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.

I was fortunate in that I arrived just in time for the guided tour (free, as is the museum itself). Highlights of the tour include the original plane the Wright Brothers flew on 17 December 1903, the “Spirit of St Louis” in which Lindbergh flew solo across the Atlantic, the Friendship 7 capsule in which John Glenn became the first American to orbit Earth, a piece of moon rook that you can touch (it is claimed that anything you wish for while you touch it will come true… sometime in the next 4.5 billion years) and the command module of Apollo 11, which of course was the first space vessel to take men to the moon with the purpose of landing on it.

As we were shown around the (incredibly small) command module, our guide gave us a little pop quiz. Could we name the first man to set foot on the moon? Neil Armstrong we duly answered. And could we name the second man to set foot on the moon, from the same mission? Buzz Aldrin, came the reply. And could we name the man who flew with them but never set foot on the moon?

“Michael Collins!” I cried out triumphantly. Our guide smiled and congratulated me, but I think in her eyes was the gleam of “Smartypants - you destroyed the point I was trying to make”. For of course it is a truism that where we all know the men who first set foot on the moon (although how many of the other ten can you name?), poor Collins is relegated to a footnote, forgotten by all except trivia buffs and know-it-alls. As if flying all the way to the moon only to never set foot on it wasn’t bad enough, it was actually the case that whilst the whole world was watching Neil and Buzz take their giant leap for mankind, Collins was orbiting the other side of the moon, in radio silence from the whole event.

So it was that I decided to compose a puzzle in honour of the men who flew the module but never got to walk on the moon. The starting point was pretty much the finished puzzle - unclued entries would be the pilots in question. The only change was when it occurred to me that Apollo 13 should probably figure in the puzzle somehow, but as a special case. So Swigert was put in the grid to be found rather than as an entry in his own right.

Ironically, Swigert is probably the most famous of all the module pilots. It says something about human nature that though we naturally remember heroes far better than the people who stood behind them in support, we remember the (sometimes heroic) failures even more, especially when they get blockbuster films made detailing their exploits!

Mark Goodliffe

“…You may start”

Click on the stopwatch, and straight to the start of puzzle 2 (no real reason, but it’s possible No 1 will be made the easiest, and that could be a useful break while solving a harder one).

Puzzle 2

1ac Officer needs energy to stay on top of things (4) Probably a 3-letter officer plus E, I’m not good on the military, COL? No. Move on.

2dn Naval administrator takes quick look through sound (5) More military, probably a homophone for ‘takes a quick look’ - glimpses, glances, it’s not coming, move on.

10ac New semi, price not fixed (9) Looks like an anagram…

Oh wait, that last one is coming - yes it’s a famous ‘naval administrator’ isn’t it, “peeps” = PEPYS.

Gives me a P in this anagram, must begin IMP-, not fixed … IMPRECISE. The P in 1ac could give … COPE for the definition: ‘officer’ = COP, that’s nice, never seen it before.

1dn Leader of community may interpret book, if Hebraic (5,5) C and I in the grid, which is good because the letter count and letters of ‘if Hebraic’ are making me think CHIEF RABBI, which is appropriate. Fill it in and understand the rest while writing.

4dn Thinking Greek child’s left in a lift (9) 3^rd letter is an I, nothing’s coming. Sort of clue that’ll benefit from more checking, move on.

12ac Sole neighbour’s evidence of powerful online connection? (7) F-S to begin with, feels like FASTNET from the shipping forecast, but check the rest: amusing broadband joke.

9dn Founder of new colony on wing (6) -E-N–, EL for ‘wing’? No. Move on, should have tried the long one first anyway.

15ac Once more straighten out what’s unnatural (7,3,5) There’s a standard phrase that fits that letter pattern beginning with A, is it ACROSS THE BOARD? No. “What’s unnatural”? AGAINST THE GRAIN? Yes, looks like there’s some anagram fodder there. Must be right even though there seem to be some O’s provided. Only recheck if the crossing goes wrong.

9dn again, PENNON fits, and it’s a wing, but other things might fit too. Ah, William Penn plus an undisguised ON - cheeky. Try the other long one next.

18ac Black bird of muted colour to alight around start of evening in Alpine area (7,8) Long clue, must be lots of wordplay, beginning with ‘black’ = B in the grid, but without knowing the area at once, no time to deconstruct now.

Move back to 4dn, ARISTOTLE would fit and is Greek, don’t really get it but not many words would fit.

5dn What happens in the middle of our life-span, traditionally (5) No idea, the middle of our is U, of lifespan FESP, meaningless. Move on.

16dn A welcome opening for people in concert (9) ‘People’ ought to be MEN, so probably ends in -MENT. Begins with an A, ADORNMENT? No, has to mean ‘(in) concert’ - AGREEMENT? Ah yes, ‘welcome’ = GREET.

18ac B-R—E for the first 7 doesn’t ring any bells - a bit worrying.

26ac Easy to understand Cambridge college making English central (5) Isn’t ORIEL a 5-letter college? Doesn’t have E in the middle, though. ‘Easy to understand’? Could be CLEAR, literally. Yes, CLARE’s a college and you make the E central.

25dn Mark or Cliff’s brief fright (4) Only halfway through the clue it must be SCAR. Wait, read the rest and make sure, this is the final and I probably won’t do any more checking at the end. Yes, SCAR(e), wordplay and two definitions, unusual.

28ac Going back, soldiers capture revolutionary city, executing leader (10) Lots of wordplay at the end, must begin RET- but not necessarily RETRO-. Try and get more help.

19dn Skill in telepathy? Nothing that makes paper (7) ESP, probably. ESPARTO fits, but it’s a grass. I suppose that could make paper, and there’s ‘nothing’ = O. In it goes.

28ac looks good for RETRO- now. RETROGRADE?

21ac Clear reputation of tyrant? (6) -E-P–. Must know this, come on, there’s not many ‘tyrant’ synonyms. But it could be an actual tyrant. ‘Clear’ = NET? No. Think about the tyrant - DESPOT of course. Must be right, but how does it work? Better check, think, think. DE-SPOT, aha, doh. Finally I get a letter towards the bottom right.

22dn Interfere damagingly - after power cut, it’s less dangerous (5) Nothing coming again, ‘power cut’ must be ‘minus P’. Think about ‘interfere damagingly’ - HAMPER, no, TAMPER, minus P = TAMER. Yes.

RETROGRADE looks better and better, where’s there a city in that? All of the middle backwards (revolutionary) perhaps? DARGO- something, no the other way round feels better - PETROGRAD! With its ‘leader’ ‘executed’. Great spot by the compiler, I’ve never seen that similarity before.

17dn Boots may be worn through - put in a bin for recycling (9) Ends in D, so probably defined by ‘put in a bin for recycling’. Begins with H - no idea. Move on.

27ac Girl worth tiny fraction of dollar? (9) Some sort of CENT, or dime or nickel? Begins with M, MILLICENT’s a girl, start filling it in, ah yes MILLI-CENT, that’s quite funny.

14dn Tiny blonde is explosive author (4,6) An N in 2^nd, could be an anagram as ‘tiny blonde’ is 10 letters, but not a promising collection. INDY, INTO, no, we need a name. Think slowly, INES, ENOS, ENID - ENID BLYTON, not the author I was expecting! Pleased with getting that anagram, it feels difficult.

29ac Tart’s thigh cut (4) FLAN for ‘tart’? Yes, FLAN(k), nice to stumble on that instantly.

24dn Read out letters that may be charming (5) –E-L ‘charming’ always means magic etc - SPELL? Yes, double definition.

23ac Excitement of drinking lots of beer with no head (7) ‘Beer’ is almost always ALE, and this ends in L, but nothing occurs to me. Move on.

20dn How Macbeth described wood in speech for recruit (6) Birnam Wood? Doesn’t fit. Think: “till Birnam wood come to high Dunsinane”? Nothing there, I don’t think I know any other Macbeth speeches about wood. Move on.

Quick think again about 17dn and 18ac - no. Top right then.

6dn Comic character needs good colouring (7) Ends in G, must be, er, TANNING? Start to fill it in. No wait? TANNIN isn’t comic- another synonym, DYEING and HUEING aren’t long enough (if words) - think. TINTING - could be but is ‘Tintin’ a comic character? Of course he is!

3ac Server’s wiped one place to sit at - it’s all wet underneath (5,5) T at the beginning of the second part - ‘table’ is somewhere to sit - WATER TABLE? Yes, it’s ‘all wet underneath’, I suppose.

8dn Clubbers’ pill: basis of life for a girl (4) Begins with E, which is a clubbers’ pill. ECSTASY? No. Is ‘basis of life’ L? No. Move on.

11ac From granny, long yarn (5) NYLON, simple hidden. Easiest clue so far.

A girl at 8dn could be, er, EDNA. Why? Ah, DNA, nice.

7dn Endless dark molten rock covers area where the Russians once attacked us (9) The checking allows BALACLAVA, and LAVA’s in the clue. Fill it in without worrying. Could it the variant spelling with a K? Not in the Times crossword. And checking will reveal if necessary.

13ac Little guy embraces wife, the jerk (6) ‘Little guy’ could be TICH, or maybe TITCH is more normal for this sort of puzzle. Around W, equals TWITCH. Yes, that’s ‘the jerk’.

5dn I’ve looked at before, still don’t get the wordplay, but ‘what’s happening’ could be EVENT. But why? Other words would fit E-E-T, work it out. (s)EVENT(y) pops into my head, that’s good, I get the clue now, things are going well.

But I still can’t think of anything for 18ac and I’ve tried the bottom right corner. Work at them, or try another puzzle and come back? The latter.

Puzzle 3

1ac Close this works daily? Not if this is used (5-5) Very vague definition, could be something to do with NIGHT for either meaning of ‘close’? Don’t waste time, move on.

1dn Hooters as one leaves sounds (5) 5-letter ‘hooters’ could be NOSES - yes, sounds are noises. NIGHT looks good to begin 1ac, but leave it again.

10ac Queen perhaps to name liquor shop (7) Begins with S, so could be SHEBEEN, and there’s a BEE there. OK, Queen = SHE-BEE.

12ac Starts naval attack without shell from torpedoes (4,5) No easy crosswordese there, wait ‘shell from torpedoes’ could be TS? SETS- could mean ‘starts’. What preposition? SETS ABOUT? Something to do with U-BOAT? No, ‘attack’ = BOUT, looks like it works.

2dn Non-resident served in pub? (5,4) Probably starts G-E-T, ah yes, GUEST BEER, the old ‘served’ pun.

3dn Start of noted elocution exercise that ends in plain rhyme (3,4,2,5) Not HOW NOW BROWN COW - something else from My Fair Lady? Yes, THE RAIN IN SPAIN fits, and it all ‘rhymes’ with ‘plain’.

14ac Long-necked female keeps touching groom (5) A PEN is a female swan. PAEAN, PAEON or PREEN would fit - PEN around RE = PREEN. ‘Groom’ as a verb, nice clue.

17ac Very suspicious about one on a charge returning (9) Can’t fit anything obvious with the R and N, move on.

14dn Nonentity, after just defeat, to make high-pitched protest (9) Begins with P, nothing occurs. Would be good to get as four words begin off this. No, move on.

21ac Dickensian villain stuffing pound into crack (5) Ends in P, I’m not great at Dickens characters (there are so many) - there was a raven that ended in P, but only 4 letters, I think. An L in it? Bingo - QUILP, with ‘crack’ = QUIP! Good work - handy that it’s from one of the two Dickens books I’ve read. That’s a good solve, and the Q must help with 14dn.

Gotta be, gotta be … PIPSQUEAK = ‘nonentity’ and there’s the ‘high-pitched’ squeak.

27ac Gesture of love may be represented in sex finally (4) Beginning with K, this looks like KISS, yes, it’s the X.

22dn Articles needed for links and chains (5) I—S Lots of possible words, IRONS? Not sure why, move on.

25ac Expert, keeping it neat, returned foreign collection (7) E—I– ‘Collection’ makes me think of the words EROTICA and EXOTICA that fit. ‘Foreign’ suggests EXOTICA more (unless there’s some Times euphemising), I can’t immediately see the wordplay, I’ll risk EXOTICA, even though it won’t be proved finally later.

22dn should be IRONS, now though ICONS (and indeed IDOLS) would fit, I can see. ‘Links and chains’? Golf links could give … IRONS, of course. And chains are made of iron, no they’re IRONS too. Duh.

18dn Amazingly well represented electorate might get this charge (7) Not much crosswordese here, except maybe ION = ‘charge’, though that’s not strictly true, I’m told. Move on. After another quick look at 17ac, to another section.

4dn Battery component once tossed in skip (3,4) What fits with the N and O? RUN DOWN? No, move on.

5dn Advice given by experienced writer (4,3) TIP in there somewhere? Don’t know, now I’ve got to start on something totally unchecked or go back to clues I’ve tried, bother. Try the long one as the other was easy.

9dn Cooked snack: old Len had to give everyone helping (3,5,2,4) Well, ‘everyone helping (3,5,2,4)’ immediately looks like ALL HANDS ON DECK, clearly similar to some anagram fodder near the beginning.

13ac Linesman nodding easily influenced ref (5) Feels like HOMER, why? ‘Even Homer nods’, and a linesman could be a poet. And the rest is another definition - glorious clue.

7dn Hand round second item from songbook (5) PSALM, would this have been as easy without the M? Hard to know.

6ac Does like seconds of pairs of lampreys! (4) The second pair of ‘lampreys’ is MP? The final check would help.

11ac Send-off by air (7) A cryptic definition, presumably, –L-A–, is there a valedictory anthem? VALE, VALETE? Could be the wrong idea entirely.

8dn Advertising agent employing the blue pencil? (9) Nothing helpful here, some sort of pun, I’m not getting enough checking in this corner.

15ac Maybe smoking spot hard to find in expensive bar (6,3) Grr, no purchase here. Better persevere with this puzzle, otherwise I’ll have three unfinished. Let’s try for a big answer in the bottom right.

28ac Quietly following contract with artist covering film (6-4) The K in 6^th place, and the ‘covering film’ is telling me something: SHRINK-WRAP! ‘Contract’ is SHRINK, go for it, despite the odd letters that must end the downs. The H ends that 18dn - IMPEACH would fit and means ‘charge’ in a way. A bit too wild a guess for now.

24dn Bar changes to plastic bottles (5) ESTOP - nice to get an easy hidden (this one definitely wouldn’t have been as easy without the P, I’ve struggled with ‘bottles’ and ‘houses’ before) to confirm SHRINK-WRAP.

26ac This gel manoeuvred craft by hand (7) Anagram - must be, wait, SLEIGHT. Yes.

16dn Superb combination of buzzer and bell? (9) Ends in G-R, so RINGER or DINGER? Yes, HUMDINGER, that all works.

20ac Old country woman succeeding in fifties after all (5) SUMER’s an old country. SUM could be ‘all’, ER = ‘woman succeeding in fifties’? Ah the Queen, very neat. Not sure why I’ve come up here again, probably because the top corner is irritating me. Go back to the bottom.

23ac Measured steps to feed balance with loan organised (9) An anagram of ‘loan’ in it, clearly, probably a dance, yes, there’s something that ends in NAISE. How to spell POLONAISE, it’s the French for Polish isn’t it? LONA in POISE, that works and feels right. Write it carefully.

19dn Look into swimsuit that’s a bit short for large figures (7) COLOSSI fits, and means ‘large figures’. The wordplay doesn’t use LOSS, so it’s LO in COSSI(e).

Now what for 17ac P-R-N—C? ‘A charge returning’ could give ION backwards, which appears in PARANOIAC. It fits the definition, I’m confident it’s a correct spelling and the only 9-letter adjective from PARANOIA, in it goes (it later turns out this ‘wordplay’ is a total fluke - it’s C 1 ON A RAP backwards).

IMPEACH must be right now at 18dn, never mind the wordplay again.

Back to 1ac: after NIGH, an anagram of ‘this’? NIGHT SHIFT would mean ‘daily’ equals FT. Yes.

4dn begins with H now. It must have an anagram of ‘once’ in it - HEN CO–? HEN COOP defined as ‘battery component’, OK. PIPING HOT would fit (and allow TIP to end 5dn) at 15ac, find a definition: ‘maybe smoking’, good enough.

Still not sure what sort of TIP at 5dn.

Back to 6ac: every second in ‘lampreys’ gives APES, which could mean ‘does like’, very clever.

8dn S—R-T-R to do with advertising - SIGNWRITER’s too long, so … SKYWRITER (‘the blue’ could refer to the sky).

I still think 11ac is a sort of song - think, think - LULLABY? Oh yes, very clever, ‘send off’ to sleep!

So FELT TIP at 5dn, not FULL TIP, of course ‘experienced’ = FELT. That’s one puzzle completed at least. Off to:

Puzzle 1

1ac Month before Cicero for one becomes painter (9) Some sort of month to begin with, at least twelve possibilities, there’ll only be one or two if I can get a letter.

1dn Supposed to get up around five, these women can be difficult (5) What’s useful there? The ‘five’ of course, could be V, that would have to be central; ‘difficult women’: DIVAS - yes, SAID equals ‘supposed’.

So the month in 1ac is DEC, and the ‘painter; is a DECORATOR, making Cicero an ORATOR. Fine.

9ac Outspoken in investing half of cash in small book (5) VOL for small book, er, VOCAL for the definition, that’ll do.

2dn Where time is regularly represented as flying? (6,5) Cryptic definition, something to do with time. Not sure what.

3dn Kindred commie burying dead (7) RED, so RELATED? Yes, LATE is ‘dead’.

11ac Minor charge for minor charged? (5,5,5) SHORT SHARP SHOCK. An instant 15-letter answer, that helps.

2dn begins with a 6-letter word C-C-O-. COCOON? No. CYCLON? Rubbish.

4dn Brave with this weapon, queen a dove but … (8) Odd clue, not sure what to think about there, even with a T and H.

5dn Look with concern (6) Almost too obviously REGARD, but the two R’s prove it.

10ac Instability of gasometer supplying large shop (9) The G makes me think anagram of ‘gasometer’. Yes, MEGASTORE.

So now 4dn probably doesn’t have a consonant in 4^th place … TOMAHAWK, of course.

6dn Treated without respect around university and no longer employed (7) MISUSED would fit with the S’s … no, DISUSED is better.

8dn I provide food across river for one going leisurely over it? (3-6) The E and K must mean ICE-SKATER, which is defined. Don’t worry about the wordplay.

6ac Knight excellent oil producer (5) Some sort of oil palm? No, knight must begin with D, so … DUB and DUBAI. Subtle definition there.

7dn Speak boldly to goose, reserve finally abandoned? (3) BOO, the definition’s a massive giveaway. So much so that I’d better check the rest in case of traps. BOO(k), OK.

14ac A verse to break depression is coming (6) The D in 2^nd suggest ODE for ‘verse’ but the ‘coming’ suggests ADVENT. That’s better.

12dn In the wrong gear, so reversed in confusion over daughter (11) O-E- suggests OVER-, and OVERDRESSED will fit and has more than one ‘daughter’ in. Yes, the rest’s an anagram. Good start into the bottom of this grid.

18ac Son embraced by love, or a target for spitters? (8) Yes, there’s some sort of 8-letter word for a spitting vessel, er, SPITTOON? No it has to end in -DOR like a thermidor, or the cigar-box word, think, think, do I know another word for this? CUSPIDOR? Yes, CUPID is ‘love’, bullseye - good solve.

25ac Passageway accessing chancels, I assume, from the right (5) ‘Passageway’ with S in the middle must be AISLE, yes, a reverse hidden.

19dn Forced apart, other ranks kept in proportion (3,4) Given a P and A, this must be PRO RATA for the definition, and has OR in.

22dn Root for Garbo, perhaps (5) Well she was a hermit, an actress - and a SWEDE.

21ac Nowadays, Alcatraz will be ruthless (4,2,9) Hmm, other words for ‘ruthless’ end in –E-S like MERCILESS but I’ve got an O in the grid. Leave it for now. In fact try and approach it from the left side…

13ac Withdraw claim, having completed mountaineering expedition? (4,4) Must end in DOWN, COME DOWN would satisfy that punning wordplay, fill it in. Though it could be something else, I suppose, as I write. If it is COME, 13dn begins with C…

13dn Evidence of early development found by supporter in Roman city (4,5) That’s a subtle definition for something like MILK TEETH, is there a Roman city ending in TH? BATH? BABY TEETH! That would have, er, BY TEE in it, yes.

So it’s not COME DOWN, it’s BACK DOWN which is better for both parts of 13ac. Ugly crossings-out in the grid now, but make sure the judges can read what I intend to submit.

16ac Black, camp, thick and spotty (6) ‘Thick and spotty’? Could that be BLOBBY? Yes. A lobby’s a camp.

17dn Something in contention, gathering wood - for this? (7) Begins with B, the whole clue suggests a campfire or something. Don’t know.

23ac A Latin dish of fish, not started, a Spanish painter sent back (9) A Dali sent back would be ILADA, so … ENCHILADA (leaves (t)ENCH).

24dn Wheels can all rotate, for starters (3) CAR. Very obvious, given the C (though quite neat).

26ac It’s addictive, gambling on it (5) HORSE is an association with gambling - and of course means heroin. Now 17dn must be BONFIRE. 21ac isn’t leaping out yet annoyingly.

20dn Possibly asparagus, vegetable finally packed in boxes (6) Just got an A in 4^th, but ‘boxes’ could be SPARS, so SPEARS. That’s good for asparagus.

27ac Having lost head, requested to go off - so do so! (9) Given all the checking, SKEDADDLE suggests itself, and works as (a)SKED plus ADDLE.

15dn To hack off limb perhaps causes ultimate damage (8) MUTILATE. Is that just ridiculously easy because of the checking? Probably not.

21ac is now obviously TAKE NO PRISONERS (that should have been obvious throughout).

2dn ends in CLOCK, so (also obvious in hindsight) CUCKOO CLOCK. Feels like some wasted time there, but at least we’re done in this puzzle. A quick look through the answers on the left where the crossings-out occur, and I have scribbled long answers late on. They all look right now. So back to:

Puzzle 2

4 answers to go.

18ac just keeps shouting BURMESE but how can that be Alpine? I can see ‘alight’ = LAND from the clue for the finish; I’m beginning to think I can’t know this answer, which is a worry.

Check 4dn’s answer - yes there’s a TOT in it and ARISTOTLE was a ‘thinking Greek’. ARISE around the outside.

23ac has ‘excitement’ and ends in S-L. AROUSAL of course, which is normally clued as (c)AROUSAL - and is again here.

So –O-I- at 20dn could mean ROOKIE for ‘recruit’ - Macbeth could have said ‘rookie wood’ (or ‘rooky wood’) but it’s not ringing any loud bells. It feels right for the definition, though, I’ll put it in, and if it fits the last checking, it’ll be right.

17dn ‘Boots may be’… HOBNAILED, I suppose? That’s got an ‘a bin’ anagram in it, it must be right.

So B-R-E-E -B-R-A-D for 18ac to finish. OBERLAND sounds good for the Alps, think about these bits of wordplay: ‘Black’, ‘bird’ (or ‘blackbird’, e.g. RAVEN, OUSEL), ‘of muted colour’ (or ‘bird of muted colour’ perhaps), ‘to alight’ (must be LAND), ‘start of evening’ (must be E). OBER? How about SOBER? Yes, SOBER LAND around E. So I need a bird that’s -R-E, beginning with a vowel. ORLE, ARLE, URGE, go through the possibilities. ERNE! ERNE of course. Check the wordplay again: B ERNE S(E)OBER LAND. It must be. It must be, mustn’t it? Fill it in.

I haven’t seen anyone handing in answers yet. Am I definitely finished? Have I got time to check? Anyone else could finish at any moment yet - I think it’s gone quite well, but obviously the slowest moments were finishing off. I’ve always planned not to check in the final, so grab my number, a quick look through for blanks, and hold up the number. A few seconds later, remember to stop the watch. 17m 43s, that’s a useful average - look around to see if everyone else is still working on the puzzles. Oh well, we’ll just have to see…