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Listener No 4621: True by Piccadilly

Posted by Dave Hennings on 11 September 2020

Piccadilly is primarily a mathematical setter these days, and his last Listener was three years ago with the superb Properties of Numbers — II. I’m not sure how setters go about clueing this sort of puzzle we had this week. Do they think of arbitrary words or phrases that just appeal to them or is there something more scientific? Whichever, RA – T + (E+N-T+E-R+S)A(BIN – N) was probably my favourite!

The straightforward way into this puzzle was through the last clue 29dn TA which could have few possibilities given that it was one of the three clues that we were told was palindromic in the preamble. T! in 14ac excluded 11², so 7³ it was with T = 7, A = 3. 21ac TA + RR + IE + R + S pretty much gave R = 5.

From there, the solution came fairly quickly with no more than a calculator required, although I’m sure some solvers would have created a spreadsheet with macros to solve it — just for fun. I’m not one of those. Once the grid was filled, converting the numbers to letters gave I hate numerical crosswords because making a mistake means starting all over again. Luckily, I wasn’t required to do any backtracking here, so breathed a sigh of relief.

However, I felt that this surely didn’t describe Piccadilly’s attitude to his artwork! I wondered whether there was an alternative, such as I love numerical crosswords despite making a mistake meaning a start all over again! Sadly no.

Very enjoyable, thanks Piccadilly.

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True by Piccadilly

Posted by shirleycurran on 11 September 2020

There is one thing I regularly say about numerical puzzles: I HATE NUMERICAL CROSSWORDS BECAUSE MAKING A MISTAKE MEANS STARTING ALL OVER AGAIN. We (or I should say ‘he’ as this three-monthly departure from the comfort of the verbal ones is his province) invariably make that mistake and the air becomes somewhat ‘blue’ at the third (or tenth) new start. This time, after a couple of hours fumbling and muttering, he announced “Impossible! I can’t do this with just pencil and paper.” (which is his approach to the things).

343 went in fairly early on at 29d, 7 cubed and a palindrome, so T = 7. That was about the limit of my comprehension but I know Tim (Encota) will be providing a detailed explanation of his progress so should leave that to him.

My other concern with these three-monthly departures is whether we can admit numerical setters to the Elite Listener Oenophile Outfit. If there are no doubles or triples, it becomes rather dicey. But there was hope for Piccadilly. All his clues made real words (quite a feat in itself). Initially I was feeling some ANGST! (14ac) and GOING BANANAS (25ac) and together with ROUT, CARNIVALS, RAT ENTERS A BINN and USE BEAN TINS (!) was wondering what was going on, but Piccadilly redeemed himself. There was MALT at 35ac. What can I say? 39d TA Piccadilly.

Postscript: Piccadilly, if you hate them as much as I do, what are you doing setting the things? If the editors received none at all, they might treat us to misprints, jumbles, Playfair codes and all those other joys.

Another postscript: A solver has sent me his solution route which turns out to be a lot more straightforward than we thought.

14a => T! < 10000 => T < 8

29a is a 3-digit palindrome => either 11^2 or 7^3 so T=7, A = 3, 29d = 3-4-3

30a => S < A => S = 1 or 2.  But S=2 => 30a = W – O + K cannot be 3-digit => S = 1

22d => R>A  => AR is at least 3*4; 17a => C^AR < 100000 => C < 12th root of 100000 ~ 2.6 => C=2

4^4 = 256, 6^6 = 46656. So the only way 21a can be 4-digit is R=5

31a => E! <1000 => E<7; 17d = 2^E(5 – 1 + M + I +2) – 1.  If E were 4, that would be at most 2^4(6 + 18 + 19) < 1000, so E > 4 => E = 6

I > G.  WAN = 3WN is at most 3*18*19 < 3*20*20 = 1200.  If I were 9 or bigger, A^I would be at least 19683, and 4d would be 5 digits; thus 19683 I=8, G=4, 21a=3-19-8

8d is a palindrome divisible by G=4 with one cell being 2-digit => 8d = 2112 or 6116.   8d = 4L(OB + U – L – 6) > 4*9(9*9 + 9) = 3240 => 8d = 6116 (either 6-11-6 or 6-1-16)

So L divides 6116/4 = 1539 => L = 11

34a = 8N^2 + 5 < 1000 =>8N^2 < 995 => N^2 < 122 =< N < 12.  L=11. So N=9 or 10.  If N=10, 34a = 805  and there are no cells with 0.  So N=9, 34a = 6-5-3, 14a=5-15-1

32a = COOL – S = 22*O^2-1 is 4-digit beginning with 4 => 4000 < 22*O^2 < 5000 => 181 < O^2 < 227 => O = 14 or 15.  If O=15, 32a=4949 which cannot be entered as 3 cells.  O=14, 32a=4-3-11, 26d=18-5-6, 7a=19-6-5

7d = 53*M^2 is 5-digit starting with 19 => 358<M^2<377 => M=19, 7d=19-1-3-3, 4a=6-9-16, 35a=4-3-8-9, 9d=5-13-1, 11d=2-5-19, 27d=19-8-3

22d = 2*B^3-7 = 19_3 from the crossing entries => B^3 <= 1000 => B=10, 22d=19-9-3, 10a=8-2-3, 18a=18-8-9-4, 25a=7-3-18, 1d=8-8-14-6, 3d=7-11-1-18

8d=6116 from above means that U=16, 13a=1-1-13 (which resolves 8d=6-1-16), 16a=6-19-3, 24d=1-1-11, 5d=9-5-6-9, 6d=16-14-2

From crossings, 15a=2-3-16 => V=17, 17d=3-3-3-17, 19d=8-6-7-5, 23d=8-1-11-9

28a = 9*(3K + 17) = _39 from crossings so must 639 =>K=18, 28a=6-3-9

30a =W^2 +4 = 1_3 from crossings => W^2 = 1_9 => W=13, 30a = 1-7-3, 20d=4-6-9-4. 4d=6-2-10

That leaves D=15 with the clues using D confirmed by the full grid.

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L4621: ‘True’ by Piccadilly

Posted by Encota on 11 September 2020

Thanks first of all to Piccadilly for a beautifully constructed puzzle!

I still recall well the puzzle The Properties Of Numbers II from three years ago, so knew we’d be getting something good. I wasn’t disappointed!

Of course the error-checking facility provided by the number-to-letter conversion at the end removed one of the most common gripes heard about Numericals: “I posted it off but have no idea if it was correct”, or similar.

With hindsight I should have made more use of the fact that no cell would contain a number greater than 19, but I kept wondering if there was some kind of trap in that logic (e.g. there might have been a 61 in the down clue and a 16 in the across clue). Luckily that proved not to be the case!

The way in with this puzzle (for me at least) was to start with the powers/ exponents used in some of the clues, e.g. 29d’s T^A. even if T=2 then A can’t be more than 9. Similarly the R^R in 21a limited R tightly.

I maintained a simple table in Excel (above), showing letters in one direction and their possible values (1 through 19) in the other. As one clue or another allowed certain values to be eliminated, I marked that clue number in relevant cells in the table. I always find this useful if (when!) I make a mistake somewhere along the way. [Aside: if you use Excel but don’t use Cntl-Enter yet – for filling multiple cells with the same value – then it can save you much time in tables such as this].

All great fun – many thanks!

Tim / Encota

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Listener No 4619, Six-pack: A Setter’s Blog by Hedge-sparrow

Posted by Listen With Others on 6 September 2020

Sometime last year I decided that it was about time I returned to my own subject of physics for a puzzle. Casting around for possible ideas, I read an article on the Standard Model of particle physics, which classifies the various fundamental particles (of which the famous Higgs boson is the most recently confirmed example), and describes the relationships between three of the four fundamental forces of nature (the missing one being the gravitational force). The thought came that quarks – with their different “flavours” of “up”, “down”, “top”, “bottom” “strange” and “charm” (or “charmed” as Chambers would have it) – could form the basis for a puzzle, with different answers being entered in accordance with the different quark flavours.

When I was studying physics in the late 1970s / early 1980s, the concept of quarks was still relatively new, with definite proof of their existence having been achieved not so many years before. These days, most people (thanks to Stephen Hawking and others) are aware of the term “quark”, and have at least some notion of what a quark is, so I hoped that the subject wouldn’t be too esoteric for a puzzle.

In diagrams and discussions of the Standard Model, the six quarks are often paired as up / down, top / bottom, and strange / charm. This suggested the idea of using sets of “double” clues, with one set for each of the three pairings; and for each double clue, the two answers entered in a manner representative of the two flavours for that set (e.g. top / bottom = top or bottom half of the grid, up / down = answers entered either going up or down). For the strange / charm pairing, the term “strange” suggested jumbled entries, and with a bit of a stretch of the imagination, so could “charm”: however, I really wanted all the entries to be real words, so I decided to try to make the answers for this set anagrams of other real words that would form the entries. I decided also to include the “corrections to misprints” gimmick in the clues in this set to yield the term “flavour” as a hint to solvers, with the idea in my mind that these clues would constitute the “charm” group (although the puzzle didn’t make this explicit).

Additional constraints were that I wanted the different flavours to appear thematically in the final grid, along with the theme-word “QUARKS”. Oh, and also somehow to acknowledge the two physicists, Murray Gell-Mann and George Zweig, who independently proposed the existence of quarks in 1964.

Writing everything down like that makes it seem like quite a lot of stuff to fit in, but anyway, I set to work trying different grid lay-outs and different entries that would give me UP, DOWN, TOP, BOTTOM, STRANGE and CHARM in appropriate positions and formats in the grid: for the latter pair, GARNETS and MARCH were obvious anagrams for the jumbled entries representing their flavours. I’m not quite sure why I decided on the 14×11 grid format – I think it was probably because I wanted the theme-word QUARKS to be at least horizontally central (hence an even number of columns), but found a 12×12 grid too restrictive (and I’m not really so keen on 14×14 as a rule). In fact the grid construction was not so onerous as it might be imagined it would be: I found that the jumbled entries, despite the need for them to be anagrams of other words, gave quite a degree of flexibility to the grid construction, and the final grid (which always grows “organically” with me rather than being fixed at the start of puzzle development) actually turned out in the end to be reasonably “Ximenean” – sadly a characteristic I don’t always manage to achieve!

At some point during the construction process I decided that the names of the two physicists could be derived by solvers by unjumbling letters from indicated cells in the completed grid, so I just needed to ensure that the necessary letters – including Z and W – were present somewhere in the grid.

With a completed grid, I turned to the process of writing the double clues, and this proved to be quite tricky. Each double clue needed to yield a pair of answers whose grid entries were appropriate to the pair of quark flavours represented by that clue set: however, I didn’t want it to be obvious that each double clue from Set 1, for example, yielded one answer entered in the top half of the grid, and a second answer entered in the bottom half – I felt this would give the game away too easily. So my first version of the puzzle had no indication of where any of the answers went, other than the fact that – within each set – the answers to the first part of each double clue were in “normal” order. Spare a thought, then, for LWO’s very own Encota, who somehow – in these almost impossible circumstances – managed to test solve the puzzle (and, even more remarkably, is still on speaking terms with me! 😊) As always, Tim gave me some very helpful comments and advice, as a result of which a much better – and fairer – final puzzle emerged, which was duly sent off to the Listener editors.

The thought of the reaction this puzzle might get still gave me quite a bit of angst, but in the end, I think it went down fairly well with solvers. The two main points of contention seemed to be: (i) the difficulty of understanding the preamble; (ii) the large number of different dictionaries referenced.

Regarding the first of these points, Tim – in his test-solver’s notes – had indicated that the preamble to my original version of the puzzle could be made clearer. I duly set about writing what I hoped would be a better preamble: I think it probably was a bit clearer than my original, but it turned out to be roughly the same length as this blog! Roger Phillips, in his review of the puzzle, managed both to clarify the preamble further and shorten it to the published length; but even so it still took a bit of careful reading and thought to get clear in the mind. Hopefully it didn’t put too many solvers off.

For the second point, I was rather shocked when Roger pointed out to me that the term “side lobe” isn’t included in any “standard” dictionary other than the OED. In my work as an engineer / physicist in a large automotive company, the term “side lobe” is so familiar to me that, when I saw it was an anagram of “obelised”, I used it without even thinking to check that it was included in dictionaries. So, along with the other Collins and ODE references, it wasn’t too good: but thankfully, Roger kindly let it go. In hindsight, I should have omitted the ODE reference, since “Foggy Bottom” also appears in Collins, and this would have reduced the number of dictionary references to two, rather than three. However, I didn’t: hopefully, again, nobody was too put off by my dictionary mania 😊.

Chalicea told me a lovely story about Murray Gell-Mann that – if nothing else – proves (if ever such proof were needed) that he was a human being as well as one of the great minds of physics. Gell-Mann coined the term “quark” for the fundamental particles he postulated the existence of from an obscure reference (one of many!) in James Joyce’s novel Finnegans Wake. It’s interesting that another of Joyce’s works – Ulysses – was the topic of the previously published Listener puzzle – I’m not sure if this was a deliberate juxtaposition on the part of the editors!

As always, my thanks go to the Listener editors, Roger and Shane, for their unstinting efforts in getting these puzzles ready for publication each week: and to the many setters and solvers who have sent me generous and kind comments regarding Six-pack – it really does mean a lot to me, so thank you.


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Listener No 4620: Six-pack by Hedge-sparrow

Posted by Dave Hennings on 4 September 2020

As one might expect from his pseudonym, most of Hedge-sparrow’s Listeners have had a flora or fauna theme. I wondered what environmental bent this puzzle would have. [Ha! Ed.]

Here we had a group of six with double clues, only one of which was given a clue number. The entry method for each pair of clues was that suggested by the group they belonged to. Well… I’m not exactly a physicist (in fact, I’m not even vaguely one), but I felt smug when, after a few minutes thought, the theme popped into my head. I knew that quarks came in pairs and remembered there was up/down and bottom/top but needed a google to discover strange/charm.

Alll that was left was to solve the clues and slot them into their correct entries in the grid. I identified the quarks associated with each set fairly quickly but even so, exactly what went where provided some nice entertainment with some good clueing from H-s.

Having got my smug hat on fairly early, I was woeful in not spotting the TOP in STOPWATCHES as I entered 1ac after 2dn TAIL and 2probably-up VIOLONCELLO. All came together very neatly although I wondered why Auguste Escoffier was chosen as the French chef in 11dn/25dn Heating vessel used for Vietnamese dish of duck meat, about to be replaced by Escoffierian article (4;6) ANTE/OMELET. I’d also not heard of FOGGY BOTTOM and PYCNON before.

Among some entertaining clues, my favourite was probably 31set1 UK zoo’s keeper initially replacing dead reptile is returning with migratory quail’s dry fruit (9, two words; 7) with its somewhat bizarre surface reading, but leading to WHIP SNAKE [WHIPSNADE with K(eeper) for D] and SILIQUA [IS< + QUAIL*, migratory=wandering].

I forgot to mention that the clues that had to be jumbled — set 3, strange/charm — had a misprint in one letter in the definition of one of the clues. This spelt out raluvof which unjumbled to give flavour, which Chambers gives as “(in particle physics) any of the five, or probably six, types of quark”. That’s quantum physics for you! The origin of Quark itself is given as “From word coined by James Joyce in Finnegans Wake (1939)”. And what a stroke of luck that the STRANGE and CHARM could be anagrammed to GARNETS and MARCH, although they were part of the up/down set.

Identifying the six types of quark in the grid, together with QUARKS itself, was a pleasing end to the puzzle with (Murray) GELL-MANN and (George) ZWEIG (who separately proposed the quark model) from the circled letters going under the grid.

Thanks for an enjoyable puzzle, Hedge-sparrow.

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