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pw, there's a separate thread for this puzzle now:

https://www.crosswordsolver.org/forum/878613/listener-3240-squaring-the-circle-by-amicus/

Finally there! And I think it was fantastic.

In case anyone still cares, I’m a mathematician and hate numerical Listeners (never do them).

I used only pencil and paper, no electronic aids at all.

Logic was all that was needed to fill, no trial and error. Was able to fill in a few cells (but not full entries) with about 50% clues solved, started filling in earnest with about 75% solved.

And the final message used the theme and coding technique beautifully, wrapping everything together. Outstanding, and more than wiped any memories of it feeling like a slog at times!

I think I spent more time on this one than on any other Listener. I used a spreadsheet to keep track of the coding, and it did look very pretty when I'd finished. In the end, though, I'm in drxx's camp. All of which leads me to ask what the criteria are for selecting POTY. Is it all about how clever the setter has been? If so, this is a shoo-in. But if the enjoyment for the solvers carries weight I'm not so sure.

A very tough and very clever puzzle. I'm awestruck, and I did enjoy solving it although I have to say that there were a few features that pulled it back from being quite a favourite for me.

I can see that this one won't be everyone's cup of tea. I was a little surprised at comments complaining at having to do more than just a crossword: if one just wants a traditional crossword, I'm not sure the Listener is the best choice of puzzle! Still, the after-puzzle in this case was truly hefty and I quite understand that not everyone will like it: kudos to anyone who managed to come here and indicate delicately that it wasn't their favourite without finding it necessary to disparage everyone else who did enjoy it and accuse anyone else who solved it of benefitting from inappropriate forms of assistance. Like others who have since commented, I too think I used electronic/online assistance LESS in this puzzle than in many others.

I came here to clarify a few parsings, and found the answers already here -- many thanks to all who have helped nudge us to unfolding some quite intricate clueing. I saw some discussion about the cold-solving requirement and questions about how much help the grid could be with finding answers. I am definitely weaker at cold-solving, so with these kinds of puzzles I do work hard to extract every bit of help that I can from the grid and other puzzle features to help me solve the clues, so perhaps I can offer a useful bit of perspective on this one. Although this puzzle looked at the start as though it was going to be a cold-solve nightmare, I actually found there was a surprising amount of help it was possible to get back, and although this was one of the toughest puzzles I've done overall, I *don't* think it's quite the one that involved the most cold-solving for me!

I started filling the grid, and making as many deductions as I could, right from the start. I made a reverse table, so I could list the encodings alongside the letters, and this helped me spot some useful features, such as the fact that all the encodings for 'i' have a 'C' in the middle, and other similar links between encodings that emerged as I started to make progress. With about a quarter of the clues cold-solved, I started to deduce my first additional encodings, and the grid started helping to eliminate answer possibilities -- not only are the answers alphabetical, but we're told which letters do not feature, and can eliminate other starting letters whose encodings don't fit (especially, near the start, the vowels), and this actually helped narrow down possibilities quite a bit. With about half the clues solved I was really starting to get useful deductions back from the grid to help me pin down what the remaining clues might be, when the answer order narrows the choice down to a few possibilities and then several of those possibilities were impossible in the grid. With about a dozen clues left to solve, I was starting to actually determine letters in the remaining answers back from the grid, and for the last few clues I got several letters -- my last to solve happened to be h*, and I was able to fully construct what all four of the letters must be from the grid so then just had to check that I could see how the clue gave that answer! Overall it was hard work, and I spent quite a lot of time wringing the deductions out of the grid, but I can confirm there was grid support to help working out answers if you wanted/needed it. Which I was very glad of.

Like many people, I did have to restart my grid, though fortunately only once, and fairly early on. It was clear to me that if you hit a contradiction, so that something had clearly gone wrong, there was NO chance to recover -- starting over was going to be the only option. That was quite a harsh feature, I feel. When I finally managed to machete my way near to the end, I don't know what I'd have done if I'd hit another problem at that stage -- I'd invested a huge amount of time solving by that point, and I don't know if I'd have had the stamina to face starting over yet again. Fortunately that did not arise for me...

Some people have said the clues were tough but fair. I thought many of them were fair, some were reasonably straightforward, some were tough and intricate, but I'm afraid a few of them I did not like the way they worked out, and I have one or two quibbles. And I thought that some stretched clueing in a tough set of clues with considerable cold-solving needed and a tough logic puzzle to follow felt a wee bit unkind. Also, a feature of the final message is that it does not help AT ALL until you have COMPLETELY filled the grid, so you can't get any help from it in the way you usually can towards the end of a puzzle like this. There were actually two options for the unclued entry, and I don't see anything to pin down which one was required -- ok, it was kind of obvious which one was meant, but that feels like a loose link to me. And a final technicality -- I felt that reusing the letters as clue identifiers did not achieve much and just added to the mindbogglingness of an already complex puzzle: it would have been simpler just to number the rows and columns from 1-12 and label the clues 3a, 5d, etc. So all in all, for various reasons, this puzzle, though extremely clever, doesn't leap to the top of my own favourites list, but was an enjoyable challenging solve nonetheless. Thanks Cagey.

PS -- and thank goodness this week's has been a more straightforward solve -- I now have some time free to do everything that got pushed aside last week because of all the time I spent sorting out my amino acid encodings...! :-)

Nicely put, mc

I'll assume you're directing the bulk of your criticisms at me, so I'll reply to them.
I've looked back over the thread and put together what I believe to be a fair summary of the thread leading up to where, I think, you've got the mistaken impression that I only want to solve 'standard' crossword puzzles without much cold-solving and even fewer 4 letter words. If this were the case I'd have to agree with your assessment that I must be quite out of my depth tackling Listener puzzles in the first place.
I've tried to dispel this impression once already, but let me reiterate -
the amount of cold solving and the reliance on 4 letter words throughout make the crossword element of this puzzle less than ideal (it becomes a rather skimpy challenge) but, unlike you, I didn't have much difficulty solving all of them.
The amount of help other solvers needed, the difficulties experienced and their frustrations are well documented in the edited version I've provided - and I've included my own, so I'm not being critical of people seeking help, I'm simply suggesting that I didn't have the benefit of the kind of help many solvers (including yourself) routinely have access to.
I should point out, although it shouldn't be necessary, that my 'guesswork' wasn't of the random 'pick a letter' kind - it was based on moving my many alternatives around and trying to whittle them down to a definite entry. I believe a spreadsheet would have been the ideal tool for this process (I didn't use one, but quite a few did - even you, although 'LESS', for some reason you don't give.)
Your other emphatic capitals suggest (to me, at least) that you disagree with my assertion that the 'message' can be used to narrow down the coded entries somewhat. Again, other posters managed the same feat, as you can see from the thread (and others managed to go wrong without having to begin again from scratch - you suggest otherwise, I think).
Yes, I was less delicate than I might have been with my criticism. I can't honestly say I'm sorry about that because I found the unbridled joy of the maths faculty all a bit too much.

(buzzb) I have all but one clue cold-solved and maybe 25% of the grid filled. This is quite a challenge...likely the hardest Listener in several years.
(dylan) I've done 17 clues, discovered one definite new coding, but now stuck.
(simond9x) I'm about halfway through solving the clues with a few tentative entries in the grid.
(riversk) I had to restart three times. Just be meticulous and keep careful track of your letters. With code variations, the grid doesn’t give you a ton of feedback (and a couple of the clues are particularly tricky). The fill is challenging even once you know all the answers - it’s easy to make mistakes if your logic is not solid.
(dodgepot) Bravo, Cagey! A tour de force. Best Listener for years in my book. Certainly since Shark’s Manhunt in 2021. An Ascot Gold Cup winner if ever there was on
(drxx) Very much dislike everthing about this... ...thing. Yes, Shark's Manhunt was excellent. Sadly we haven't seen anything like it since (in my opinion).
(nxe) Just finished this. Commiserations to any of this year's other setters who had hoped to be in the running for the Ascot Gold Cup.
(andyp) i had to do lots of cold solving - i found a couple where the half-filled grid helped - but what didnt help was making mistakes with the grid fill.
(cockie) After 3 print-outs, all of which went swimmingly until an inconsistency appeared I've decided that it's impossible. Clearly a false conclusion. Would someone be kind enough to email me... ...where I can show my reasoning, and my error can be pointed out?
(simond9x) I sympathise, Cockie. I hit an inconsistency last night so started a second gridfill today. After nearly 3 hours, working carefully and with only 11 cells left to fill, I've hit another inconsistency. I can't face starting again. I think it's only happened in the last few letter codings but I can no longer see the wood for the trees. I wonder if I could make the same request as Cockie and ask someone to email me... ...so I can show my code table and the couple of areas in the grid where I may have gone wrong?
(s_pugh) To anyone daunted by this one, persevere! Admittedly it has taken me until Sunday afternoon to cross the line after a false start yesterday, but it was worth it for what must be one of the best Listeners I've seen in the 12 years I've been attempting them. Definitely one where you need your wits about you as the slightest slip or assumption can be terminal.
(simond9x) I second that. A wonderful puzzle and an absolutely astonishing construction. Thanks to the two who confirmed my code table and nudged me back on track.
(acornz) This may be the best Listener puzzle I have ever done in over 15 years of solving. Better than Manhunt, in my opinion, although that was a great puzzle and Shark is a great setter. But this one was perfect,
(kitsune) Just finished. That construction is utterly mind-blowing and I thoroughly enjoyed the solve. Chapeau to Cagey! Surely a shoo-in for POTY?
(buddy) Let me add my admiration for this monster of a puzzle - more logic problem than crossword (and thus somewhat like a numerical) but an unbelievable construction.
(drxx) Good to read a comment with a sense of perspective after the intemperate praise this 'thing' has elicited. Yes, it is very like a numerical, or a perverse sudoku at best - it hardly counts as a crossword to have to cold-solve clues for a load of 4 letter words...
...I resent every moment I've spent working on it (and I didn't appreciate the 't' joke either - not exactly helpful was it?).
Anyway, yes - I'm sure it'll be the winner this year, given the excitement it's generated amongst those who can lay their hands on every mechanical 'aid' in the book, but it was a horrible experience for me + pen + paper (and anyone else with a taste for themed crossword puzzles I'm sure).
There are too many mathematicians editing, setting, solving crosswords these days. If they hadn't invented anagram solvers it would never have come to this!
And I'd just like to take this opportunity to thank my wife, who has a knack for sudoku solving. Without her help I couldn't have got to the end of it.

Thanks, throck - I really appreciate the support.

Managed to finish today and now It's up to Postman Pat for the next stage in what was an epic process.

This half-crossword/half-logic puzzle must hold some kind of record for the most comments received. And my contribution is only to say that it was overall worth persevering with, despite eservations about some of the clues (a few loose definitions). Like other posters, I was lucky not to have had to restart the whole thing - then "life" would certainly have been too short.

drxx, I guess by "bulk of your criticisms" you mean one sentence in my second paragraph in quite a lengthy post that was mostly meant to provide a perspective that I thought some people were interested in. If I was critical at that point, it was meant to be of tone rather than substance. We should perhaps all remember that sometimes thoughts can come across a bit abrasively when perhaps not accompanied by the smile or wink of an eye that was intended to go with them.

Oh, I certainly didn't mean that I'd formed an impression that you or anyone else only wanted to solve 'standard' crossword puzzles "without much cold-solving" or "4 letter words", or that you were in any way "out of your depth". The observation was nothing to do with cold-solving at all. There seemed to be a very delicate subtle current of objection to being given a non-crossword sudoku-like logic puzzle to complete during and after the crossword solve. As I said, I can entirely see that this wouldn't be to everyone's taste. It's just that The Listener quite often presents us with more puzzle to solve when the crossword clues are complete, so it seems a shade ironic to then complain about being given more puzzle to solve when the crossword clues are complete...!

My comment about using electronic aids LESS (using capitals for emphasis is quite a common device, when other forms of highlighting aren't available) was simply that the circumstances in which they can be helpful to me just didn't crop up as much in this puzzle as they do in some. One concrete example: this puzzle didn't involve (for me) any googling to try and identify an unrecognised theme, whereas often they do. Also, the answers all being four letters meant there perhaps weren't as fiendish anagrams as there might sometimes be. I'm not actually sure what other electronic aids might be meant. I did not, incidentally, use a spreadsheet; I never have, though I know some people do, and I can see how they might help in various circumstances -- sorting the final encodings into alphabetical order would have been one obvious example where that might have been helpful in this puzzle, but it so happens that when I got to that stage I did not have anything electronic to hand so did the final sorting using good old pencil and paper.

I'm interested that you said that you thought the 'message' could be used to narrow down the coded entries. Producing the message required putting the fully-encoded rows and columns into alphabetical order, and until the final few encodings were in place I didn't see how this could be usefully begun at all -- too many of the rows and columns had large gaps, and the alphabetical sequences were in many cases extremely similar. So I found that obtaining the message was a most welcome confirmation that things were correct, but not a help in actually solving any clues. If I've missed a way I could have used this earlier, I'd be very interested to know what that might be.