Solve One Get Another One Free

It’s spring-time 2018 and one of our cats — Tango, he of EV1118 fame, had been put to sleep a few weeks earlier. I was coming to terms of life without him, he was almost 18 and been part of the family since he was about 8 weeks old. So, to keep myself occupied I had launched into a bout of puzzle setting. They were short puzzles and most of them weren’t up to much. I needed something that would be really taxing, time demanding and require a lot of concentration.

I’d always been impressed by the way setters could get a message into a puzzle and as I hadn’t set one like that for some time, I revisited the idea. I decided to use the old mod10 trick whereby a digit can be one of two or three letters. Then came the message — what would it be? There were various possibilities — leaving a pretty pattern with ERASE ALL ODD DIGITS or ERASE ALL EVEN DIGITS or to give John Green a week off, ERASE ALL ENTERED DIGITS.

Eventually I opted for REVERSE ACROSS ENTRIES. At this stage it had never crossed my mind to have the clues still hold true when the entries were reversed. I set to work finding a suitable grid which meant that the zero which would appear for T would have to be an unched cell or a cell which wasn’t the first or last cell of an entry before and after it was reversed. It was easier to do the former. This didn’t take too long and I entered the relevant digits for the message in their correct cells and got to work

One thing I like to try and do is to introduce solvers to a variety of different sets of numbers other than the usual suspects square, prime, triangular, Fibonacci, Lucas etc. To this end I decided to use Happy numbers and Lucky numbers as well as the multiplicative persistence. To make things easier for the solver I decided that the Happy and Lucky sets would be restricted to 2-digit numbers and to list them in the preamble. Calculating the 2-digit and 3-digit Happy numbers as well as the 2-digit Lucky numbers isn’t that hard by hand. It is a different matter entirely though for the 3-digit Lucky numbers as the method is akin to the Sieve of Eratosthenes for finding primes and requires a clear head.

Setting was going well and I had a few entries in place when I took a step back and began to wonder what the comments would be like on the various forums. I reckoned they would be along the lines of “yeah and”, ”so what” or worse still “why?”. It was just a random set of numbers that were being reversed. There was nothing special about them.

I looked at my entries again and noticed that I’d put in 169 for 3ac which when reversed remains a square and there was another entry that when it was reversed had the clue still hold. However, the rest of what was entered didn’t. My subconscience was telling me something. So, I removed those offending entries and continued with the new idea that the clue would still hold when the entries were reversed. This would make it more difficult for me but also more interesting and the end result more pleasing for the solver as well. I took the opportunity of re-clueing some of what was already in place by adding digit sums and digit products to some. This had the effect of cutting down some of the numbers in the sets as well as making my life a bit easier in that the digit sums and products don’t change when they are reversed. I had used Σ for digit sum and Π for digit product however it seems that The Times can’t handle Greek letters in puzzles!

I had another few entries in place when a devious thought struck me — could I have the same holding true for the down entries as well? That would surely have a PDM and/or wow factor.

This would require careful checking and be far more difficult for me to set but as that was what I wanted; I went for it. If I failed then I’d still have a puzzle where all the clues for the across entries would still hold. So, I made two copies of the grid side by side with a clue list underneath and painstakingly went through what was already in place. This necessitated a few changes to what was already in but thankfully nothing major.

After a week I had the puzzle completed and cold-solved. I was concerned that my solution had involved having to find the letters or potential letters of the message about half-way through. However, I decided to go with it as I thought that that is what solvers would try and do anyway and sent it off to my test solvers. Both testers solved and enjoyed the challenge. All that was left was to decide where to send it, Listener or Magpie? I felt that it deserved the widest audience possible and so, with apologies to the bird, this tribute to the sadly missed Tango who I’m sure would have approved of the deviousness of the puzzle, went to The Listener.

Thank you for all the kind comments about the puzzle which are much appreciated. A number commented regarding why they didn’t get the reverse grid instead as their first solution. The answer is that the message would have been gobbledegook. According to one poster there are 3432 different grid-fills that satisfy all the clues! I presume that there’s only one of them that gives the message though.

PS. I note from The Listener site that the reverse puzzle number 1574 appeared in July 1960 with the title Auto-suggestion-II set by Fudge. The grid was car-shaped and each entry was a word from which three consecutive letters had been omitted; the clue was a “number plate” showing the discarded letters, the entry length and sum of the letter-values of the entry. Looks interesting!

Having just completed the submission of a collaborative thematic series in Enigmatic Variations on the climate emergency problems and solutions [EV 1546 – 1550] and with the collaborative Avian Listener puzzle on Watership Down [New Arrivals] moving up the queue, I was considering other facets of the global environmental issues we are facing. It was in this context at the start of 2022 that I was pleased to find that WOMBLE is in ODE and that I might still just be in time for the 50^th anniversary of the original TV series if a slot were available.

The consideration of the various thematic elements came about in a different order to the way it was laid out in the final puzzle. ENWOMB/LESS… was there from the start, and the idea of having the Wombles as locations on a map, since the original characters had chosen their names by pinpointing Uncle Bulgaria’s old atlas. I wanted the map to be accurate and I expended a lot of effort to achieve that within likely limits of space in the paper. That is why the grid ended up being asymmetrical and 13×13 as I did have an earlier draft symmetrical grid with many more clues. It was fortunate that WELLINGTON refers to the place in Somerset, not NZ, but the historic Japanese province BUNGO still had to move about 30 degrees west. On the other hand, OCOTEA was a very helpful find in Chambers to allow ORINOCO to be as far to the SW as possible.

During the month required to come up with the final grid fill, most of the other thematic elements fell into place, including the RE(F)USE idea. The missing EVERYDAY and associated COMMONPLACE title was a relatively late inclusion as I considered how many clues I needed and what message to supply, while SCAVENGER HUNT was a fortuitous find on one of the later grid fills.

The editors, as usual, expertly rewrote the preamble and trimmed some clues to make everything fit. I was initially a little sad to lose a few of my favourite clues in the process, but on review realised that it was just a few of them, and after further honing on correspondence, those ended up among my new favourites in the set of clues as published.

I’m writing this late in the day, having just returned from a very enjoyable weekend in Bristol for the Listener Setters’ Dinner. Hence I can add thanks to setters and solvers for their very kind comments in person as well as those received electronically and in the post via John Green. Probably the best encouragement from solvers is “I enjoyed that one” or “that was fun” repeated again and again this weekend.

On that note, I do now regret perhaps trying to be too clever rather than considering the overall solving experience in part of the endgame. The items of LITTER recycled in clues were definitely not random but were chosen as thematic items occurring in specific episodes, and their initial location in the clue numbers was according to the episode number that they appeared in. Six recycled items of rubbish appearing in various episodes are:

• LIGHT BULB episode 10 (10A => 1A)
• INK episode 7 (7D => 10A)
• THE TIMES episode 1 (1A => 13A)
• TV episode 13 (13A => 18A)
• ELASTIC episode 27 (27D => 7D)
• RACKET episode 18 (18A => 27D)

x

This is verifiable in the episode synopsis at Fandom (excludes ‘racket’) and Tidy Bag (excludes ’The Times newspaper’), but to assemble a shortlist of items in the first place, I purchased second-hand copies of the original TV series and watched each of them at least twice. Hence I can definitely identify with those who were left with an earworm after solving the puzzle!

I’ve been keen for some time to write a crossword where all the clues were thematic in some way, but had a little difficulty settling on what the theme should be. I’ve got somewhere a half-written puzzle with Agatha Christie references in each clue, and had considered one or two other possibilities that I won’t disclose in case I ever come back to them, before deciding I’d found the right idea when I settled on Bob Dylan. After all, even Agatha Christie only reached double figures in her number of published books, whereas Dylan has written many hundreds of songs, giving lots of thematic possibilities. If, say, I found myself needing a one-word title beginning with H, he was sure to oblige: Hurricane — or, if by any chance I’ve used that in another clue, Hazel — would fit the bill.

I hesitate to call myself a big Bob Dylan fan, as in the world of hardcore Dylanologists I am certainly out of my depth, but I have nearly 40 of his albums and count him as my favourite artist other than the Beatles. I’ve only seem him once live, though; 18 years ago in Birmingham (Midlands, not Alabama), so perhaps it’s time for me to go to another gig and experience his genius afresh.

Having decided on a Dylan theme in the clues, I needed something to draw them all together in a final grid — but what? It felt a bit unsatisfactory just to have some highlighting related to a particular song, say, because that would be picking one from his catalogue, whereas the puzzle would already be drawing on so many. For a while I went down the route of a Dylan Thomas crossover (not as arbitrary as it may seem, as Bob Dylan chose his pseudonym in honour of the poet — and it would also be a cheeky reference to my own surname), but since I know little about Dylan Thomas, it also didn’t feel very satisfactory. I also spent some time tinkering with a George Bernard Shaw link, as he and Dylan are currently the only two people to win both Nobel prizes and Oscars (Kazuo Ishiguro could join them this year, having received a nomination for the Living screenplay), but couldn’t get it to work — and then that idea was done beautifully in the Magpie last year by Porlock.

Separately, I’d started musing on the Listener puzzles in the past where the solver has had to erase the entire contents of the grid, and wondered if there were a way to go one step further — perhaps by cutting out the grid altogether? And… maybe using the space left by the excised grid as a frame? I enjoyed the idea, and realised I could combine it with the Dylan crossword I was already trying to put together, given his (infamous) Self Portrait album. By the bye, it was pure luck that this was his tenth studio album, allowing me to use ‘X’ in the preamble.

Thinking up a new (or newish) way of hiding a message is always difficult, and in this case I wanted to make it as unlikely as possible that solvers could figure out what to do without solving all the clues, or at least the significant majority. Unchecked cells seemed to work, even if it wasn’t particularly thematic, and it also made for one of the easiest grid creations I’ve ever done, as there wasn’t too much to work around. I was even able to use an existing grid structure I found online, rather than creating one from scratch, and make it work with minimal tweaking.

The only answer I put in the grid with an idea in advance of how I was going to Dylan-ise the clue was DADOES, as I wanted something I could use with ‘Tangled Up in Blue’; for the rest, there were some song titles I was confident I could adopt somehow (‘Stuck Inside of Mobile’ was perfect, if an abbreviated version of the actual title), and I certainly wouldn’t run out of anagram indicators, but I didn’t try in particular to use grid entries that matched Dylan songs. In fact, writing the clues worked in both directions, either with ideas from song titles coming first — ‘Dylan’s Fourth Time Around’ gave obvious cryptic possibilities, for example — or the other way round, as the ‘Hazel’ example above demonstrates. I think my favourite was ‘Man of Constant Sorrow’, as I enjoyed the definition for EULER and the way that ‘rue’ could work in the clue.

The feedback pack has come through the post, and it seems that I have divided the audience once again. Among the many kind and positive messages, including a Mr. Happy card (I don’t know if the sender knows that I am a big fan of the Mr. Men, but it made me appreciate it even more), there were a few missives that drew their inspiration more from Mr. Grumpy. That’s fair enough, I think I knew in advance that this wouldn’t be everyone’s cup of tea, but I was a little surprised by those who found the instructions ambiguous. Obviously I’m far too close to it to be objective, but I’ve genuinely struggled to think what ‘cut out grid’ could mean other than to cut out the grid, and from there I didn’t think it was a huge leap to work out that the frame was what’s left. I did spend time trying to make the instruction as clear as possible, and I was grateful to the editors for adding to that clarity with the phrase about ‘replacement’ in the preamble, to emphasise that the self portrait alone was needed (although I don’t believe anyone was penalised for sending in the grid as well). Still, it’s a shame if that marred anyone’s enjoyment, and I do thank them for their gentle — and sometimes not so gentle — words to the wise.

To prove that I’m on the side of those without artistic ability, here is my own submission, which I couldn’t resist sending in. A few people have asked if we’ll see a gallery of the self portraits at the Listener dinner, which I’ve also suggested would be fun — I don’t know if that’s on the cards, but I’d love to see it. As I write, the dinner is a week away, and I’m looking forward to it immensely either way.

Thanks as ever to my test solvers, to John Green, and to the editors for letting me get away with this.

Have you heard of Gregor Mendel?’ asked my wife in the garden one September afternoon as we were doing justice to a decent bottle of pink. Adele was reading a ‘history of science’ and Brother Mendel’s metaphorical tonsure had popped up. I don’t succeed on every have you heard of … question that comes my way at home, but I was on safe-ish ground with this one. Genetics was one of the more interesting subjects of my A level biology classes and I could just remember enough to deliver a reasonably authoritative precis of his contribution.

GREGOR MENDEL and PISUM SATIVUM with 12 letters each made the first step of a 12×12 grid with a side column and row an obvious way in. But after that, I got stuck in a series of cul-de-pods. Dominant/recessive traits occupied me for some time, as did trying to represent F1/F2/ F3 generations. In the end, I decided to keep it to crossing peas. I liked that the letters of GREEN were in Gregor Mendel. As were the letters of GENE, but as that term was not in usage in his time, I discounted that. I tried playing on GM as in ‘genetically modified’ but that didn’t feel right at all. I chose alternating misprints to give the idea of ‘crossing’, not sure if that was picked up.

Thanks to Wan for his time and advice in getting this puzzle into shape. And a posthumous nod to the greatly missed Neil Shepherd who test-solved.

Nick (Karla)

Transposition Cipher was inspired by my previous Listener puzzle Impossible Construction. In that puzzle, a central panel in the completed grid contained a word square, will all grid entries outside the central panel being real words. I thought it would be interesting to see what other content could occupy a central region of the grid.

The message TRANSPOSITION CIPHER BY SERPENT has 28 characters which would fit nicely into a 4×7 panel that could be incorporated in a 10×13 grid. I was going to use a standard columnar transposition cipher but then thought it would be more interesting to use the Myzskowski variant with ANAGRAM as a rather natural keyword.

I used the approach of Impossible Construction of jumbling entries that intersected with the central region, with the constraint that the three letters of these jumbles outside that region should form real words. The excellent Qxw software confirmed that a grid-fill was possible. From there, I incrementally refined the grid in order to exclude as many obscurities and inflected word forms as possible.

The ambiguity in the grid-fill was irritating, but I realised the bug could be turned into a feature because it is disambiguated by (what is unambiguously) the correct plaintext.

As always, I must thank my test-solvers, David and Norman, and Shane and Roger at the Listener for their feedback and help in producing the final version of the puzzle. And many thanks to all the solvers who have been kind enough to send comments in with their solutions.

A number of solvers commented on the dimensions of the ciphertext panel being identical to the puzzle number (4747). That’s not something I’d noticed when checking the proof and Roger assures me that this is pure coincidence.