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Listener No 4308: Sub-prime More-guess Relief by Ruslan

Posted by Dave Hennings on 12 September 2014

It surprises me almost every time! I open up the Listener only to find a small grid and lots of letters and mathematical expressions in the clues. Ok, this time the clues had lots of numbers and brackets, but it was undoubtedly a mathematical puzzle… and alas, Ruslan’s last. Previously, this setter has entertained us with betting on the horses and Cleopatra’s needle!

Listener 4308A long preamble explained how all primes above 3 can be expressed as 6n + 1 or 6n – 1, the clues here giving the sum of two such values of n for two (not necessarily different) primes. The (hidden) answer is the product of the two values of n, with the entry being the lower n followed by the difference between the two. Thus 65, which is 5 × 13, is entered as 58. Answer and entry lengths are also given, the actual answer being irrelevant for solving the puzzle.

It seemed logical to start with the lowest sums for the two n values. 4dn and 19dn were both 2 followed by 10ac and 15ac, both 5, and 8ac and 16ac, both 6. A simple table was really all that was needed, once I had got my head around the basic concept. u and v are used for the two ns.

It was a just question of listing the two possible values for u and v, their associated primes (6n ± 1) and all the possible resulting entries. For example, if the clue were 5, then that could be expressed as 1 + 4 or 2 + 3. For 1 + 4, the primes are (5, 7) and 23 (not 25, obviously) and the possible entries are 518 or 716. For 2 + 3, the primes are (11, 13) and (17, 19) and the possible entries are 116, 118, 134 and 136. Some could be excluded as too short or long for the entry, others because they were not prime or didn’t fit with cells already completed in the grid. I entered all the possibilities for a given cell as I solved each clue, and then struck them out as crossing entries conflicted. I have included a sample from the table below.

At every stage of a mathematical, I expect to come across an anomaly that means I have to go through all my notes looking for an error. It is very satisfying as entries are slotted in the grid one by one. This was the case here… until I got near the end and found that 10ac/3dn could be either 134/674 or 136/676. Bugger!

Listener 4308 My EntryLuckily, it didn’t take too long to realise that I had to check for “no two entries are the same”, and found that 136 was already in the grid at 15dn. It was then particularly satisfying to solve 12ac as 5839 × 6827 with the latter appearing in column 6.

An enjoyable last puzzle from Ruslan, and I’m sad there won’t be more.

Clue u + v 6n ± 1 Possible
4dn 2 (2,2)
length 2
2 = 1 + 1 5,7
10ac 5 (3,3)
length 3
5 = 1 + 4 5,7
   25 is not prime
5 = 2 + 3 11,13
8ac 6 (3,3)
length 3
6 = 1 + 5 5,7
6 = 2 + 4 11,13
   too long
6 = 3 + 3 17,19
6ac 7 (3,3)
length 3
7 = 1 + 6 5,7
7 = 2 + 5 11,13
   too long
7 = 3 + 4 17,19


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Sub-prime More-guess Relief by Ruslan

Posted by shirleycurran on 12 September 2014

Having a complete break from the Listener this week so no blog. I (with a distinction about a century ago in what was then called O level maths which is supposed to be the solver level for numerical Listeners) am totally useless at deciphering the complexity of phrases like “…a clue answer of 65 which factorises as 5 X 13, would be entered as 58. If the clue answer is a perfect square then the prime factors are identical … So I scanned those columns of numbers for traces of alcohol addiction, found none, drank a toast to Ruslan and recorded the reactions of the other Numpty.

Comments as the other Numpty approached the Ruslan.

“Are there any Listener setters still left alive?”

“Five minutes later – well this just looks like a pain in the ****.”

Five minutes later “Four down is obviously the way in” – followed by his explanation of that … then, “But that has three possible values – what is one supposed to do? This is just a total bore. One needs a rather large list of prime products.”

“Most of the differences are rather small.”

“4 across starts with 5 or 7″

Ruslan 001“I’m going to have to write a programme for this but one shouldn’t have to.”

“It is so tedious as it is really indirect. The grid entry is not really related to the answer at all.”

(Friend has just commented that he has completed it with a spreadsheet in 45 minutes – encouraging as that means it can’t be too tough.) “But I am no good with spreadsheets. Just got to do it by hand – it’s a bore!”

I’ll stop there as we are Listenernumericalcrossrowdiphobes (and that’s not even in the grey words omitted from the 2014 BRB) so I’ll have to rely on brilliant scientist Jaguar and Dave Hennings for blogs this week. (.. and rely on one of them to explain the title!)

However,  twenty-four hours later, after long gardening breaks, and a session in the roof sealing holes that the bats were using to get in, there was a contented “Well, that has worked and it wasn’t quite as fearsome as usual”, so, posthumously ‘Thank you, Ruslan!’

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Listener 4307, Spiral of Salami and Walnuts: A Setter’s Blog by Wan

Posted by Listen With Others on 9 September 2014

The idea for setting a puzzle based on a prime spiral came to me about two seconds after seeing that such a thing existed – it just leapt off the page as perfect for a theme. I sent a note to my mentor, the dearly-missed Radix, and asked him what he thought. He loved the idea and said that he couldn’t recall seeing its use in a puzzle before. My original thought was to call it ‘Prime Locations’ and then have ‘SEA FRONT’ etc. in the locations of prime numbers. However, at some point I noticed that the discoverer’s name, STANISLAW ULAM, had an anagram of either SALAMI or WALNUTS in it (I can’t remember which) and was nicely surprised to find that the remainder anagrammed the other, and so the finished form was born. I thought that it would be fun to actually put definitions for salami and walnuts in the prime spots, thinking that a lot of solvers might have worked out the anagram of the title before getting to the endgame, so that they wouldn’t be expecting it. If my logic was sound I suspected that it might raise a smile, which would be a nice conclusion to a crossword.

I was keen to use 90 degree symmetry as it seemed more ‘spirally’, so it took me a while to build a grid that I was happy with (I see from my files that I used my nineteenth grid, a rather apt number, but more on that later). I sent the grid to Radix before writing any clues, as I always did to get his view. He was very strict on grids and had his own Radixean standards of barring and best-avoided ‘bad words’ like plurals with an S – there are a couple in the grid used but the S’s form part of the salami and walnuts which met with his approval. (I had written this before learning that a number of solvers had inserted BATEAUS instead of BATEAUX which saddens me, there was certainly no intention on my part to trick anyone.)

Radix was also keen on thematic gimmicks where possible and it was very possible here as I only needed to draw attention to prime numbers. I came up with the gimmick of reading only prime-numbered letters in a word in prime-numbered clues, one that I hadn’t seen used before. I set about writing the clues, which came very easily and naturally, giving me a feeling of confidence about the puzzle. Unfortunately though, when I sent the finished puzzle to Radix to check the clues, he realised that I had misspelt part of my salami and walnuts in the grid, thus the whole puzzle was useless! He was very upset and blamed himself for not having checked the grid properly before I started on the clues. It took some effort to convince him that it was my fault alone and that I liked writing clues anyway, so it was all good practice. A few more grids later, I started on the second set of clues but for some reason these were not easy at all, and in fact I really struggled with some, so it was very reassuring to read that solvers enjoyed them. Radix taught me to sit on my clues for a while, and during that time I will highlight what I think are the weakest half a dozen or so and try to improve them. Then I do the same again and again until I am happy with them as a set. Of course I then may need to rewrite a few (or more than a few in the case of a Listener) during the editorial process.

From the original puzzle I lost a few thematic clues which I liked, but I gained a few too. Of those that I lost, I particularly liked ‘Animals calmly going about farm’ (cALmLy) for LLAMAS, and ‘Wingless birds! Hearsay according to Edmund’ (hEArSaY) for EATHE. Of those that I gained I particularly liked how ‘…burnt twofold perhaps’ worked for ‘…burnt wood perhaps’.

It wouldn’t be fitting to write about the puzzle without acknowledging the role of the editors. They are incredibly patient and helpful to newcomers like me who can be a bit slow in understanding the strict requirements of clueing for a Listener. They also insisted on a change to the preamble which I thought wrong at the time, but have to admit has been proven to be right.

It wouldn’t be right either to finish without paying respect to Radix. No-one has ever helped me so much for no return. I think of him often and I think that I always will.

I hope that solvers enjoyed the puzzle.


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Spiral of Salami and Walnuts by Wan

Posted by shirleycurran on 5 September 2014

Wan Two 001“There has to be an anagram in that title!” Those were the first words of the other Numpty while I was scanning the clues and finding lots of food, the odd drug, a few animals and birds, evidence of dancing, ships, Keynesian economics and a fair smattering of Scots, but not the usual Listener setter tipple.

What I did notice, though, at once from the few very evident solutions was a feature I always appreciate – the very ‘close to Chambers’ nature of Wan’s definitions.

Yes, there was an anagram and what a generous gift from Wan. STANISLAW ULAM took us straight to Wikipedia and an account of his doodlings (during a dull presentation) when he was working on the Manhattan project and the spiral of prime numbers that he produced.

Two clues into our solve and the other Numpty also had the device. We were discarding the non-thematic elements (the letters in alphanumeric positions that were not prime – thus, for example, the first, fourth and sixth letters of GREASY) from a single word in each prime-numbered clue.

“An oral examination – not before greasy Scots food (6)” gave us VIVA less A(before) + (g)RE(a)S(y) = VIVRES and Chambers confirmed that that was Scots food.

Walnuts and Salami 001We worked on those clues first and found some that were sheer delight: “Legal reps losing money, burnt twofold perhaps (6)” It had to be MEMBERS less M but the word play was ‘Laugh out loud’ when we realised that taking only the prime-numbered letters of (t)WO(f)O(l)D gave us WOOD.

Indeed, we were working backwards from the solution for a few of these. TAIRA must be the ‘weasels cousin (5)’ and we had to construct that from (m)AR(z)I(p)A(n) with Toffee’s first.

“Will’s long spanglet (4)” gave us 8s)PA(n)G(l)E(t) and we somehow had to relate PAGE to a Shakespearian word for LONG. Mrs Bradford came to our rescue this time with SIDE.

The solving was entertaining from start to finish and within a couple of hours, we had a full grid. I laboriously numbered the cells in a spiral, got out a table of primes and highlighted those cells in the grid then checked that I had 39 pink cells. I tried to read a message there and found a rather odd EEDESUR and so on, but it only took a few seconds for the other Numpty to pronounce happily that we were being treated to HIGHLY SEASONED SAUSAGE AND EDIBLE TREE SEEDS.

A lovely diet. Many thanks, Wan.

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Listener 4307: Spiral of Salami and Walnuts by Wan

Posted by Jaguar on 5 September 2014

A Listener solving year is surely the cruciverbalist’s equivalent of a marathon. In which case, we’re approaching the 18-mile mark with this, the 33rd puzzle of the year. For Marathon runners that is  known as “The Wall”, the point where the body’s main energy reserves run out and running (or solving) becomes noticeably harder. Will Wan’s wordy work worry wary Wall watchers? OK, that was terrible…

Wan makes his second appearance in the Listener this week after a scientifically-themed debut last year, Listener No 4233, featuring Mendeleev and elemental symbols moving between clues. For this puzzle the first thing I noticed, naturally, was the bizarre title. Surely an anagram of some sort? Especially with that “together representing a relevant discoverer” in the preamble. Unfortunately for now nothing seemed to emerge so I suppose I’ll have to gloss over that certain hint and get on with solving the clues.

And what a set of clues, too! Some of my particular favourites:

  • 32ac Denoting a type of therapy people of Kerala take to get self-confidence back (8) ([NAIR EGO R] reversed: lovely surface reading)
  • 42ac  Method of dyeing’s naff, sounding backward? (4) (homophone of “tacky” reversed!)
  • 1dn Starts to regret eating after meal (6) (R[egret] E[ating] + Past; again a lovely surface).
  • 25dn A bird impression done by a seal sounds just the same (6) (Another homophone of “signet”)

Indeed many of the clues had a very elegant surface, and one or two also had particularly inventive wordplay. But what was going on on those “thematic clues”? In many of these it wasn’t too hard to track down the modification, e.g. in 3dn the answer was TAIRA and strongly suggested Marzipan should become Aria for (aria+t[offee]) reversed, and then 7dn was “Slip [m]ON[k] paper…” for TYPO. But I couldn’t seem to see the connection between the words or the discarded letters; and, as the grid became filled, I was staring at words such as at, wood, um, aria, eye’s, on, oral, us, eat, angle… and (obviously, in hindsight) seeing nothing between them. And there was nothing obvious appearing in any spiral in the grid, either.

4307So with a complete grid, the modified clues included 2dn, 3dn, 5dn, 7dn… oh. Prime numbered clues? I’ll bet that’s no coincidence. And then you look at the words affected. Marzipan lost its 1st, 4th, 6th, 8th letters and retained the prime 2nd, 3rd, 5th, 7th to make aria, and so on through the set of modifications. So that’s the connection! And perhaps this will explain the highlighting, too? Highlight the 2nd, 3rd, 5th… letters in a spiral growing out from the centre. Going clockwise starts off promisingly enough, yielding “A GIT…”, or “SIT HEY…”  but soon breaks down after that. Going the other direction and we find, eventually, HIGHLY SEASONED SAUSAGE AND EDIBLE TREE SEEDS. An odd message, but it defines “salami” and “walnuts”, and very artistically hidden.

All of which leaves just the one mystery of who the “discoverer” is. All such mysteries break surprisingly easily on Google, and a search for “prime spiral” brings up the Ulam Spiral on Wikipedia, discovered by Stanislaw Ulam. Whose name can be anagrammed to make “salami walnuts”. As is often the case in such puzzles, the setter’s route and solver’s route are almost exact opposites. I can well imagine Wan scribbling down all sorts of anagram possibilities for such a weird name, and might well have considered “satsuma in wall” or “animal was slut” before settling on this particular choice. Or perhaps he came across it first time. We may never know.



We’re approaching about the time in the year for the third numerical puzzle of 2014. I was expecting it this time, actually, and sort of got my wish, even if it took me a while to realise that! Presumably we can enjoy that one next time out. In the meantime: a bizarre title, but a fine construction and some lovely cluing. Thanks, Wan!

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