# Archive for December, 2015

## Listener No. 4373: Semirp by Kea

Posted by Dave Hennings on 11 December 2015

A second mathematical puzzle from the normally word-oriented Kea, his first being 4164 back in November 2011. If memory serves me, that was fairly straightforward. I wondered if he had used the intervening four years to come up with something a little more tricky. For a start, it seemed there were only 15 clues. Closer inspection showed that there were actually only 7, the others just telling us to look at another one. (In fact, as I would suss later, these were clues since they ensured the referenced one was distinct.)

Every entry was the reverse of a prime, so I put 1, 3, 7, 9 in the cells that were the first digit of an entry, being the options for those cells. The 2-digit entries B, F and M now had those options in both digits so were 13, 17, 31, 37, 71, 73, 79, 91, 93 or 97. 93 was not the reverse of a prime and 91 was the only non-prime which enabled distinct values of B and N in clue I (B + B) / N where N ≠ 2.

Thus 2B was 182, which factored to 1.2.7.13 leading to N being 13 or 14 (26 not reverse of a prime and 91 not distinct). If N = 13, then I is ·3, ie 13, 33, 73 or 93, only 73 being distinct, with no consecutive digits the same and reverse of a prime; Y = 59. If N = 14, then I = ·4, only 14, 34 and 74 being valid; Y = 34, 74.

Valid values of D with middle digit 9 and non-prime are 391, 393, 791 and 793. Only 793 is divisible by one of the values for Y, ie 61, giving T = 13, N = 14 and I = 74.

O NUN came next, with only 392 fitting the rules and U = 2. From A D + O / W we get A = 797 and W = 98.

Using H SC / F, SC / 17 = 713. SC = 17.23.31 so S = 23 or 31 and C = 391 or 527, ie 391.

Using adjacent digits, E = 904, 924, 934, 954, 964 or 984. Only 904 and 934 are reverse of a prime. Using adjacent digits, K begins with 3, so M = 73 and J = 34, 35, 37 or 38.

Inspecting the last digits of J + J – G + L, we get 35 + 35 – 1·9 + 152 = 73 and G = 149.

Finally, E (K – L + U – T)Z with E = 904 (2.2.2.113) or 934 (2.467). 467 is too large with K = 3··, as are 452 and 904, and 113 too small. Thus K =369, giving (369 – 152 + 2 – 13).4 = 904.

Not too tricky a puzzle in the end from Kea, but an entertaining couple of hours in the company of primes, thanks.

The final table of all values is:

 A B C D E F G H I J K L M N O S T U W Y Z 797 91 391 793 904 17 149 713 74 35 389 152 73 14 392 31 13 2 98 61 4

## Listener No. 4372: Seldom Seen by Piccadilly

Posted by Dave Hennings on 4 December 2015

This was Piccadilly’s first Listener since April 2004. Since then, he has primarily been an EV setter, and I’ve tackled many of his puzzles there. Despite that, I didn’t know whether I was in for a tough or easy ride here. Everything that was going on centred on just nine clues: their wordplay had an extra letter, and the answers themselves needed to be replaced thematically on entry.

Starting at 1ac, and CAPSTAN was an easy solve, so it seemed logical to try the crossing downs. 3dn was AO DAI, the third time in about a month I’ve had that (not just here), except this time it was thematic with an extra E in the wordplay. Interesting theme… Asian women’s clothes.

Half hour later and another dozen downs had been solved. The central row –C—M—L—X looked like a strange Roman numeral. Moreover SOU’WESTERS and CHATELAINS (one of the longest hidden words ever … retained by Neuchatel a[s] inspectors) didn’t seem to have much in common with their crossing grid letters.

APOSTROPHE was the obvious entry at 20ac, and with the I from PASTRAMI, all became clear for 30ac as CIRCUMFLEX. We had accents and other things (SPACE, APOSTROPHE and HYPHEN) that we normally leave out of crossword entries, despite being in Chambers.

All was done and dusted in under an hour. Well, almost. The answer with an umlaut at 17ac Nanny takes married woman back after cutting countess (6) took 20 minutes on its own. Even though I knew of ‘graf’, the female GRÄFIN was new to me.

So what was the 9-letter word that told us how the grid should be filled. A bit obvious really? Not quite! It took 5 minutes of doodling OWASLERCE to get LOWER-CASE. Isn’t this the sort of situation where the preamble should include “solvers are advised to use a pencil at first”? But I suppose that would give part of the game away.

A nice simple idea for an enjoyable puzzle. Thanks, Piccadilly.

Posted by shirleycurran on 4 December 2015

A mere three and a half lines of preamble – that was a change from recent crosswords and there were going to be only nine clues where an extra letter  in the wordplay would lead to a word specifying how the entire grid

should be filled. The nine words in question were to be replaced thematically in the grid. It sounded feasible and promising so we started our solve.

Not, of course, before I had checked Piccadilly’s membership of the Listener Setters’ Alcohol Appreciation Society; hmm! What do I find? Three clues into my quick scan, ‘Private tutor accepted cases – rum (7)’ Mrs Bradford suggests ‘c[o]achaça’ and Chambers suggests that that word needs a cedilla. Interesting!

I read only two clues further down and find that not content with cases of rum, Piccadilly is into the Tokay. ‘Member of old religious fraternity bottles cold Tokay wine (7)’ (essene round c = essence).

I can hardly believe my eyes when a mere two clues further on Piccadilly is into the Chianti and the Champagne; ‘Finishing off Chianti and bubbly serves to show inebriation in Paris (7)’ [Chiant]i + serves* = ivresse. I wonder what is coming next and find a couple of prostitutes; ‘Lacking shred of evidence book prostitute (3)’ (tome less e[vidence] = tom), and ‘Prostitutes initially lacking practical skills (4)’ ([t]arts) and a joint, ‘A very small amount gets Republican a joint in Greenwich village (5)’ (mite + r).

Solving was speedy and soon we were faced with an intriguing dilemma. ‘More than one lord of the manor retained by Neuchâtel as inspectors (10)’ seemed to suggest ‘châtelains’ – hidden – with an extra S produced by the wordplay, but intersecting with ‘pastrami’,’orc’, ‘tom’, ‘owl’, ‘afar’ and ‘hexagon’, there was only one word that would fit – ‘circumflex’! Penny drop moment. We were on home ground and, as we are still traveling in the USA, I even have my nasty little French P.C. with its ludicrous French keyboard.

We realized that diacritical marks were a feature of Piccadilly’s game and ‘lavallières’ could become the name of its mark, ‘grave accent’. ‘Vendémiaires’ went in as ‘acute accent’. Our set of nine was completed by the ‘space’ in ‘ao dai’, the ‘hyphen’ in ‘ukiyo-e’, the ’tilde’ on ‘señor’, ‘apostrophe’ in ‘sou’wester’ and, of course by ‘umlaut’, we guessed that one.

Our grid was full and we had the extra letters O,A,S,L,E,R,C and E. Obviously they were telling us that we had to complete our grid in’lower case’ so that those accents would be orthodox but we had one gap in our process – what was the umlauted word that would lead to an extra W? It was amusing really – here I am in Silicon Valley toddler-sitting for my half-German little grandson as his small sister comes into the world but could I solve that one? ‘Nanny takes married woman back after cutting countess (6)’ Of course ‘Gran’ takes [w]if (e)<, producing Gräfin.

What an enjoyable and polished construction that gave us the p.d.m.s nicely spaced and an entertainingly different finish. Many thanks to Piccadilly.