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Listener 452: ‘Bobs’ by Nud

Posted by Encota on 16 June 2017

‘Nud’ has, according to the Preamble, arrived home the worse for wear and presumably is at least partly seeing double.  When looking at what had been entered in the grid the following morning it appears that letters thought to have been entered twice unfortunately hadn’t!

In at least two cases this had got even worse, with ANANA at 42a losing one of the ‘AN’ pairs and so with only ANA entered in the grid.  Similarly OROROTUND reduced by ‘OR’ to be entered as OROTUND.  In every other word one pair of letters became a single letter – e.g. the answer DESSERT at 51a is entered as DESERT.

On the second diagonal the word HAPLOGRAPHY appeared.  It’s defined in the BRB as “The inadvertent writing once of what should have been written twice” which neatly sums up the puzzle’s entry gimmick.

2017-05-27 17.08.58 copy

Is that a Personal Announcement from ‘Nud’ hiding in the Central Column?  Intriguing…

And the Title?  Was it simply ‘Boobs’ by ‘Nudd’, entered in error?  I’m assuming yes.  Or do we have a new setter ‘Nuud’ or ‘Nunud’ in our midst?


Tim / Encota


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Bobs by Nud

Posted by shirleycurran on 16 June 2017

“Nud?” I queried “Surely there can’t be a Nud as well as the Nudd who is (with Shark) part of the Rood combination that won the Ascot Gold Cup a couple of years ago”. We solved our first clue and smiled as APPS had to be entered as APS. “They are BOOBS, not BOBS, aren’t they?” said the other numpty and we were off with a steady grid fill that kept us smiling all the way and was nicely completed in time for dinner. It became easier when we had the framework of a word that we could enter into TEA doubling up the most likely letter (or pair of letters) that had to be omitted from the entered word.

Of course, I don’t have to confirm Nudd’s continued membership of the Listener Setters’ Tipsy Club. The preamble said it all; “The setter accepts that it was not a good idea to populate the grid on that night out with the lads …” However, his clues added evidence. ‘In Fort William buy early English drink (6)’ looked promising but proved to be a disappointment as COFF + EE merely gave us COFFEE that had to be entered as COFE – but perhaps Nudd needed that strong drink after ‘Half heartedly Lapp sees off rice drinks (8)’ giving SA[a}M + SHOOS  which gave us rather potent alcoholic fermented rice drinks, SAMSHOOS, to be entered as SAMSHOS. No wonder he was abandoning the bar later on. ‘Crossing river, don’t use abandoned bar (6)’. SPARE, going round R(iver) giving us the obsolete word SPARRE.

The grid filled nicely but we were temporarily flummoxed by the three cells where we had to enter ANANA (Pineapple accepted by head of Australia (5)’ That gave us A(ccepted) and NANA,an Australian slang word for ‘head’ but we were not sure how we were going to omit one of a pair of letters from that. Of course, TITIAN solved our problem (Note dish in striking red colour (6)’ giving us TI + TIAN), so that we realized that we were going to omit the pairs of letters in those two words (and, of course, in that lovely word for ‘sonorous’ OROROTUND with such a delightfully deceptive clue, ‘Sonorous old canon’s jazz in the middle (9)’ O + ROUND circling ROT).

I expected the 11-letter word to appear in the leading diagonal, but it was not to be. ?A???GRAPHY appeared in the other diagonal and, of the words Chambers offered, HAPLOGRAPHY was clearly the one we had to highlight. Great fun, thank you Nudd.

The HARES? They are multiplying! There were a couple entangled at the top right of the grid and a third at the opposite corner. A real hare bonanza!


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Listener No 4451, Numerical Playfair: A Setter’s Blog by Zag

Posted by Listen With Others on 11 June 2017

I enjoy solving both ordinary and numerical puzzles but tend to focus on numerical setting. Sometimes the devices employed in normal crosswords suggest a parallel numerical treatment and I’ll earmark that for a future puzzle. The Playfair puzzle idea arose from my earlier addiction to AZED. When his Playfair puzzles appeared I always approached them with a certain amount of trepidation but I did recognise the numerical potential of the idea. For a long time I never took it any further, possibly because of my mixed feelings about the format. I then had a spell when I produced a series of puzzles involving different aspects of coding and decided that the time had come to overcome my doubts and tackle a Playfair based challenge.

As those of you who are familiar with my puzzles know, I like small grids, using number palettes that are readily available in tables and requiring only a calculator to achieve the solution. Sometimes the theme may force a departure from the ideal, but that is always the aim. The compactness means there are only a limited number of clues and so the challenge is to find a suitable start that supports the theme without being too obvious.

AZED’s application of Playfair usually limited it to the 6-letter entries present in the grid (it only works with an even number of letters to encode). The natural numerical equivalent would be 2-digit or 4-digit numerical entries and with my desire to avoid larger numbers I chose to use 2-digit entries. With 10 digits, the equivalent to the 5×5 Playfair letter square is a 3×3 Playfair code square which could then operate in exactly the same way. Whereas I/J are often used to do double duty in a normal Playfair there is no obvious double digit combination. The simplest option, which I adopted, is using the digits 1-9.

A traditional approach would have been to create a grid fill establishing some of the 2-digit entries. Then, comparing these entries with the corresponding clue answers, the code square could be derived and any outstanding 2-digit entries encoded. That was my original plan until, when considering a starting logic for the puzzle, I came up with the idea of using a 2-digit Playfair code number as one of the entries. The nature of the code square means that the encoded entry corresponding to its 2-digit code number can only end in 1, 2 or 3. With a crosschecking clue requiring that digit to be the last digit of a square it could only be 1 and the puzzle was underway. Always gratifying to find a neat way of starting a puzzle.

Another intriguing possibility was to use some aspects of the code square as part of the puzzle. I thought it would enhance the Playfair theme, complementing the use of the code number starting point; hence the appearance of a row and a column of the code square in the grid. There was a danger such additional content could prematurely reveal too much about the code square so it was crucial to be careful how much information I gave away at each stage in the solution path.

With so much of the code square targeted for the grid, I felt the puzzle was best served by only having a small amount of additional structure. I aimed for a compact grid, one with possibly no more than 25 squares. I wanted a balance of about a quarter to a third of the entries being 2-digit and the rest 3-digit. The starting logic provided an L shaped section which naturally could occupy the bottom right part of the grid and, through symmetry, the top left. Experimenting produced the final grid.

The code square row and column that were to be present in the grid should not be discovered too early, nor should they interlink as that gives away too much information. This dictated that the left side of the puzzle should include these two elements since the right hand side provided the logical starting point for entries and progress would be made from there. The finish would be the top left hand corner and to keep options open to the end probably meant that 1d was not the best location for the code row or column. That left 4a&8a as the locations for these entries.

From there, it was a case of playing around with the armoury of numerical tools to allow a gradual development of the solution and progressive determination of the code square. From the start I had hoped this puzzle would be suitable for the Listener and so aimed for an appropriate level of difficulty, hopefully about the average for a numerical whilst offering satisfaction to the solver. Hopefully the challenge will have demonstrated that a Playfair puzzle need not be as intimidating as I and many others had found them to be in the past.

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‘Numerical Playfair’ by Zag

Posted by Encota on 9 June 2017

It’s that week in the quarter when the Listener Numerical appears.  I suspect that the combination of the words ‘numerical’ and ‘Playfair’ may well have deterred some regular solvers, as they both do seem to be in the Marmite category for some Listener regulars.  However, this was a great puzzle and I hope most people gave it a try…

As a precursor I skimmed the grid and marked every cell that couldn’t be a zero – it might be important later, I thought.  All 2-digit entries, every starting cell and those implied by reversals left only a very few cells that could be 0 (and even most of those soon disappeared once I got started).

Then this was actually quite a gentle puzzle, once a few items were spotted.

  1. The top right square of the Playfair (PF) can by definition only be 1, 2 or 3.  7d is a square and so ends in the usual 0,1,4,9,6,5 choices.  And 9a once converted via the Playfair square must end in the top right square too.  So the end of 9a Entry (9aE) is 1.  First cell filled!  And this significantly limits the options for 6d.
  2. As 3d is the reverse of 2a, then their centre digits must be the same, so 3d must be of the form xxy, i.e. its first two digits are the same.  Where 7a meets 3d, and with 7a defined as a divisor of 3d gives a very limited set of 7a/3d pairs in the form xxy.  3d  can only be one of 558, 882, 992 and 996.
  3. The options for 5d as an anagram of 6d are again very limited, especially when it is clear that the 1 must be its central digit.
  4. After a while it becomes clear that 5d can only be either 316 or 613.  As the 3 and the 6 are both in the centre of a row or column of the PF square, then neither 3 nor 6 can be in a corner of the PF square.  This allows two options for the Playfair square to be created, one based on each value at 5d – remembering that in rows two and three of the PF square then there can only be three possible numbers in each cell.  Using these partially completed squares then the options for 2d can be fully reduced.
  5. The last couple go in at 1a and 1d.  One option can be eliminated as it results in 16 entered at 1a, which isn’t possible as it is already in at 7d.  And the final one uses one of the cells that could be 0, at the end of 1d.

Double-check that all Answers and Entries align and I’m sorted.  I hope!  Feeling good about Numericals – I must soon have a go at the couple in the last Crossnumber Quarterly issue that I haven’t started yet (just in case the feeling wears off!).

One thought: I wonder how easy it is to use Sympathy software as a solver-assist tool for numericals?  I have been creating a lot of custom Sympathy dictionaries (.tsd) recently for various puzzles I’ve been writing, but I have never delved much into using Sympathy for Numericals except as a general purpose editor.  Could I get the Playfair gimmick to work on this puzzle for example?  If anyone reading this has already done similar then I’d love to hear about it!

Cheers all,

Tim / Encota

P.S. Can you provide the answer to the following deep and meaningless question: “What number do you get if you take all digits not used in the grid and place them together in descending order?”

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Listener No 4451: Numerical Playfair by Zag

Posted by Dave Hennings on 9 June 2017

Zag’s last puzzle was 4295 Codebreaker. In my blog for it, I wrote that it was a very small puzzle (5×7) with precious few clues (16). This week, we had an even smaller puzzle (5×4) with even fewer clues (12). I suppose the first thing that crossed my mind was “Why has nobody thought of this before?”

All 2-digit answers had to be Playfair-encoded before entry, which I suppose meant that one of the 3-digit entries was the place to start. 2ac intersecting with 3dn Reverse of 2dn which in turn intersected with 7ac Divisor of 3dn seemed as good a place as any.

The first two digits of 3dn had to be the same given its intersection with 2ac, so I listed all the possibilities together with the 7ac equivalent. The middle digit of 7ac was the last digit of 3dn, so that eliminated a lot in the list. In fact, there were only ten such values for 3dn/7ac, from 336/168, 442/221, 558/186 through to 996/166.

Given that 2dn was Sum of the digits of 7ac, values for 7ac such as 221 could be eliminated as their digit-sums were less than 10.

Further entries in the list could be eliminated where 2ac Multiple of another grid entry was prime, eg 775/155 where 2ac was 577. I was left with 336/168 where 2ac 633 (factored by 3 and 211), 558/186 with 2ac 855 (lots of factors) and 996/166 with 2ac 699 (factored by 3 and 233). If 3-digit factors, they had to go at 1dn since they weren’t square (6dn) or an anagram of one (5dn) or had all digits different (4ac and 8ac were rows in the Playfair grid).

You’d think I was home and dry here, but realising that the relevant factor of 2ac was the 19 at 1ac took me quite a long time, much of it thinking that I’d missed something somewhere.

In the end, I had 89 as the code-number and the full code-square:

8 9 1
2 3 4
5 6 7

Great fun, thanks Zag, but I just hope you’re not working on Hexadecimal Playfair!

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