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Listener No 4477, Word Squares: A Setter’s Blog by Elap

Posted by Listen With Others on 10 December 2017

The Theme

I started by creating a file containing all of the five-letter words from TEA 2.11. There were 12,125 words including proper nouns.

Out of curiosity I wrote a program to see how many ways ten of these words could be fitted into a 5×5 grid. It took three hours to find that there were 1,152,602,603 different filled grids (excluding reflections).

I then decided to see how many grids there were where the two diagonals were also words, and the answer was 575,560. This took 163 seconds.

I was unhappy with the number of unacceptable words in these, and so I produced a set of 10,508 words which did not contain any proper nouns. There would obviously be other unacceptable words, but it was easier to ignore grids which contained these than to go through the list deleting them (it was easy to remove the proper nouns because they began with a capital letter).

I reran my programs. There were now 229,858,145 grids (the run took 70 minutes) and 115,265 with the diagonals too (taking 71 seconds).

Since there were so many ways of fitting words into the grid, and since I wanted my final grid to be special in some way, it struck me that there was scope to see whether two of the grids could be anagrams of each other.

I decided that the grids should contain ten or fewer different letters so that they could be replaced by digits, thus forming the basis for a mathematical puzzle.

For each filled grid, I wrote the 25 letters (in alphabetical order), followed by the words in the grid, to a file. I then wrote a wee program which sorted the records into ascending order and which then scanned the file to see whether two adjacent records had the first 25 characters the same.

It turned out that there were six possible pairs of grids. Two of them contained similar words somewhere and three contained mildly rude words, but there was one pair which was acceptable. This was very satisfying.

Nature of the Clues

Since I was dealing with word squares, it seemed appropriate to use squares in the clues. The clues would consist of expressions in terms of letters whose values had to be deduced.

I wrote a program which determined which substitution of digits would produce the largest number of perfect squares in the grids. The idea was that some clue values could be squares or square roots – but how would the other clues work? After a lot of dithering, I decided to have some clue values as square roots of the entries, and some consisting of the required answer which was equal to the sum of the squares of two other values. The advantage of this is that the roots could be negative, which might fool some solvers (it fooled me too, because the first vetter spotted that I had two letters round the wrong way in one of the clues which led to a negative answer!).

In line with the theme of two squares, I decided that appropriate letter values could be numbers which could be expressed as the sum of two different squares.

The Hint

I needed a hint, though, which would appear when the letters were sorted by their values. Part of the hint would be the ten letters, in order, by which the digits 0 to 9 were to be replaced. Another part needed to indicate that the grids were anagrams of each other. But how? – there were not enough letters to convey the message. I then hit upon the idea of using lower- and upper-case letters in the clues so that a better hint could be constructed.

The ten letters, represented by 0 to 9, were ILAPCREMST. For the anagramming hint, I first thought of BYJUMBLING to indicate how the second grid was to be derived from the first, but I had also to indicate that the diagonals were words too. I was quickly using too many letters for the clues to be solvable without there being too many of them, and anyway I didn’t want an L in lower case because it would look like the digit 1.

I needed to say that there were TWENTY-FOUR words in the grids, but with ILAPCREMST that used three Ts already! Wait! What about TWO DOZEN?

The hint could then be ILAPCREMST……TWO DOZEN…… with some of the letters in lower case.

Some solvers, though, would assume that there were twenty words in the grids, and so a Y was needed to reinforce this. The word which contained the Y would have to indicate that the grids were anagrams of each other. Hmmm…

What have we got so far?


What word, containing Y, could indicate an anagram? If the word had more than, say, six letters we would again be heading for too many letter values for comfort. I needed a short word.

It was a few days later that VARY suddenly sprang to mind. It could be the positions of the letters in the first grid that would have to VARY to arrive at the second grid.

Our hint was now looking like one of these (some of the letters will be in lower case):


The chortle that my wife heard from the study was when I looked at the third option, ILAPCREMST VARY TWODOZEN, and a mean streak in me began to surface.

If there were at least four available letter values between the first T and the Y, wouldn’t some solvers assume that they were the first and last letters of TWENTY? Tee hee!

I changed the case of one of each of the duplicated letters to arrive at this hint:

I L A P C R E M S T V a r Y t W o D O Z e N

The trap was about to be set.

The Clues

I won’t go into details of the derivation of the clues (mainly because I have forgotten now), but the letter values were these:

I L A P C R E M S T V a r Y t W o D O Z e N
5 10 13 20 25 26 37 40 41 50 52 53 58 65 68 73 74 80 82 85 89 97

Intentionally, amongst the first values deducible were T = 50 and Y = 65, encouraging some solvers to jump to this conclusion:

…… T W E N t Y ……
50 52 53 58 61 65

If this assumption is made, the values of e, L and O would be incorrect, as well as the values of W, E, N and t.

Solvers would most likely end up with these incorrect values:

Letter Correct
E 37 53
e 89 68
L 10 17
N 97 58
O 82 89
t 68 61
W 73 52

All the clues except for 7ac and 18ac (the most complex, and likely to be solved relatively late) would still work. Whether or not the correct or incorrect values are used, we have:

In 5ac, 13dn and 14dn O + t is 150
In 6ac and 10ac O – L is 72
In 6ac |N + R – C – e| is 9
In 15ac L + t is 78
In 19ac L + L + t – O is 6
In 2dn |A + t – N| is 16
In 3dn and 13dn e – W is 16
In 13dn |E – C – P| is 8
In 4dn |C + W – e| is 9

As a retired programmer, one of the lessons I learned early in my career was not to unnecessarily assume anything, and maybe this is a lesson to some of the solvers!


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Listener No 4476, His: A Setter’s Blog by Nebuchadnezzar

Posted by Listen With Others on 3 December 2017

This crossword all started after a long day’s travelling to Croatia, and I remember trying to merge ‘Thinking Outside The Box’ with the 9 dots on a piece of scrap paper. It was approached with the mindset of a doodler, as opposed to “right, I’m going to sit down and write a Listener Crossword”, accompanied by a loud cracking of the knuckles. It was only when I realised the TH could do double-duty that I suspected this was a goer (although, in the interests of my relationship, I postponed the gridfill until my partner and I returned from our holiday).

The puzzle-within-a-puzzle theme is a well-trodden path, but I wanted to pay tribute to what I think is a particularly ingenious challenge of one’s lateral thinking. I was also careful to find a way of citing my references, hence DUDENEY and LOYD down the side — I didn’t want anyone thinking I was trying to pass this off as my own work! I was pleased that there wasn’t too much head-scratching in actually cracking Dudeney/Loyd’s puzzle, I think — I didn’t want to give those who already knew the solution too much of an advantage.

Finally, I needed to create a box outside of which one could think. A bit of research led me to the EGG OF COLUMBUS, and that old ‘letters omitted from wordplay’ trope enabled the square to complete what I felt was quite an aesthetically pleasing final grid.

The gridfill came next, which was achieved using Quinapalus’s magnificent Qxw software. In retrospect, I would have preferred fewer 3/4 letter words with wordplay leading to 2/3 letters, but I was generally pleased with the unching and average length. For the record, the ambiguity of the clue for BULB was recognised by myself, testers and editors prior to publication. I apologise to anyone who felt it affected the overall quality of the puzzle, but I’m of the opinion that, since the endgame removed any ambiguity, all should be forgiven? Perhaps I’m opening a can of worms — please feel free to argue against in the comments!

With my apologies, I don’t remember a great deal of the cluing process. My rule of thumb with these matters is to find a ‘hook’, around which I can build the rest of the clue. To use 25a as a case in point, my mindset will have been something along the lines of: enderon = skin; hen and heron are birds… birds and skin… ah, there’s some sort of surface there about dirty magazines! Then fill in the gaps, whilst trying not to be too clunky when fitting it all together. Those who were kind enough to test the puzzle, and of course the editors, were merciless with some clues. Any that I tried to ‘get away with’ – usually on the grounds that the surface made good sense, but the wordplay was unsound — were rooted out without hesitation, and I’m very grateful for that!

Last and very much least in the process was the title (His = •••• •• ••• in Morse = 9 dots), probably the least satisfying aspect of the puzzle. In my defence, I did feel as though a theme like this justified something that required a bit of lateral thinking. However, I soon realised it was perhaps a tad unfair, and I can only apologise if it detracted from the satisfaction of completing the puzzle. A small part of me still quite likes it, but then again I never had to figure it out.

Finally, I owe a huge debt of gratitude to everyone who contributed to the puzzle’s testing/editing. I know everyone says it in these blogs, but the level of expertise on display when it comes to proofing a Listener crossword is remarkable. I’ll stop gushing now for fear of appearing sycophantic, but I could go on! 

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Listener No 4475, Follow the Directions: A Setter’s Blog by Artix

Posted by Listen With Others on 29 November 2017

I think the Daily Mail may have been responsible. Yes, seriously. I was on a ‘plane home from somewhere and asked for a newspaper and was given a 3-day-old copy of the Mail. Old news is no news and so I quickly moved on to the Puzzles page. Amongst a wide selection, I found a simple dissection problem of a square into two heptagons…which pointed in opposite directions.

The cruciverbalist’s brain rarely switches off and I thought this must have potential. Vague prepscholic memories of Westward Ho! somehow came to mind; I’d read it some 40 years ago but couldn’t really remember much of the plot. Uncle Wiki helped fill in the gaps and produced the basis for the puzzle.

I really liked the idea of one arrow carrying Amyas Leigh westward and then him returning homewards with his new-found Indian sweetheart. And so it began.

I’ve checked my files and there were six grid attempts before the final version emerged; and, with each new grid, I seemed to be able to incorporate more and more of the key elements of the story, and also offer some help to the solver as to the shapes required.

I had thought about a clue device but, perhaps a little wickedly, there was something inside me which wanted to have the endgame all come after the grid had been completed. To compensate (in a way), maybe I could include vaguely thematic surface readings in some of the clues? Or perhaps even a direct hint to the theme (or at least the location of the story)?

I usually draft a version of the preamble before embarking on the clues. And then come back to it — normally several times to get the wording right — as the process progresses.

Then testing (thank you to both of you), some clue and preamble modifications, and then sending off to the Editors, acknowledgement, then the long wait. (It’s not really such a long wait but it always seems like it is.) Murmurs of a positive response at one get-together, then confirmation that I was getting near to the top of the pile.

As ever, there was some “tweaking” required and a few of the more outrageously Artixesque ideas had to be toned down or were just flat rejected. In every case, I am sure the final version was fairer, if perhaps not so innovative. Of course, there was a little bit of the habitual to-ing and fro-ing, gentle arm-twisting to keep the surface readings sound, even mild persuasion to accept my originals.

Quite genuinely, I thank them for their input and their patience and their tolerance. I am also flattered by the positive response that the puzzle has received from the majority of those who have commented. It’s always most encouraging. Thanks.

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Listener No 4474, Rock Group: A Setter’s Blog by Llig

Posted by Listen With Others on 20 November 2017

The theme haunted me for some time but exploiting it to Ximenean/Listener standards was a Sisyphean task in itself, and the final least/worst option was not wholly to my taste. So it was rather a surprise, and very gratifying, that it gave considerable pleasure to a large number of an above average entry.

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Listener No 4471, What Can the Matter Be?: A Setter’s Blog by Flying Tortoise

Posted by Listen With Others on 29 October 2017

Much as we may like to give the impression that we setters are intellectual giants who are struck by brilliant ideas which we then carry though every phase with aplomb to produce a sparkling jewel of a puzzle, the truth is that some days it’s just a question of throwing everything currently on your mind up in the air and hoping that it lands in some kind of coherent pattern. In no particular order, I had been giving thought to:

  • word squares, having read a learned article on the search for the perfect order ten square
  • word ladders, having been surprised to find that Lewis Carroll invented the puzzle as a Christmas amusement
  • unusual ways of providing checking letters, having a devious and cruel mind
  • ways to avoid the nightmare that grid composition can become, having had a particularly irritating battle with a previous submission

Having settled on the quartered 12×12 grid as a reasonable solution to the problems of the last on that list, the hunt was on for a way to justify it in a way that would still present an interesting puzzle. The four natural elements was an .. er .. natural candidate but it was only when I realised that it was possible to represent them best by emphasising the difference between them using a unique method of entry for each of the four quadrants that it really started to come together.

One problem, remained, of course. How to ensure that the entries were placed in the correct quadrants. I thought I remembered from my days studying Chaucer that the elements were linked in some way to the ‘humours’ and was very pleased to have this confirmed by a Wikipedia article. Although it gave me all I needed to complete the puzzle this would actually prove to be a stumbling block as after submission it became apparent that the direct link that the ordering of the quadrants relied on was not verifiable by any of the standard reference works which Listener solvers are assumed to have available to them. In keeping with its somewhat chaotic beginnings, it was only a piece of quick-fix thinking in providing the pre-highlighted cells in the grid that rescued the puzzle from banishment to the place of wailing and gnashing of teeth. Still they do say that every beautiful swan swims with grace only because of the furious paddling out of view!

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