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Archive for September, 2019

Listener No 4569, Bearskin: A Setter’s Blog by Elap

Posted by Listen With Others on 15 September 2019

I decided, one day, out of pure curiosity, to see in how many different ways words could be fitted into a 4×4×4 cube, but it wasn’t necessarily for a puzzle. A 3×3×3 word cube would be too small to be interesting and a 5×5×5 one too large to have any chance of even one way of filling it. I produced a list of just over 3000 words from TEA, and graded each from 0 to 8, 0 being an ordinary, common word, and 8 being used only by Shakespeare, Spenser etc.

In the first version of the word-fitting program it soon became apparent that there were hundreds of millions of ways of filling the grids and so I restricted the words to grades 0 and 1 (i.e. no foreign, obsolete, archaic, Shakespearean words etc). The program still produced millions of filled grids and so I put in a condition that the four diagonals from the top grid through to the opposite corner of the bottom grid should also form words.

I ran the program for a couple of hours and then had another idea: what about grids which contain only ten or fewer letters? Each letter could then represent a digit. This could be the basis for a numerical puzzle with the grid ending up full of words after each digit had been replaced by its corresponding letter. A 4×4×4 cube would have 48 words, and this was about the right number of cells for a numerical puzzle. I had to disable the diagonals checks because it was very unlikely that the program would find any filled grids at all — I could always check for diagonal words afterwards (it turned out to be too restrictive).

By now it had become apparent that certain letters only occasionally appeared in any of the ‘solutions’ and so I decided to use only those words which were formed from combinations of A, C, D, E, I, L, M, N, O, P, R, S and T. The final dictionary contained 1115 words.

The program now had a sensible running time, taking just over six days to generate 370 grids. It fitted words at the rate of 50 million per second, filled grids being written to a text file. During the processing, as soon as there were more than ten different letters the program backtracked so that no time was wasted producing unacceptable grids. A second program scanned this file and analysed the grids to find what was considered to be the best one for a puzzle.

The main criterion was that at least one of the ten different letters must not appear anywhere in the first across and down words of any layer, because then a zero would have appeared there somewhere, and this would have been inelegant. The next criterion was that, just for my satisfaction, no filled grid should be similar to another one – I wanted at least ten letters different between the chosen four-layer grid and any other one. A further criterion was that no two words should have the same root, e.g. ‘alma’ and ‘alme’. The final criterion was that there must be a single-word anagram of the ten letters. Three grids were found which satisfied these criteria.

It was time to decide how one of them could form the basis for a puzzle but I forget now why I chose the one I did!

Since a word cube is involved, it seemed appropriate to use perfect cubes for the clues. The anagram of the letters was DEPILATORS – how could this be used as part a theme? In the end I decided that the letter values in the clues would be cubes with their first digit trimmed (it looked like ‘hair’ was going to be the theme) but Roger, having removed ‘trimmed’ from the preamble because the connection was not strong enough, came up with the much better term ‘shaved off’. I managed to get the letters of ‘razor’ in one of the clues and that led me to call the puzzle ‘Bearskin’. I was very tempted to call it ‘Hare’, but I thought that that in-joke had been worked to death! (Did I miss a trick here?)

The entries needed to overflow from one layer to another so that there were some decent-length numbers in the grids and not too many clues. I wanted the number of different letters in the clues to be a perfect cube, and so there had to be 27 of them. I originally had 27 clues, but that created unwanted redundancy.

The letters, when sorted, needed to include DEPILATORS and I thought it would be nice to have A WORD CUBE as well. That left eight letters with only the vowels I and U available which was quite a restriction. The only word which could have had any link to a puzzle was, fortunately, PUZZLING.

Presumably some solvers will now know that those little slits between the treads on their car tyres are called sipes!


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Listener No 4569: Bearskin by Elap

Posted by Dave Hennings on 13 September 2019

As usual with an Elap mathematical, I get a feeling of dread. That said, all mathematicals fill me with varying degrees of dread. Elap’s last gave us two 5×5 word squares. This time, we had four 4×4 squares, and it seemed they would be wordy as well, given that the digits had to be replaced “preferably all in upper case”.

The letters in clues stood for 27 different integers formed by taking a perfect cube up to five digits and truncating the first digit and any remaining leading zeros. In fact, they had to be “shaved off” and that, together with the title and 13ac’s r-A-Z-O+r would undoubtedly mean something!

As it turned out, this wasn’t too tricky a puzzle. Listing all the 5-digit primes, minus their first digits and zeros, gave 42 such numbers ranging from [2]7 (3³) through to [9]7336 (46³). After truncation, they were from [6]4 to [2]9791.

The starting point was 4through where UUU (3) was a 3-digit number and had to be 7³ = 343. 17dn (E – pp (3)) came next, with p = 4 and E = 331 or 375. Next was 8th (Uz – pp (3)) with a couple of options for z followed by 12ac (CU – UU (5)) where C had three options but, crossing with 17dn, gave 6656 as its value.

From there on, progress was fairly steady although not as quick as I initially thought it would be. It was nice to just have to rely on pencil, paper and a calculator. No doubt some out there decided that a program written in C#+ would be a good way to tackle it!

Sorting the values into numerical order, we ended up with pUzzLiNG (solvers’ activity in filling the grid), dEPIlaTORS (what replaced values 0–9) and A WorD CuBe (what solvers should end up with). The word cube that resulted had 4-letter words running across, down and through the cube.

Thanks for an enjoyable and easy-going mathematical, Elap.

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Bearskin by Elap

Posted by shirleycurran on 13 September 2019

Bearskin indeed! We really dislike the three-monthly numerical Listener puzzles so there was plenty of bear-like growling and gnashing of teeth from the other Numpty while I discreetly got out of the way and converted a massive bag of greengages to jam then prepared the supper. Yes, of course I had already hunted for traces of alcohol in those verbal clues and had discovered only a dubious B + ir – i – r. Pretty second-rate beer but cheers anyway, Elap.

The other Numpty’s comment was “Why so many letters in the clues, and why do we have some in both upper and lower case – in particular what was the need for a lower-case l that meant that it had to be specifically distinguished, in the pre-ramble (yes it was a bit of a ramble wasn’t it?) from upper case I?” and “That final clue to ‘pz + Z + L (3)’ must be a gentle joke – or does it have a meaning?”

Clearly it did. After solving U and C the growling began and lasted for hours.

It is only in retrospect that I have wondered how Elap managed to create this puzzle and surmised that he must have struggled initially to create four word squares using only ten letters that could be converted to the digits 0 to 9 (and leaving letters to give ‘A WORD CUBE’ and ‘PUZZLING’) without using any letter more than twice. No wonder he needed that preambular clarification of the lower case l.

With a table of cubes of integers to 100 in Adrian Jenkins’ Number File (you can obtain second-hand copies on the Internet) we constructed a list of potential digits and were ‘puzzling’ from then on for rather a long time, but it was the guess that the first word (‘Sorted by numeric value’) was pUZzLiNG that finally got the Numpty Bear moving forward dramatically rather than sharpening claws (and pencils).

The ‘throughs’ helped us by providing intersecting digits and after many hours of working from letters we had to letters we needed, three of the four layers were completed but we could see no way to produce numeric equivalents for d O u A R and P and fill that bottom layer. It was well after midnight that we decided to place the letters we had in numeric order and that produced:


Penny drop moment at last. The final three words were A WORD CUBE and we could place the remaining d P and O to give DEPILATORS. Ha! So that explained the “Bearskin” heard as BARE SKIN.

Finally there was a smile from the Numpty Bear and as it was by now well after midnight, we jointly converted those nine digits to DEPILATORS and produced our WORD CUBE. What was most astonishing was that it didn’t just have real words on all four layers, going aross and down, but also that the through words were all real too. What a fine and challenging compilation.

(Did I say that? I hate the things and am breathing a sigh of relief that it’s three months until the next one and last one of the Listener year.)


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Listener No 4568 Howsat!: A Setter’s Blog By Skylark

Posted by Listen With Others on 8 September 2019

Though my husband introduced me to cryptic crosswords in the Times, and we used to tackle – and sometimes complete – the Jumbo Cryptic on Saturdays, I had always considered the Listener as far too hard to solve, except occasionally when I noticed a numerical, which were great fun, when I could (very occasionally) finish them.

But when working away, my husband moved on to the Guardian cryptics with a colleague, and raved about many setters, but in particular about Nimrod. Having discovered Nimrod was one of the pseudonyms of John Henderson, I then petitioned John for a bespoke crossword to celebrate a significant birthday for my husband. I was delighted when he accepted (and produced a delightful crossword we treasure) and started attempting the Inquisitor with my husband. It took us about a week to solve.

But after a few weeks, it clicked – and I was hooked, making the Inquisitor and the Listener, and occasionally the Enigmatist too, a delightful part of my week. After a year or so, I started trying to set a few puzzles, and after encouraging feedback from test solvers, sent a couple out. But I would never have dared submit one to the Listener if John and Jane Henderson hadn’t kindly invited Neil and I to the 2019 Listener Setters’ dinner. I thought I’d be a charlatan if I hadn’t at least tried to be a Listener setter, so the night before we left for York, I submitted Howsat!

I’d been looking at significant anniversaries for my musical and literary loves, and discovered Miles Davis’s wonderful Kind of Blue was published almost 60 years ago, with the anniversary approaching in August 2019. It was reassuring to read that it was probably the best-selling jazz album of all time. Envisaging mainly blue grids, I’d been playing with grids for weeks, challenging myself to get as many cells as possible to be blue themed. At that stage, I enjoyed creating grids more than clueing. Now, I enjoy both.

Wondering about the title, I noticed that an Ashes series would also be occurring during August, so took the first track, So What, and anagrammed it into Howsat!

I was stunned and delighted when I got the acceptance email – though couldn’t help a smidgen of disappointment that Shane and Roger considered colouring so much of the grid rather tedious – but made up for it by creating spaces for Kind of Blue and Miles Davis underneath the grid. They were so helpful on editing clues. Hardly any of mine slipped through untweaked.

Also, Roger mentioned that he was disappointed my extra letters, which initially read: Evans, Chambers, Adderley, Coltrane, Cobb recording, didn’t mention pianist Wynton Kelly, who had been substituted with Bill Evans for this recording, though Davis gave Kelly one perhaps consolation track, Freddie Freeloader. I had been disappointed by this too, but had thought using DISC might be unfair, because people have bought Kind of Blue in other formats too.

I asked if it was too late to reclue the last nine down answers with extra letters: KELLY DISC rather than RECORDING, was told that it wasn’t, and that because it was originally a record, they considered KELLY DISC fine. I used Shane and Roger’s feedback to help me write hopefully improved clues for the 6 clues that needed changing. I loved exchanging ideas with Roger, emails pinging back and forth between us that day.

So thanks to all the setters who regularly delight me, Shane and Roger for their huge support and all the solvers who have taken the trouble to give me feedback. It was lovely to hear that some people had enjoyed it and that I’d inspired a few others to play Kind of Blue again, as I was doing on August 17th.

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L4568: ‘Howsat!’ by Skylark

Posted by Encota on 6 September 2019

I think I can find 24 out of 42 entries with something of a ‘blue’ theme involved – especially those featuring sea, sadness or colours.  Definitely more that 21, so they are in the majority …

Was it only me that found it took ages to nail down the final few parsings?  I had a tentatively filled grid after about 20% of the time, then spent most of the rest of the time trying to make sense of around ten clues.  1d and 2d were the final two of these, where I’ve assumed that DOWN = ‘in flood’ (the BRB’s nounal definition 7 for ‘flood’ = ‘any great inflow or outflow … e.g. …of tears’ seems to support this) and that LOOS is a Scottish word for ‘loves’ (ah, I’ve just found this meaning of LOO in the BRB!).

Of course the theme was 1970s rock albums.  David Bowie’s LOW appeared on Row 2, Neil Young’s HARVEST on Row 12.  There was even the Pink Floyd Track DOGS (from ‘Animals’) on Row 5.  So, given many of the clues seemed to have a Blue tinge, then the missing album is clearly Bob Dylan’s TANGLED UP IN BLUE.  Not quite sure whether I need to call him BOBBY DYLAN or R ZIMMERMAN as the Creator to make it 10 letters but I’m sure JEG will be lenient.  Won’t he?

Or, alternatively, I submitted this.

SCAN0626 copy

Finally I tried for a while to makes sense of the Title – then thought ‘So What?’.

Joking apart, a fun puzzle from Skylark – many thanks!

Cheers all,

Tim / Encota

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