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Archive for March, 2016

Cycle 20% More by Smudge

Posted by shirleycurran on 25 March 2016

Statutory duel 001

I quite like the way the levels of Listener difficulty are varied from week to week so you never know whether you’ll be done by 9 on Friday evening or still be sweating over it till Monday. I suppose this raises the whole question of how challenging and time-consuming Listener puzzles should be. Had we but world enough and time …

The title of Smudge’s ‘Cycle 20% More’ told us nothing at all. Were we meeting a new setter who is a fanatical ‘Green recycler’ or a seasoned setter sheltering himself (herself – I’m perpetually hoping that a few more lady setters are lurking in the wings) under a new identity to deflect all the flak that he/she suspects will come his/her way when solvers see his/her astonishing grid with three unches in six and strings of open lights? One seasoned solver commented to me “This will have to be something special to get past the editors with that atrocious grid!”

Half an hour after downloading the puzzle we had re-read the preramble (it was one wasn’t it!) and solved a mere eight clues and I hadn’t even checked whether Smudge earns his/her entry ticket to the Listener Tipsy Gang – so a check was due and I didn’t need to read far down those clues (with their sometimes highly implausible surface readings; if I said “Girl in family circle keeping bit of jumbly sofa and tree”, they’d think dementia has set in).

What do I find? ‘Lawfully gobbed spot of alcohol, 50% proof (3)’ We decided this was A(lcohol) + TE(st) giving ATE and that the L was moving into ‘gobbLed’ meaning that ‘Awfully’ had to exit the clue. I think Smudge will be staggering ‘awfully’ at the setters’ dinner in Windsor next weekend if he is into 50% proof! Next I find ‘Glass with whisky is often halved slate (6)’ We move the S here producing ‘late’ as the word to exit and S with MALT O, which Chambers tells me is coloured glass. Yes, I’m writing this blog in retrospect, when we had realized that those exiting words (WANED, DECEASED, GONE, WRAITH, LATE, JUMBY, HAUNT, SPIRIT and so on), are all, as the preamble told us, ‘loosely thematic and must be discarded’.

A music expert has explained this to me saying of the last two Gilbert and Sullivan creations that the song that gives the discovery that resolves the plot has the line, ‘The Ace is lowest, lowest, lowest, so you’re the gho-est, gho-est, gho-est’  (not one of WSG’s finest moments, though the generally overlooked last two have very good music).” he added. However, at this stage, we simply noted that lots of dead, deceased and wraith-like characters were leaving our clues.

In retrospect, too, I realize that Smudge had a BARMAN pulling a pint in clue 2d. ‘Weak thing that baRman may pull with note for its top (5)’ with the ‘baTWOman’ moving in from clue 33d, shedding the TWO to be used in the endgame and taking in an R as part of TENETS SURELY, as well as giving us FA + [p]INT = weak. and he was into the rum babas too! A definite entry ticket to the LTG with this mixture of malt, beer and rum!

What a stroke of luck that the letters that seemed to be moving in those across clues gave us A S SULLIVAN. GILBERT had to be there and as we were told that ‘the moved letters show the Creators going their separate ways’, we looked in the opposite direction and teased out WilliaM S Gilbert. Wikipedia time as usual in our Listener solves. What was their last production before they went their separate ways? Not my father’s favourites that I know well, The Mikado or the rather lovely Iolanthe, but a relative flop, The Grand Duke – and as I read the plot, my thought was ‘No wonder!’ Still, it did talk about the STATUTORY DUEL (which was likely to be the ‘thematic Contest’ that was to be revealed), the secret Sign which was eating a SAUSAGE ROLL (so we knew that sausages were going to ‘roll’ and were probably jumbled in ‘five rows of the filled grid’). Even better, we learned that the ‘discovery that resolves the Plot’ and dethrones The Grand Duke is that Aces count low in the ‘Statutory duel’ and that he has not, therefore, in the contest for the title, drawn the winning card.

I have been blogging this puzzle for at least five years, ever since Chris Lancaster asked for more contributors. My response, then, was ‘Sure, I’ll write blogs but they will probably be blogs about failing to solve’. (To which his response was ‘No problem, they would be just as valuable as blogs about successful solving’). The Numpties have made a few errors since then but never ‘failed to solve’ – even the Sabre Knights’ moves or Mash’s Klein Bottle. However, until that p.d.m. of the Aces dropping to the bottom of clues, I was despairing of completing this one. Suddenly we began to enjoy it as crossing letters helped us to solve clues and the grid filled.

Grid to submit 001As we were confident that THE GRAND DUKE had to go into 1across, we could almost side-step the complicated moving of words in the down clues and the extraction of parts to change the PFDFMJESTTCD of 1ac. and leave the jumbled letters of TENETS SURELY, though we still had to link clues 1 to 12 with the remainder to tease out the solutions.

A fellow setter who laboriously worked out this complicated step gave me his findings: FOURier -> Tier/  baTWOman -> baRman / lAgs -> lEgs/ babAs -> babEs/ FIVE-bar -> T-bar/ Quit -> Suit/ adeNINE -> adeN/ sKim -> sLim/ subJection -> subSection/ slEIGHT-> slY/ mAst -> mUst/ Ass -> Ess, which, of course, tell us that to those letters we had to add were 4, 2, A=1, A=1, 5, Q =17, 9, K=11, J=10, A=1, 8 and A=1.  and leave the jumbled letters of TENETS SURELY.

A sausage hunt ensued. This was verging on the ridiculous – but then, so was that plot, and, of course, we speedily spotted SAVELOY, SAUSAGE, BALONEY and LORNE and my newest edition of Mrs Bradford’s gem gave us CORN DOG. Making those adjustments revealed the STATUTORY DUEL and we breathed an immense sigh of relief and returned to normal life.

What an unusually critical Numpty blog and, in truth, I am very impressed indeed by the ingenuity of the compilation, the vast amount of relevant material incorporated, and the superb use of this rather obscure theme. Perhaps it could have been made a little less tortuous, though, by removing a step or two? These were some of the toughest clues I’ve ever encountered and I imagine a number of solvers are still head-scratching. So many thanks, Smudge. Dare I say that we’ll look forward to your next compilation or should I say we’ll dread it?

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Listener No. 4388: Cycle 20% More by Smudge

Posted by Dave Hennings on 25 March 2016

Spoiler alert: This was one tough nut to crack!

OK, so it’s not really a spoiler since, if you tackled it, you would know exactly that. This, was, apparently, the work of a new setter. With my detective hat on, it seems that it was. And what a stinker stunner.

For a start, the preamble was, to say the least, convoluted. It seemed that we were destined to find Creators (going their separate ways), a Plot, a Contest, a Title and a secret Sign. Describing the clues in a nutshell also proved tricky, but here goes…

Listener 4388Acrosses had one letter travelling between words, one of the words needing to be ignored to solve. The downs had words travelling between clues with minor modification of “a section of one or more letters” on the way. I presumed this meant that ‘setter’ could become ‘letter’ or indeed could become ‘solver’ (but I wasn’t sure too sure about that). One of the differing parts would eventually need adding to the top row. The across letters spelt out the Creators, but were otherwise entered normally. Down answers needed to be entered according to a discovery which resolved the Plot.

I suspected that Smudge had been honing the preamble for several years.

The 12-letter entry across the top had no unches. Unfortunately it had no clue either. 13ac Northern Irish rustic cared, wanted Scots pinched (6) looked like ‘cared’ could become ‘carted’ with ‘wanted’ becoming ‘waned’ and, with ‘wanted’ being discarded, we got NIRLED. I had to check that ‘to cart’ meant ‘to lead’; in fact, under lead1 we had ‘cart (dialect)’. All that took nearly 5 minutes. The next few failed, but 17 Lawfully gobbed spot of alcohol, 50% proof? (3) became Gobbled spot of alcohol, 50% proof? (3) and led to ATE from A + TE[ST].

I thought I’d give the down clues in the top left corner a go.

I soon came back to the acrosses having failed miserably! After about 40 minutes, I had gone through them once. Although I had only a few actually solved, I had made a note of letters which could be the culprit in each clue. Some eluded me, but already I had T•ebli•s•wassu•li•a•. It didn’t take too long to pick out Gilbert (OK, in reverse) and Sullivan.

I was over the hill and half way home. Except I had no idea how that was going to help me with the down clues, or indeed any other part of the puzzle. (In hindsight, I was probably only 10% of the way there.)

Time to give the down clues some serious attention. 19dn Pairing complex Fourier analysis with positive entropy for nearly all (8) seemed a good place to start, with S, N and I already in place. This looked like an anagram of ANALYSIS with AL replaced by PS (S = entropy). SYNAPSIS tumbled out, and ‘Fourier’ needed dropping.

That ‘Fourier’ looked suspicious, especially with ‘five-bar gate’ next door at 20dn. And don’t forget ‘batwoman’ at 33dn. Exactly how these were transformed into words that were needed by their partner clues eluded me. There were even words like ‘light’ at 3dn which could become ‘eight’. My brain was beginning to hurt, and I was already two hours into the solve with no end in sight.

Here, one of the problems was trying to deduce what words needed adding to the downs to enable the clues to make sense. That was equivalent to jogging up to the starting block and then having to run the race, without knowing whether it was going to be a 100 metre sprint or a 1500 metre. (I’ll ignore the marathon for now.)

Back to SYNAPSIS at 19dn: the I that I had was in the sixth position not the seventh, so presumably we were looking at anagrams with both Ss in the unchecked squares. Well, it was a start.

I was solving clues gradually as I teased out wordplay, definition and word/letter movements. 6dn League must quit [from suit in 35dn] fold after German assent; I’m not moving (7) gave J’ADOUBE which I’d not heard of before — JA + DOUBLE (fold) – L (league). 10 Sailor with line cutting mast head up once covering wound on head (6) enabled TURBAN to be slotted into place without needing to resolve the wordplay!

I think I can say that, for a novice, Smudge’s clues were incredible, and used devices that I hadn’t come across before. Take 1dn Painters missing bits of basins (4) which needed a word based on ‘Fourier’ to be added. The answer was fairly obviously PANS, and it looked as though it was progressive elements of PaiNterS. In fact, ‘Fourier’ became ‘tier’ to give Painters missing bits of tier basins (4). OK, it doesn’t make any sense, but it wasn’t meant to. The answer was PAINTERS – the letters of TIER.

It was as I was concentrating on the bottom right corner that all those As finally hit home. We weren’t dealing with simple anagrams, but even simpler movements of letters A to the end of their answers.

At about the same time, the top row was beginning to take shape with the numerical value of letters, or indeed just numbers, being added to their true letters. So far, I had TH••RA•D•UK•, and The Grand Duke by Gilbert and Sullivan finally revealed itself to be the theme. I won’t go into the plot in detail here; as with many G&S operettas it is tortuous. Suffice it to say that part of it deals with a statutory duel which replaces dangerous swordplay with the drawing of cards, the man with the lower card losing. (Go here for Wiki’s description of The Grand Duke.)

So all those As at the bottom represented Aces which beat, or at least didn’t lose to, the opposing card which was added to the top row. This seemed the wrong way round to me, but another piece of the jigsaw was fitted. I still had about a dozen clues remaining to either solve or rationalise the wordplay for.

Needless to say 15 and 16ac were two of these, since the answer to 10dn wasn’t TURBAN but TULBAN. Thank goodness the L was checked. This enabled 15 to make sense [Every] one of Highland kin kine in a state before … (5) with the … representing what came next and giving KYLOE.

The last clue that I rationalised was 7dn Earl, not baron, in one of four including wealth (4) which gained a modification of ‘Aden’ in order to make sense. Seeing a word lose a number (eg ‘sleight’ giving ‘sly’) was easy; realising that there was a word which worked the other way was trickier, and here it took me ages to work out that ‘Aden’ became ‘adenine’, despite having known the answer was EASE since very early on.

Finally, what was the secret sign? Wikigoogle tells me it was a sausage roll, so we had to find anagrams of types of sausage in the grid. They turned out to be LORNE, BALONEY, SAUSAGE, CORN DOG and SAVELOY. LORNE and SAVELOY could each be entered in more than one way, but only one way gave STATUTORY DUEL running NW–SE in two of the diagonals.

Actually, that wasn’t quite ‘finally’. The wiki article tells us:

Ludwig and the Princess are about to go off to yet another wedding party, when Ernest, Rudolph and Dr Tannhäuser burst in. The Notary reveals that the Act regulating statutory duels specifically lays down that the ace shall count as lowest, so Ludwig did not win, was never Grand Duke, and cannot have revived the act. Within seconds, the Act expires, returning Ludwig to the living. All dance off to get married — Rudolph and the Princess; Ernest and Julia; and Ludwig and Lisa.

Thus, the Aces are correctly placed at the bottom of the grid. You also get a flavour here for how convoluted and bizarre the plot is!

Listener 4388 My EntryI breathed a huge sigh of relief as I finished this puzzle on the morning of the Listener Setters’ Dinner in Old Windsor. I just needed to work out the title, but that eluded me… and still does.

What a phenomenal puzzle, and dare I hope for another tour de force from Smudge again sometime. Thanks for the challenge.

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Listener No. 4387: One-man Band by Emu

Posted by Dave Hennings on 18 March 2016

Here we have Emu’s first Listener, although he has a string of Evs under his belt, albeit the last being back in 2006. We were in fictional territory this week, with a race and obstacles which would, with the help of unwanted characters, reveal a quotation. Just to be awkward, the quotation and a final instruction were interleaved so probably wouldn’t become clear until most of the clues had been solved.

Listener 4387I started on the acrosses, but after half a dozen clues got nowhere so decided the downs were a better bet. Luckily, 2 DISHWATER and 4 Spirits perish in albatross shoot (12, two words) ASTRAL BODIES were slotted in. (OK, so I needed help to disentangle DIE in ALBATROSS* and was lucky that the anagram indicator contained the extra letter — shoot for shot.)

5dn was SOME, and I felt I could go back to the acrosses for the top left corner. ADMISS, FIASCO, TAY and STABS went in before I tried 10dn Mangles data covering second quarter of year (6). At first glance, it looked like M was the extra letter and FICHES (angles) and FICHES (data) were first guesses, but the T of TAY finally led me to FACETS.

The bottom left corner was equally forgiving, and most entries west of the Greenwich meridian were soon complete. If only the eastern bloc had turned out to be as easy, but no. The long 13dn Bill, a Newfoundland fisherman, is enthusiastic about reactor (12, two words) wasn’t as helpful as its opposite number, despite the extra character almost certainly being the A in ‘reactor’. As a result of this, the quotation and instruction were still a mystery.

Gradually, the grid filled with some devious extra letters needing to be discovered. My favourite clues were:

10ac If turned away after [c]losing time, a Scotsman produces a flask (6)
IF< + A SCOT – T
FIASCO
23ac WWI soldiers about to hold tru[c]e following petition for release of prisoner (6, two words)
BEF about GO + F
BEG OFF
9dn Feline cry of assent in Rome[o] and Juliet concealed from James the First of England (7)
SI + JAMES – J + E
SIAMESE

 
It was very late in the grid fill that I managed to identify the quotation although the instruction had to wait until the end. Before disentanglement, they gave Ancdisimprleclfaiththeao from the acrosses and nnonrevomanwnelblood. Thus, “…and simple faith than Norman blood” was the quotation from Tennyson’s Lady Clara Vere de Vere and Circle one vowel was the instruction.

The quotation is preceded by “Kind hearts are more than coronets…”, and the classic 1949 Ealing comedy Kind Hearts and Coronets immediately came to mind. The film is told in flashbacks of the life of Louis D’Ascoyne Mazzini (played by Dennis Price) as he awaits death on the gallows. The film depicts his killing of eight characters of the D’Ascoyne family who stand in the way of his becoming Duke, a title that he believes he deserves. All the victims are played by Alec Guinness: the DUKE; Lord Ascoyne, the BANKER; REVerend Lord Henry; GENERAL Lord Rufus; ADMiral Lord Horatio; Young ASCOYNE; Young HENRY; and LADY AGATHA D’Ascoyne.

These characters could all be found in the grid in the shape of the gallows and hanged man from the children’s game. Unfortunately, my first spot of the ADMiral at the beginning of the top row didn’t look quite right. I searched the grid for an alternative. This was found diagonally as the support for the top beam and resembled hangman as I distinctly remember it. Was this a deliberate trap? The hanged man’s head that needed circling was the A of BANKER.

Joining all the lines into a continuous grid may have been aesthetically pleasing, but I decided against this since, in theory, this didn’t demonstrate that I had identified the names accurately — ALADY AGATHAN and YADMY?!

Listener 4387 My EntryA most enjoyable puzzle, thanks Emu. It’s a shame that I only possess the VHS tape somewhere that I cannot now watch. I decided that my animation wouldn’t be too gruesome!
 

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One-man Band by Emu

Posted by shirleycurran on 18 March 2016

Hangman 002There is nothing too troubling in Emu’s preamble but we clearly have to fill the grid and spot that ‘interleaved’ line of poetry before it is going to mean very much to us.

Naturally I check that Emu has earned his place as a Listener oenophile and he doesn’t disappoint, in fact he almost exceeds the limit. He begins with ‘If turned away after closing time, a Scotsman produces a flask (6)’ (IF< + A SCOT [C]losing T[ime] giving FIASCO). Then we find ‘[M]orally turned the wrong way for whisky (3)’ (“Wry” heard giving RYE). Not satisfied with all that whisky we find ‘Not much to drink – one of Will’s cron[I]es has run out (3)’ (TROT less R[un] giving TOT).

The down clues continue the drinking – ‘Spirits perish in albatross sho[O]t (12, two words)’ (ALBATROSS* + DIES = ASTRAL BODIES) then ‘Doctor’s other half is pocketing a five[R] in the Bull (6)’ – A difficult clue that one HYDE [i]S(Jekyll’s other half) takes in A, giving ‘five in the Bull, which Wikipedia tells us is a constellation where the HYADES are five stars. I am not really surprised when clue 31 tells us ‘Tipsy old b[O]y I guided by the hand (5)’ (O + I + LED – indeed, Emu must have been pretty well OILED after all that tippling. Cheers, see you in the bar at Windsor, Emu!)

A lovely set of clues and our grid fills steadily until, with a few hiccups, we have a rather strange set of extra letters to decipher. It puzzles us for a while before we see words that we can feed into Wikipedia AND SIMPLE FAITH ….. BLOOD and, as usual, Wiki comes up trumps with a Tennyson poem I have never encountered before (and I am not really surprised – it is a rather vicious attack on the lady isn’t it, and not really her fault if she is of noble birth)

Trust me, Clara Vere de Vere,
  From yon blue heavens above us bent,         50
The gardener Adam and his wife
  Smile at the claims of long descent.
Howe’er it be, it seems to me,
  ’Tis only noble to be good.
Kind hearts are more than coronets,         55
  And simple faith than Norman blood.

Of course, line 55 is the prompt we need and we have to go back to Wiki to see who were the characters who had to be eliminated in Kind Hearts and Coronets. What a story! I find, of course, d’ASCOYNE, HENRY, the BANKER, LADY AGATHA, the ADMiral, the REVerend, the DUKE and  the GENERAL and drawing lines through all of those produces the game we used to play at school in those silly hours before the holidays – Hangman. Yes, I originally highlighted the first ADM(iral) I encountered and that produced a convincingly counterbalanced scaffold but I remember that the diagonal strut was part of the game and switch to that.

One thing left to do. Interleaved with that quotation were the words CIRCLE ONE VOWEL. I have a rather wonky Mazzini on the gallows with warped legs and the only convincing vowel to circle is that A, which provides him with an extremely small head but sobeit.  Thank you for the entertainment, Emu.

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Listener No. 4386, Hailstorm: A Setter’s Blog by Elap

Posted by Listen With Others on 13 March 2016

The Theme

I have long been intrigued by the Collatz conjecture. Looking at Wikipedia, it has all sorts of names: Ulam conjecture, Kakutani’s problem, the Thwaites conjecture, Hasse’s algorithm and the Syracuse problem, none of which I had heard of. The Wikipedia entry continues, “The sequence of numbers involved is referred to as the hailstone sequence or hailstone numbers, or as wondrous numbers.”

The conjecture states that if you take any positive whole number greater than one, and if it is even, halve it, or if it is odd, multiply by three and add one, and keep repeating the process on the resulting number, you will always end up with 1.

They are called hailstone numbers because they rise and fall rather like the movement of hailstones after they have been formed in a cloud.

It was while doing something totally unrelated to puzzles (designing a humane badger trap) that I suddenly wondered whether it was possible to fit a sequence of hailstone numbers into a symmetrical grid, or if not then a sequence with just one number missing (“Solvers are to write the missing number underneath the grid”).

The Grid

Once more resorting to my trusty 20-year-old Pascal compiler, I found that it was not too difficult to fit an all-but-one sequence into a 7 x 8 grid, and so I set myself the challenge of filling an 8 x 8 one.

I didn’t want any single-digit numbers or many with four digits, and after a little investigation I found that the number of lights in an 8 x 8 grid was far more likely to be 38 than any other number, given my criteria for the nature of the bars in the grid. I looked at various sequences, and the one which had 988 near the beginning had plenty of 2-digit numbers and no more than two 4-digit numbers. This sequence was the first one I tried when trying to create the grid.

I ran my antique Grid Generator specifying 38 lights and other strict criteria and provided a hailstone sequence of 41 numbers, all but three of which were to be fitted into each generated grid, filled grids being written to a text file for subsequent analysis.

Listener No 4386 Grid Analysis

The idea was that I would scan the text file (using another program) for filled grids for any where two of the three missed-out numbers were at the ends of the sequence, thus implying that there was just one number missing in the middle somewhere. If there was a filled grid which had no missing numbers (because all three omissions were at the ends of the sequence) then so much the better – I’d have a grid which contained a whole sequence. A complete sequence in the grid would be the ideal, but it was unlikely.

Many of the filled grids were based on the same base grid but with permutations of some of the entries. For example, 71 and 91 would be interchangeable if the first digits were unchecked. For my own satisfaction I wanted to find a grid that could be filled in only one way, but again this was unlikely.

Eureka! The 445,153rd grid contained a whole sequence and was fillable in only one way! I decided to let the run finish in case there was a more pleasing grid, and this took a few more days and quite a few kWh of electricity. This, and my wife’s wish to install an electric fence to keep out the badger, would clearly trigger an increase in my direct debit to Good Energy.

Out of over 25 million grids which fitted my criteria, 4,724 different ones were filled in 36,247 different ways. Out of these filled grids, 459 contained a hailstone sequence with one number missing, but 5 of the filled grids contained complete sequences. Two pairs of these were the same grid with two entries interchanged, but one grid contained a hailstone sequence which could be fitted in only one way. This was my chosen grid and was way beyond my expectations. I was so pleased that I decided to let the badger carry on as before, and anyway that electric fence wouldn’t be very nice for our neighbour’s numerous cats.

The Clues

What form would the clues take?

Since the theme was hailstone numbers, which many solvers could be unaware of, I decided to explicitly explain what they were in the preamble. The clues would then need to feature the hailstone sequence concept – but how? I thought of secretly making the letter values form a hailstone sequence, but that would have made the puzzle too easy for solvers who twigged, since given one hailstone number the rest of the letter values could be determined.

After a rest and some further thinking, during which time I thought further about the badger trap, I decided to use a hailstone relationship between upper- and lower-case letters. Since the preamble would remove the surprise of a hailstone sequence in the grid, I needed to have a further think. I created over six dozen variations of the same hint which said that the grid need to be filled with a hailstone sequence, and wrote a wee program which would show which, if any, of these could be used as a message in the completed grid, where A = 1, B = 2, etc. The number of digits in the hint had to be exactly 64, none of the lights could begin with a zero, and they all had to be different. Just one of my hints was successful, reading ‘PRODUCE 38 HAILSTONE NUMBERS FROM 988 AND FILL GRID’. It would have been nice to have the hint also request the erasure of the cells, but 64 digits was just not enough.

Having come up with this hint, I wondered whether it was acceptable – does ‘from’ include the 988? I looked up ‘from’ in Chambers, and one of the meanings is ‘beginning at’ and so the hint was equivalent to ‘PRODUCE 38 HAILSTONE NUMBERS BEGNNING AT 988 AND FILL GRID’ and I was happy that this implied that the sequence started at 988.

It is sometimes possible to fit the numbers into an empty grid without using any trial and error, but it is not possible to use the method in this case. I therefore decided to place the unchanged digits in shaded squares (they ended up as circles in the final puzzle).

The less-than-usual cross-checking of the digits could make cluing difficult, and so I arranged the clues in ascending order of their value.

I called the original puzzle ‘Hailstone’ but one of the vetters suggested that ‘Hailstorm’ would be better, and I agree!

Update

It is with much mournfulness that I must mention that our mighty mass of moving muscle met his maker after being mown down one misty morning by a moving motor vehicle.

However, my wife, who had recently read that badgers rarely live alone, has just found three more holes in the lawn. Such is life…
 

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