the clueing method, in a similar manner to a recent Listener (#4038, Playtime by Samuel). Later, I realised that by incorporating further instances of ‘take two’ into the preamble I could account for the slight asymmetry by including rogue bars in the first row and column, making the presented grid perfectly symmetrical (which made me feel much better), and for the removal of ‘one’ and ‘two’ from the names ‘Stone’ and ‘Bowtie’. Further consideration led me to the jigsaw entry method, since this would make the entry of the film title on the top row less transparent.

As the preamble was an integral part of the puzzle, I wrote it as I went along - in fact, the majority was written before I had even made a start on a grid - and I managed to include several phrases from One-Taker in my original preamble:

“The filled grid depicts a famous film scene ([...] shot in a single take), with the star of the film represented by two clashing letters”

“The 15-letter film title [less any leading article] is symmetrically located in the upper part of the grid, and must be highlighted”

“…must then be ‘moved’ to its resting position, obscuring other cells as a result and leaving empty cells behind”

“In the resulting grid, [...] to complete the picture”

“Numbers in brackets are answer lengths”

Some more re-jigging of the grid followed, the last when I decided that ‘tap issues’ was an unacceptable plural, and finally it was time to write the clues. This part always takes me an age, but I hadn’t appreciated just how difficult it would be to write clues which would need two letters removing and real words always resulting. The awkward consonant pairs (e.g. MK) were probably the hardest.

Some of the ideas I didn’t use included:

using “21 letters must be shaded” from One-Taker’s preamble as part of a hint to shade the squares under the staircase (which would have numbered exactly 21 with the removal of one step);

referring to an earlier scene in the film in which another of Capone’s bookkeepers is shot dead and the word ‘touchable’ written on the wall in blood (so the solver would have had to write these letters in red);

making reference to the time of the shootout (midday, since the gangsters planned to catch the 12:05 to Miami - another chance to use ‘one two’?);

leaving ‘WP’ (for ‘Walter Payne’) in the grid, through use of words like cow-pilot/co-pilot, pawpaw/papaw/pawaw, tawpie/tawie etc;

incorporating an anagram of ‘Walter Payne / bookkeeper’ into the preamble as further confirmation, but I decided the preamble was more than long enough already (my original draft had required the solver to write BOOKKEEPER, described as ‘an English word with a unique property’, i.e. three consecutive double letters, below the grid, but the editors felt this was disjointed and unnecessary and on reflection I agreed);

writing themed clues, as per One-Taker, but my film knowledge wasn’t up to this, and anyway the double-letter removal clue type was hard enough;

using exactly the same preamble as One-Taker, but this would have been too contrived;

putting NESSES in place of NOSEYS in the bottom left and requiring ‘Ness’ to be highlighted, but though this was possible I felt it was inelegant since ‘EN’, representing Eliot Ness, already appeared in the grid;

making the grid a pangram, but though again this might have been possible I felt it would make too many answers obscure;

making the grid ‘carte blanche’, but there was no real justification for this and it would have spoilt the need to ‘take two’ bars from the grid, unless bars were required in the solution which would have been messy with the staircase to draw as well;

having the second arrangement of the first set of ‘taken’ letters (giving ‘Untouchables’, etc) fixed by alphabetical order of clues (or similar) rather than simply being numbered, but this just seemed to require extra donkey work from the solver (not to mention the extra restrictions that would have been imposed on the clues).

After a ‘stewing’ period I had the puzzle test-solved, topped and tailed it and then sent it off. Shane responded in very generous terms; he and Mark had changed a few things, notably the preamble in which they felt that the nod to ‘One-Taker’ was clear enough so had adjusted several of the ‘borrowed’ phrases for clarity (e.g. ‘star’ became ‘leading character’ to distinguish between Eliot Ness and Kevin Costner). They also removed the requirement to highlight the title and location, which I had only included because this was done in ‘One-Taker’, as well as the need to write ‘bookkeeper’ under the grid as explained above. After a few final clue adjustments and tweaks the puzzle was ready for publication.

I am very grateful to my test-solver and the Magpie editors for their extremely helpful suggestions and improvements, and also owe many thanks to Harpy (collectively, Charybdis and Ploy) for unwittingly giving me the idea in the first place and for generously agreeing to the publication of this sequel (and for their comments prior to my submitting the puzzle). Thanks also (in advance) to all who have submitted feedback via the Magpie website. Finally, when I set the puzzle the film scene was readily available on YouTube; unfortunately this is no longer the case. It can however be viewed in full at the harder-to-find location of http://www.mefeedia.com/watch/29769380, but apologies to anyone who was stymied through being unable to locate this.

Elint (Jun ’10)

This background was my motivation for trying to create a puzzle relating to one of Escher’s works. I knew of one other – in the August 2004 Magpie, Charybdis had provided a puzzle based on Escher’s Bat/Bird/Bee/Butterfly drawing of 1951. So what aspect of Escher’s work should I choose? I decided on the “impossible triangle” which inspired his 1961 lithograph “Waterfall”. This was appealing as it suggested a novel grid with triangular cells. I hadn’t seen many such grids, and was soon to discover the probable reason why they are rare! The triangle itself is often termed the “Penrose Triangle”, as it was devised and popularised by British mathematician Roger Penrose, though it turns out it was discovered earlier by “father of the impossible figure” Swedish artist Oscar Reutersvärd.

My first attempts at designing the grid assumed across entries and two sorts of “down” entry, with bars employed in the usual way. It soon became clear that the topology of a triangular-celled grid gave very little scope for this approach, as it is extremely hard to get the unching right. After trying a number of alternatives, I settled on a bar-less grid with meandering grid entries. At this stage I’d also decided how the impossible triangle in the grid would be indicated to the solver, and had produced an unambiguously-filled grid meeting the layout constraints, which also had the word WATERFALL in place.

I had no real idea if such a grid would be fair to impose on solvers, and so called on the help of my trusty test-solver to check this out before I wrote any clues! Filling was found to be possible from a (randomised) list of answers, but unreasonably taxing. At that point, I introduced gaps in some of the cell edges (one per grid entry) so that the first two letters of any answer could be entered, and I increased the number of words in the grid. Both would give solvers a better chance of making progress. It was now time to write the clues.

I find devising clues an enjoyable process, and always made more so if there is a clue gimmick involved. In this case, apart from the extra letters generating a message, I hit upon the idea of grouping the clues in threes, with no obvious start point, to reflect the nature of the triangle to be found in the grid. It was fun trying to get a single “story-line” to run through each triple. It was then back to my test-solver for further vetting and refinement of the puzzle. My thanks to him/her! The completed puzzle was then submitted to the Magpie team, where it got a good reception.

Feedback from solvers was almost universally positive, and some very encouraging remarks were made. Most solvers seemed to twig the reason for the title, it being a play on the first two of the three meanings of “force” in Chambers. A couple of people referred to plausible alternative answers, e.g. FIBULA for ROTULA (42), and CLEW for TAEL (43). This eventuality is always there, and such possibilities won’t necessarily be spotted before publication. I’m sorry for any problems this caused. At least five pairs of eyes looked over the puzzle before it was published!

Thank you to all solvers who took the time to comment, and to the Magpie editorial team for accepting and publishing this puzzle, with special thanks for beautifully rendering the grid.

There are many websites referencing Escher’s work. The official website is a good place to start, and I can recommend Escher and the Droste Effect.

A period off work led me to resuscitate a long-considered idea to apply to appear on Countdown. An emailed entry form soon led to an invitation to attend a local ‘audition’ for the show, and when that came round I found myself in a room with five other hopefuls, tackling six word rounds, two numbers rounds and three conundra.

I was annoyed to find I had missed a maximum on the first round EEPICETRS, though the audition rules were kind enough to let me attempt SETPIECE and fall back on PRECISE. I picked off two more 9-letter words, from ELISTHORE and SERTAVONE, having realised that there was a better than usual chance of their availability. Another twist for the audition was being told that the two numbers games were both possible before attempting them – it was a bit feeble to miss one of them by one (with two identical numbers unused). And getting two of the three conundra seemed another good-but-not-great return.

Of the six of us, I would have said that we formed three pairs: two good enough to qualify, two borderline and two not good enough. And I was happy enough to receive a letter saying I would be contacted to be told an appearance date within the next six months. This was followed a couple of weeks later by a phone call offering me a slot in two weeks – as I couldn’t make that one, I was offered another one about two weeks after. So I had an effective month to refine my skills.

My two great practice tools were an archive of all the Countdown games, round by round; and an ODE word-list that Chris Lear sent me. With these I improved my knowledge of allowable words dramatically, and my numbers game skills appreciably. I formed strategies in the event of being well in the lead, just in the lead, just behind and miles behind. I filled in my form of family, hobbies, favourite places, achievements and anecdotes. Importantly, I concluded that in each series there were four or five contestants who were definitely likely to beat me, and that my odds of meeting one for my (first) programme were about one in four.

And so to Manchester. I was able to visit my father in Ludlow Hospital on the way, which proved more than providential, as it meant that he saw a member of the family on his final day – the news that came later rather took the edge off any enjoyment of an evening in Manchester before the recording.

Arriving at the studio at noon, I found out that a wunderkind was currently ‘on a run’, though information was hazy about whether he had completed 4 or 5 wins overnight – an important fact, as I was scheduled for the fourth game filmed on the day. Eventually, it became clear that I would be likely to play the remarkable Oliver Garner – Chris has told me since that Oliver has played over 1,000 online games of Countdown in the last 2 years. Lunch was slightly tense therefore, and the sight of Ken Barlow tucking in at the next table seemed more surreal than amusing.

The afternoon filming began strangely, with a joke contestant offering a 2-letter word and then hymning Jeff Stelling the presenter vocally – it turned out to be a disguised Charlotte Church preparing a spoof item for a new series, to the amazement of the presenters. Then came the last chance for Oliver to be beaten before my show – but there was no joy for the self-proclaimed punster and monster-in-law Daphne, except when she got the conundrum.

My moment in the spotlight was just as it appeared on January 21st – I was amazed to find that the filming of an episode takes no longer than its airing (indeed it’s shorter as the ad breaks are briefer). My amazement at amassing a 26-point lead – the first half of which was all down to two rare errors by young Oliver – was only matched by its predictable dissipation. The culmination was a one-second conundrum spot by Oliver, especially frustrating as his conundrum record had been average to that point. I estimate his chances of beating me based on his other showings at about 75% in any game, so I couldn’t claim to feel hard done by.

The show’s presenters were all very kind and complimentary – Jeff Stelling, a sports fan through and through, had clearly enjoyed a rare thriller; John Stapleton and Susie Dent both kindly reckoned that I’d have had a great chance against anyone else. Rachel Riley formed a poor impression of my hearing after she had to ask me four times what scene of Bridget Jones’s Diary I was in.

Back in London, I pondered about how wide to spread the word that I was appearing, especially as the impetus to get people to watch was reduced by the result. I wasn’t due for a Magpie editorial – but maybe a puzzle would be in order? The conundrum formed a neat and obvious centre-point, and I carefully picked another couple of rounds where a performance by me to equal Dictionary Corner’s would have led to a win. A number of people have expressed surprise that I tried DENOTER in another round – they had the same sinking feeling that struck me as soon as I had said it – but in fact settling for 6 points there would have taken the game into an extra tie-break conundrum.

I liked the idea of a puzzle in which the necessary words were formed from the letters in the rounds – though of course I couldn’t remember the order in which the letters were drawn. So contrasting Dictionary Corner’s suggestions with my own poorer efforts suggested itself. Not wanting the grid, or project, to be too large to overwhelm the idea (or compile in the time), I quickly accepted asymmetry and a restricted average answer length for the sake of creating crossing entries that could be words in either arrangement.

The letters that could form ‘removals’ from longer words in the draft grid were almost suited to a message about Countdown on Twenty-One January, but the J proved impossible, and I decided that as long as the puzzle came out in January’s issue, ‘the twenty-first’ was unambiguous. I hadn’t originally planned a full jigsaw but once I’d had the idea of tweaking and arranging the initials of the other answers into a rueful message of self-appraisal, that was really the only way to go. And at least there was only one word longer than six letters to give a start, though I gave no quarter in its clue.

It didn’t occur to me that anyone would not be able to divine the meaning of the message – given especially that we have featured Countdown in the magazine before, but then I am an aficionado of the show and can’t imagine people who have never watched it. I’m conscious that it discriminates against non-Brits, but plenty of our stuff does, and we just ask them to bear with us. Generally, friends and Mr Magoo fans (there are some) have been generous both about my TV performance and the puzzle, and I thank them whole-heartedly for their support. And yes, I do derive an odd form of therapy from the closure that setting such a puzzle gives, as with Emulation from October 2008.

It was always going to be a problem for foreign solvers to watch the show (apologies to them), so I tried to make it solvable without the confirmation from the TV, though of course it will have been a little harder. There was also clearly a chance that some solvers would solve too late to be in time for the show. The proliferation of Channel 4 repeat channels and Internet availability seems to have made this matter less – the title was a small steer towards early completion, I vaguely hoped. The comment that I must have landed a Channel 4 advertising contract recently is amusing, but a bit wide of the mark. I shall have to try to avoid popular culture for a while!

Mr Magoo

Invited to tackle the Times puzzles, I managed the 1980 one all right, and eventually worked my way through the slightly different style of the 1960 puzzle. The example from 1940 utterly defeated me, and I gave up after half an hour with only 11 answers filled in with any confidence. The reporter was delighted to observe, accurately, that the puzzle had reduced me to the level of a novice solver. Readers of the Times will have the chance to assess for themselves, but the differences in accessibility were dramatic to me.

The 1980 puzzle had a slightly different style from those of 2010, but was readily recognisable to the modern solver – I was surprised to note one of the famous ‘quotation’ clues (Shakespeare) and happy to leave it till I had all the checking. Other than that, there was little significant delay and I think most regular solvers will find it reasonably straightforward. The 1960 specimen was markedly different, though I wasn’t good at explaining what the extra obstacles were. Certainly a couple of clues had no definition, and a few others used devices which were tenuous and unlikely to pass muster today – however, it’s hard to quantify how much the level of uncertainty this creates knocks on to delaying the solving of other clues. I remember spending lots of time wondering how one particular clue would turn out to be vaguely alluding to its answer, only to find that it was completely sound and normal. I gave myself about a minute at the end of the puzzle to decide the most plausible answer to another quotation clue.

I certainly was not expecting the seismic shift to 1940. I decided that if this was a standard example, I give little credence to anybody’s claim to complete every daily puzzle in that era. As far as I can see, some pretty significant guesswork would be necessary to come close to filling the grid, and probably some more guesswork to fill the last few spaces as well. In half an hour, I couldn’t come up with more than one or two answers in the bottom half of the grid that even looked likely. Unless there is a bogus enumeration in that section (as there was for the 1960 puzzle, by modern standards), I can justify almost nothing there – and was quite proud of a little arcane knowledge that helped me get even a few answers in the top half. The specific problem is that so many clues are just hints, without any of the certainty that comes with a modern clue. I wait to see whether many people will claim greater success than me.

The One Show provided a different form of awkwardness. In this case the largely pre-scripted idea requires the youthful presenter to investigate the cryptic crossword by first talking to a doyen amongst current setters, then the son of the original Times compiler, and finally coming to the current champion to ‘challenge’ him to a competition. For my part, I was asked to try and give Alex the briefest of tips on how to solve, and then to try the Times’s daily puzzle at the same time as him. The tweeness of the scene is emphasised by the Victorian classroom setting, the pointlessness of a novice trying to complete a crossword at speed, the difficulty of providing any real help in about a minute, and then the cardboard crown awarded to the winner and the cheesy end-line, with an answer for the presenters to reveal.

Frankly, I suspect regular solvers would enjoy their day more without watching this item. I might well have done so, had I not taken part. We’ll see what happens in the edit, but I have little doubt I’ll come across (reasonably accurately) as a pompous jerk. I didn’t even have the satisfaction of recording a decent time on the puzzle, due to the necessities to intercut ‘humorous’ lines and provide close-ups and retakes. I do fear that any attempt on my part to show crosswords as being fun and accessible would have been vetoed by the director anyway. Of course crossworders might hope for that outcome, but perhaps that’s as unrealistic as the likelihood of a popular programme wanting to show that side. Or perhaps the other interviewees had more joy? Monday’s programme will reveal all.

Mark Goodliffe

Weaving messages into numericals is not as straight-forward as for those found in word puzzles and the best approach seemed to be to include the instructions in the grid. This had the advantage of being able to be explicitly flagged in the preamble so solvers knew what to look for.

The biggest drawback of this method was the second grid would have only 9 different digits (0-8) to chose from, meaning the encoded message had to be written using just 9 different letters. So the first major problem was producing a relatively clear and concise message that would fit neatly into a grid using just 9 letters of the alphabet. Considerable amounts of hair and white-board marker were wasted at this stage.

With the message selected the grid dimensions had also effectively been defined. It seemed best to place the words in the central two rows for symmetry and gathering all the letters together would allow for as few lights as possible passing through these critical cells. At this stage the only decision about letter-values that had been reached was which letters would fall in the range 0-8. Which additional letters would be used and even how many variables were kept back as extra “degrees of freedom” for later on.

It was at this point that the true secret of the puzzle was deployed - designing the grid by placement of the bars. The grid is very close to being what is known as “simply connected” that is to say all the bars (including the outside edge) are joined. Only the island of bars in the centre stand in isolation. The even dimensions of the grid and the desire for eye-pleasing symmetry prevented an entirely simply-connected effort. The upshot of producing a grid like this means there are very few alternative routes from one light to another. This would be quite tedious in a word puzzle, where letters entered in the grid are the general way of gaining feedback and the solver tends to slowly build to the solution. Whereas the more peripatetic nature of numericals, where a deduction can produce information all over the place, allows for a much more constricted grid design including higher percentages of unches.

There were now 6 across lights entirely defined in both grids by the letters of the message and a certain amount of playing around with the first 9 letter-values was done to produce relatively “nice” entry values. Generally speaking smaller numbers made up of lots of factors are easy to clue than walloping great primes. The need to avoid leading zeros left L and S as the only possibly candidates to be zero, one in each base, so that was a starting point. A certain amount of back-tracking and moving of bars was done in an attempt to improve the overall set of target values for entry.

It was then necessary, with the aid of some computer power, to consider these 6 acrosses along with any down lights where the majority of the cells were already fixed en masse. All the remaining flexibility as to how many variables and which double-digit value was which was used up at this stage finding suitable clues for these entirely and mostly predefined answers.

Now the simply-connected aspect came into its own. With just about all values assigned in both bases, the grids had their central rows full and a few digits sticking out into the top and bottom sections. By considering each light in turn working out from the middle it was possible find a double (base 9 and base 10) clue where only 1 or perhaps 2 of the light’s digits were fixed. Each new light generally entering digits into virgin territory, meaning there was never a point where an entry was fully decided upon before its clue had been sought.

There was, however, a price to be paid for the nature of the grid. The lack of inter-connectedness and the high number of unches meant not enough information could be gleaned in grid feedback. In short the puzzle was completely unsolvable. It was possible to return to an earlier stage and try again, but this merely produced a different, equally unsolvable puzzle.

A desperate remedy was required. Hence the introduction of equals clues. Not the most elegant solution to the problem, but when the lifeboat is sinking something has to be chucked over the side! Fortunately the manner of considering each light in turn was good enough to allow some clues to have alternatives that produced the same entry values in both bases. Test solving allowed a suitable number of these to be included to leave a reasonable route to the solution.

The only remaining question was - is it fair to ask solvers to deduce that 2 digits must be entered in the odd, earmarked space? Essentially this is the only logical solution and solvers must abandon all prejudice and read “All entries are in base 10₉” correctly as “All entries are in base NINE”.

Providing an almost respectable excuse to seek out and digest arcane information is a seldom recognised benefit of solving and setting thematic crosswords. A crucial step for the setter is assessing interesting titbits as possible themes, and while with sufficient guile any subject can be worked up thematically, some topics seem to cry out for such treatment. The ogham (or ogam) theme sits in the latter category and was inspired by its entry in Brewer’s. Ogham appealed partly because it had apparently not been used before, and partly because I knew how much solvers relished transliteration devices. I soon realised that because several of the character symbols (including, notably, the vowels) could be viewed as side-by-side fusions of two other characters, ogham was readily exploitable as a cryptic theme. This could be achieved by forcing entry of two consecutive letters of an answer into one relevant cell, so that e.g. WISHBONE would become WIS(ogham-A)ONE. I rapidly abandoned that idea because ogham-I would have to be formed from Q-N, and the nearest thing to a word containing that digraph seems to be the unappealing abbreviation SQN LDR (which probably also means something rude in Welsh). I also reckoned that this method would lead too easily to a solution, and I was aiming for at least a C grade (despite earnest editorial entreaties). I therefore chose to adapt a widely-used gimmick: entries should create clashes to be resolved by substituting the ogham character representation of the conjoined clashing characters. Usually such clashes are created by intersecting across and down entries, but for reasons that will become clear, this was not appropriate here. I decided to form the clashes by overlapping the last and first letters of pairs of answers: e.g. ogham-I = Q-N could arise from an overlapping clash between IRAQ and NAMIBIA. Numbering the grid under these conditions would look odd and give too much away, so grid numbers would be dispensed with. The solver was to be appeased by presenting the clues in alphabetical order of answers, with answer length enumerations supplied as a special treat. Finally, a suitable message or word would have to be generated by resolution of the clashes.

Next, the grid. I started with the conventional assumption that symmetry should only be dispensed with if the theme could not otherwise be elegantly implemented. I also wanted to arrange the ogham characters linearly a full grid row at a time to encourage solvers to join them up along their principal axes. To maximise symmetry, that would mean an even number of rows in a Px2Q grid or an odd number of rows in a Px(2Q+1) grid. However, I feared that incorporating appropriate crossing words with clashes in a grid resolving to even two rows of ogham would be difficult without prohibitive unching, so I plumped for a single central thematic row. As 12×12 is the modal grid size, I went for a 12×13 grid as neither the amount of thematic material nor the fee on offer justified a 14×15 one.

For setting purposes I use a mixture of free software and embarrassingly poor self-written utilities in a Linux-only environment: I suspect I now have most of the functionality of TEA with much less of its celebrated user-friendliness. Another quirk is that I never write anything down on paper at any stage of the setting process, freeing me from the tyranny of abysmal handwriting.

When adding bars I wanted to provide as many longer words as possible that involved the middle row. I deliberately allowed generous checking in the central zone, and regarded it as essential that every cell of the middle row was checked. I knew at this stage that filling would need bar adjustment, but a start has to be made somewhere.

Before the fill, I needed to work out an apt dénouement for the ogham row. (At this point I will draw a veil over the considerable time wasted working with the inexplicably wrong depiction of some ogham characters in my edition of Brewer’s. Imagine my anguish at discovering that other authorities, including Unicode, agree on a different character correspondence. From then on, I used the version at ogham.lyberty.com.)

To simplify matters, I ignored ogham characters formed with slanting lines, and the five characters added later, leaving a subset alphabet of 15 characters wherein clashes are resolvable as A=H+B, O=D+L etc. Since there were fewer possibilities to consider than for phrases, I first looked at the small number of 12-letter words constructable from the subset alphabet that contained all the fully crossed characters (the vowels). One such word was DISCOUNTABLE, and most of the others were too. However, of the remainder, DECUSSATIONS rang a bell. On looking it up I immediately realised the search was over: it came to me later that a form of the word was used famously and gnomically by Sam Johnson in his definition of network, “anything reticulated or decussated, at equal distances, with interstices between the inter-sections”. A perfect gift of a dénouement, arrived at entirely by chance.

The road ahead was now clear: the vowels in DECUSSATIONS would be indicated by clashes and the consonants would stand for themselves. (Later I realised this caused a minor but annoying inconsistency: in clash-resolving ogham cells, there is a notional bar separating the original overlapping entries; in non-clash ogham cells there is no such bar. This would have been fixable by making all cells of the latter type correspond to the first or last letters of words, but at the cost of grid symmetry.) The rest of the fill was achieved semi-automatically using a variety of subterfuges to accommodate the clashes, and involved several bar relocations. Incidentally, I know that computer-generated fills are frowned upon by some setters. However, they throw up many interesting and unusual words that are not in the setter’s vocabulary, and provide useful first drafts that can be knocked into shape manually.

The next question was how to reveal the theme. I considered that not to hint at all — given the theme’s obscurity — would be grossly unfair, even by doleful Magpie standards. What kind of hint? A message generated by the usual suspects (misprints, extra words) seemed unnecessarily helpful, so I decided that hiding the word itself in the grid was sufficient. Despite trying hard with an unusually large amount of manual rejigging, I was unable to hide OGHAM within existing grid constraints without resorting to horrible words. OGAM was a lot easier, and had the advantage (from the gratuitous cruelty point of view) of being the less common form of the word. I wanted OGAM to be quite difficult to spot to make solvers solve a reasonable proportion of clues before any pennies dropped, hence the fairly tough device used for signalling the relevant letters. Eventually a diagonal OGAM was shoehorned into the grid as shown.

On returning to the grid after a long interval, I researched ogham more intensively and became dissatisfied with having orientated DECUSSATIONS as a horizontal entry when in reality carved texts were traditionally depicted vertically and read from bottom to top (see e.g. ogham.lyberty.com/oghamintro.html). I decided to rejig the grid entirely in 13×12 form, with DECUSSATIONS reading upside-down in the central column. Despite the significant chore of completing a new fill, I was happier with the result. For one thing, a 13×12 grid is aesthetically more pleasing than a 12×13 one.

I wondered about adding other thematic material — for example, ogham characters are named after trees — but couldn’t see how to do that fairly or consistently. I wrote the special OGAM-indicating clues first, making sure they functioned as required. 42d gave me a lucky opportunity to give another (possibly retrospective) hint in the form of the word rune. The last step I always take is to check that alternative entries made possible by unchecked cells are strictly excluded by wordplay.

In clueing I strive (not always successfully) to make as much sense as possible in the non-cryptic reading. Not only does this almost invariably make the clue more challenging and satisfying to solve, but it also adds to the setter’s sense of achievement. I dislike setting styles that seem wilfully to ignore the sense of the non-cryptic reading: you might as well use something like, “Put the first letter of tram into a word for ill to get a word for a piece of wood”. I mainly follow Ximenean principles, but cannot for the life of me see what is wrong with car crash = ARC and the like. Afrit’s injunction trumps Ximenes any day.

The preamble took ages, and went through many drafts. Being concise and accurate without revealing too much is difficult, and I wanted to avoid any of the dreaded preambliguity (sorry) that causes so much angst among solvers. There was also the matter of steering solvers away from the aberrant Brewer’s entry. I don’t have a test solver, so rely on forgetting my own clues after a couple of months and do my own test solving. This is surprisingly effective at weeding out useless or unsolvable clues, and helps troubleshoot the preamble.

The working title was Use a ruler. Only at the very end did I realise the aptness of Crossword on the grounds that (i) ogham is written using crossing lines, (ii) DECUSSATIONS itself can mean “crossing lines”, and is therefore a crossing or cross word. In addition, I hoped that some solvers would remember Dr Johnson’s definition of network, which is also an approximate definition of a crossword grid. Serendipity strikes again.

So off it flew to the Magpie nest. Seasons came and went; banks collapsed; policemen grew younger. Finally, a beautifully composed PDF file arrived from Shane. The preamble was slightly altered, and gratifyingly few clues had changes — negotiations commenced and an amicable consensus was soon arrived at. In my submitted version, I’d asked solvers to write DECUSSATIONS under the grid. The editors deemed this unnecessary.

I regret not having included more thematic material, and a red herring or two might have been fun. The grid would have looked better with mirror-image symmetry to emphasise the central column. A more skilled setter such as Charybdis would no doubt have been able to make all non-ogham entries in the final grid spell out real words. Which brings me to …

I have been asked to explain my pseudonym. Chorybdis was chosen because it is an anagram of my real name, and — although a neologism — was close enough to Charybdis of classical mythology to lend it a spurious authority. It also seemed to chime with the whimsical naming style adopted by many setters. Only after my first puzzle was in press several years ago (for One Across) did I discover the setter Charybdis. It was then too late to change, but I propose to stick with Chorybdis unless there are heartfelt and serious objections. In mitigation, I would point out that similar pseudonyms are not unknown among the ranks of setters: e.g. Buff and Bufo; Sam, Samuel and Samson; Duck, and Duck and Hen; Rex and Rex Kinder; Leo and Leon; Sol and Solo; Oz and Ozzie. Also, I would hope that solvers are better able than most to distinguish similar words.

The solution is also available.

We arrived 24 hours late due to cancellation of the previous day’s flights from Reykjavik because of bad weather, and tucked into an introductory boiled seal dish with a display of heartily insincere relish. I’d brought some Guardian crosswords for those idle moments between glaciers and icebergs, and noticed another member of the group (Richard Chamberlain) with a sheaf of Times puzzles. Though we naturally chatted about our mutual interest, it wasn’t until waiting for the plane back after a superb (but tiring) trip that Richard spotted me poring over Magpie #68 and said, ‘you do the Magpie!’.

So Greenland, incongruously, turned out to be the venue of my first encounter with a fellow subscriber. We compared notes on our solving modi operandi and favourite puzzles (studiously avoiding discussion of the current issue), while our partners bemoaned the frankly negligible travails of being ‘Magpie widows’. The likely impossibility of setting crosswords in eastern Greenlandic (or ‘tunumiit oraasiat’, a language of long words liberally sprinkled with q’s and u’s, not usually together) was also debated. We wondered aloud whether it was wise for two subscribers to share the same flight back, given the Magpie’s small circulation. Fortunately, we arrived home safely, well before any kind of Iceland-associated crash. I look forward to meeting more subscribers in improbably remote places.

One of many picturesque icebergs

Mysterious sign in Greenlandic

Magpie 68 outside Kulusuk airport

Pandigital and zero-less pandigital (ZPD) curiosities have long since held a fascination for me and I am not alone in this affliction. Madachy and Beiler both devote chunks of their books Mathematical Recreations and Recreations In The Theory Of Numbers respectively to them. In addition the most prolific setter 40 odd years ago was Rhombus who set many puzzles involving them. John Gowland in South Africa also sets puzzles in the Rhombus style and his work can be found in the mathpuzzle.com archive.

Rhombus’s puzzles rarely had the dreaded dénouement which plague mathematical puzzles nowadays relying instead on the satisfaction of having obtained the relevant solution sets used as being more than enough of a reward.

Whilst surfing the WWW I came across a site which had lots of ZPD niceties. I homed in on the problem that was used in the puzzle and I wrote a program to check and found that there were 101 solutions. The contributor Peter Kogel found chains and also a loop of solutions and so I decided to use the loop of 9.

The first stage was to come up with a grid and given that P, Q and R were 3 digit numbers as well as the solutions X, Y and Z I opted for a grid containing only 2 and 3 digit entries. I could have used some entry lengths of 4 or 5 and clued as divisions but I felt it was better with only 2 and 3. Rhombus used rectangular grids quite often and so I chose 9×7 and barred it off. Normally in puzzles like this I have started with a blank grid and barred off as I went along however on this occasion I wanted to try something different and start with a barred off and lettered grid which makes the clue writing much easier as you don’t have to wait until the puzzle is completed to code them.

The next stage was to list the 9 sets used and find their prime factors. I was able to get all of this, grid included, on a single A4 sheet along with 9 rows for the clues.

Flushed by this success I spent a long time studying the prime factorisations and the P, Q, R, X, Y and Zs looking for

· Any that were the same apart from those in the loop.
· Any that were multiples of one another.
· Any that were multiples of 5.
· Any that were reversals of each other.

Eventually I spotted 976 which was 16 x 61 and felt that that could be a good lead in as there couldn’t be too many to test which only give 3 digit numbers with no repeats or zeros. In order to eliminate 23 x 32 a clue which was 5 times a 3 digit number was required so as to fix a 1 at the start and putting all that in one clue solvers would have minimal testing and could enter x and U.

I wanted to make use of deductions which could be made regarding the terminal digit of Z from the sum of 3 cubes and so soon finished off the clue.

Setting continued well and before long the grid was filled. I deliberately left some parts of clues blank in that having bits missing is quite useful especially if you can’t fit them in! Getting solvers to sum those missing bits (something they are quite used to doing!) and writing it under the grid would show that they had obtained all the solutions. I had wanted solvers to write the sum in an appropriate mathematical shape made up of one line to show that they had spotted the loop, basically a circle or any closed loop, but this was rejected by the editors as being too much of a quantum leap. However given the quantum leap dénouement of One Day I have to wonder!!

The editors did come up with an alternative dénouement which used the sum of the numbers that did not form the links in the chain (4807) and its prime factorisation of 11, 19 and 23 which could be found with minor modifications at P, Q and R respectively namely 11, 18 and 33. This was quite an incredible achievement however I vetoed it in that it didn’t involve the missing parts and also gave the game away in that the loop was mentioned in the introductory waffle!

It will be interesting to hear what solvers thought of the puzzle and apparently some have given away their age by commenting on the similarities with Rhombus.