garethrees.org

Quartet by MynoT

Fri, 05 Mar 2010 00:00:00 GMT

Listener crossword 4073: Quartet by MynoT (2010-02-13)

No clue numbers! Answers to be fitted in jigsaw-wise! This crossword was divided into four quadrants, each of ten entries, and there were four sets of ten clues, one for each quadrant, each given in “alphabetical order of its answers”. One letter of each answer was to be moved to the perimeter “disclosing a relevant quotation (minus one word)”. But on the plus side, every letter was checked.

I got stuck into set 1, which had a shoal of fishy words: a GED eating an ASP to make GASPED; scombroid SEIRS; tunicate SALPAE; and a hydroid SEA FIR to which an E could be appended to form SEA-FIRE. The four six-letter answers from this set—GASPED, SALPAE, GNEISS and PER PRO (clued with the smoothly misleading “A professional by agency of another”)—were already enough to work out which of the four quadrants this set belonged to, and how to fit in the words.

This gave me enough crossing letters to get the remaining words in this quadrant, revealing the letters ...IRCOU_SEAND... going clockwise around the perimeter. These suggested the words THEIR COURSE AND, and going to Google I found a quotation from the ancient Chinese book of divination, the I Ching:

Sun and moon revolve on their course and cold and hot seasons take their turn.

If this were right, the theme was the four seasons, which would fit the title, but unfortunately at 63 letters the quotation was too long, no matter which word was dropped. So I moved on to set 2.

“American playwright to serve superior loud soldier” seemed likely to be the name of a playwright containing “superior” ⇒ U followed by “loud” ⇒ F. That’s a rare digraph, and a trawl through Wikipedia’s Category:American dramatists and playwrights found George S. KAUFMAN (“serve” ⇒ KA, “soldier” ⇒ MAN). Together with “Knight runs playing hard balls” ⇒ KNURS, it looked as though set 2 went in the top right, and after a couple more clues I had much of that quadrant filled in.

For some reason I assumed that the U would be moved from KNURS to the margin, even though at that stage it could, for all I knew, have been the N. But it was a fortuitous mistake, because it suggested the quotation might go RUN THEIR COURSE AND.

Searching for that phrase found a quotation from Wing-tsit Chan’s translation of the Analects of Confucius:

Confucius said, “I do not wish to say anything.” Tzu-kung said, “If you do not say anything, what can we little disciples ever learn to pass on to others?” Confucius said, “Does Heaven say anything? The four seasons run their course and all things are produced. Does Heaven say anything?”

The emphasized phrase has 51 letters, and with SEASONS removed per the rubric, that left 44, a perfect fit. And with the corners filled in, I spotted SPRING along the diagonal of quadrant 1 (with the R moved to the corner) and SUMMER similarly along the diagonal of quadrant 2. So I could fill in WINTER in quadrant 4 and most of AUTUMN in quadrant 3 (it wasn’t yet clear which of the ‘U’s was moved).

It had been quite a struggle getting this far, but the rest of the crossword was a romp, with some great moments of deducing implausible words and looking them up to find they are for real: “I wonder if ROY is Australian for ‘dandy’?”—“I bet TANGUN is a type of pony!” This is the essence of advanced cryptics for me.

The final stings in the tail were a couple of words missing from Chambers 2003, but which I eventually found in the OED: MITUMBA (“In eastern central Africa: second-hand clothing”) and NGOMA (“In eastern and southern Africa: any of various kinds of drum”). The rubric noted that “one answer in set 2 is in Collins” so I guess the other must be in Chambers 2008.

I can imagine some purists objecting to “Cell’s self-contained down under?” ⇒ ASCUS (since there’s a double indirection in the wordplay: “down under” ⇒ “in Australia” ⇒ in AUS) but I thought it was amusing.

Given the convenience for the setter that the four seasons all have six letters, I was surprised to see that this is only the second time the theme has been used. The previous occasion was number 2446, A Happy New Year by Duck.

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The Isolated Word by Ten-Four

Fri, 26 Feb 2010 00:00:00 GMT

Listener crossword 4072: The Isolated Word by Ten-Four (2010-02-06)

The rubric was short and sweet today. “The wordplay in eight clues indicates the answer with an extra letter that is not entered in the grid. These eight letters can be rearranged to form a word that will provide a hint as to how to identify the isolated word (as well as 29 Across, which defines it loosely) that must be entered to complete the puzzle.”

After about an hour I had a full grid, apart from the two thematic entries. I had found seven clues with extra letters in wordplay:

1a “Erratic singular comet’s moving with some spin” ⇒ SOMERSAULTING. Anagram of SINGULAR COMET’S with extra C.
12a “To get to know king? Not at all” ⇒ LEARN. “King” ⇒ LEAR and “Not at all” ⇒ NO, with extra O.
16a “Acted in a leading role—looked hard” ⇒ STARED. “Acted in a leading role” ⇒ STARRED, with extra R.
19a “Eavesdrops on sort of Mediterranean bar?” ⇒ TAPS. “Sort of Mediterranean bar” ⇒ TAPAS, with extra A.
1d “Undisciplined cop’s so lost organ parts!” ⇒ SOLO STOPS. Anagram of COP’S SO LOST with extra C.
14d “Influence young bird (not European)” ⇒ PULL. “Young bird” ⇒ PULLET, with “European” ⇒ E removed, and extra T.
18d “Eating rock dries up small arthropod” ⇒ SEA SLATER. “Rock” ⇒ SLATE inside “dries up” ⇒ SEARS, with extra S.

There were also three clues whose wordplay I didn’t understand:

20a “Twelve, possibly concerned with organs” ⇒ RENAL.
8d “Resulting from the actions of five at a funeral, I give out and take money” ⇒ TELLER.
9d “Saddo, desperate and shown up” ⇒ NERD.

The seven extra letters I found were ACCORST, which could lead to ACCOURTS, ACROSTIC, CAR-COATS, ECTOSARC, or SOCRATIC. Of these, ACROSTIC was the only one that I could imagine being a “hint as to how to identify the isolated word”. That required an extra I somewhere, and indeed the wordplay in 9 down could be explained as “desperate” ⇒ DIRE, “and” ⇒ N, all “shown up”. (20 across is explained as an anagram of 12 across, LEARN. For 8 down we need another sense of TELLER, “one of the strokes made by a church bell ringing a funeral knell”; this is the result of the action of the RINGER from 5 down.)

At this point I spent an embarrassingly long time trying to work out the hint. I noticed that none of the extra letters was in an answer that goes below the isolated word: they are all in clues that start in the top half of the puzzle. So I started looking for hidden words that extended downwards from the isolated word. A point in favour of this idea was that that the word extending down from the tenth letter of the isolated word would have intersected with 29 across and resolved the five-way ambiguity there. The trouble with this idea was that there were far too many possibilities for the words, for example the word descending from the first letter of the isolated word could be CUE, DUE, GUE, HUE, RUE, or SUE.

Then I looked up ACROSTIC in Chambers. It’s “A poem or puzzle in which the first (or last) letters of each line spell a word or sentence”. Of each line. An across-tic. And indeed the initial letters of the clues spelled out EXTRA LETTER FROM CLUE N OCCURS N TIMES IN FINAL GRID.

(I should have paid more attention to the advice given to Shirley Curran by Chris Lancaster: “he invariably quickly scans the opening and closing letters of clues—just in case”. Lesson learned, I hope.)

Anyway, after counting up letters, I found that I was left with the twelve letters AACIOORRSSTT to finish the grid. These spelled ARISTOCRATS, leaving an O for NOBS.

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Five Dots by Franc

Fri, 19 Feb 2010 00:00:00 GMT

Listener crossword 4071: Five Dots by Franc (2010-01-30)

After several straightforward weeks, I have the feeling that we are due a difficult puzzle, and this looks like it’s going to be the one. There are extra words in all the clues, “the first and last letters of which contribute to a common version of a thematic statement attributed to a name.” The name, or rather “six contiguous cells” of it, is to be found and highlighted. There are four clashes in the grid, with dots to be entered at the clashes, and a fifth dot to be discovered.

The grid has numbers but no bars. Why no bars? If I understand the rubric correctly—“Numbers in brackets give the numbers of cells used for the grid entries”—I should be able to just fill in the bars right away based on these numbers. Surely the setter wouldn’t just omit the bars to create a mechanical task for the solver? There must be some thematic reason that I don’t yet understand, some need to disguise the lengths of entries, perhaps.

So to be careful, I’ll only enter the bars that I believe are absolutely necessary: that is, the ones to the left of across entries and the ones above down entries.

The clues, now that I come to them, are really hard. I guess it’s my inexperience, but I find clues with extra words very difficult. My clue-solving technique depends on parsing all the words to form theories for the structure of the wordplay, but the extra words thwart this. After an hour of staring at the paper, I have only half an answer. 47 down, “Husband sources of manganese, uridines and nitrates (3)” is MAN (if the extra word is “uridines”) or MUN (if it’s “and”).

By Wednesday evening, I’ve spent about three hours on the puzzle so far and I have only thirteen entries, with no clashes yet discovered.

However, the letters from the removed words are suggestive. If I take them in order by clue, first—last—first—last— etc, then I get nonsense, for example, ...LEILELVEECTTHH at the end of the across clues. So maybe I need to take all the first letters and then all of the last letters?

Across clues, first letters: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _LIEVETH
Across clues, last letters: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ELLECTH
Down clues, first letters: _ _ _ _ _ _ _ _ _ _ _ _ _H_ _ _S_ _ _ _ _EDUS
Down clues, last letters: _ _ _ _ _ _ _ _ _ _ _ _ _O_ _ _G_ _ _ _ _RUSE

This is suggestive of the words BELIEVE and INTELLECT. There can’t be all that many quotations with these two words. So, off to Google, and sure enough, it’s by Galileo:

“I do not feel obliged to believe that the same God who has endowed us with sense, reason, and intellect has intended us to forgo their use...”

This is an extract from Galileo’s 1615 letter to Madame Christina of Lorraine, Grand Duchess of Tuscany. Galileo is arguing that in the physical sciences, the accumulated evidence of our senses, and the conclusions we can deduce from them, are to be preferred to conclusions derived only from unclear passages in the Bible. He continues:

“... and by some other means to give us knowledge which we can attain by them. He would not require us to deny sense and reason in physical matters which are set before our eyes and minds by direct experience or necessary demonstrations. This must be especially true in those sciences of which but the faintest trace (and that consisting of conclusions) is to be found in the Bible. Of astronomy, for instance, so little is found that none of the planets except Venus are so much as mentioned, and this only once or twice under the name of “Lucifer.” If the sacred scribes had had any intention of teaching people certain arrangements and motions of the heavenly bodies, or had they wished us to derive such knowledge from the Bible, then in my opinion they would not have spoken of these matters so sparingly in comparison with the infinite number of admirable conclusions which are demonstrated in that science. Far from pretending to teach us the constitution and motions of the heavens and the stars, with their shapes, magnitudes, and distances, the authors of the Bible intentionally forbore to speak of these things, though all were quite well known to them.”

Back at the crossword, the quotation identifies all the extra words, making the pace of solving merely very slow, rather than glacial.

After another hour or so, I’ve filled getting on for half the grid, but I still haven’t found any clashes. However, I can see Galileo’s name starting to appear in the unchecked letters at centre left.

Let me think a bit more about the rubric. I need to find five dots associated with Galileo. The obvious possibility is that the five dots represent JUPITER and the four Galilean moons, IO, EUROPA, GANYMEDE and CALLISTO, which Galileo first saw through his telescope 400 years ago, some time between December 1609 and January 1610. Each of these moons has a name that’s even in length, so could be indicated by a clash with half the name in each part, for example I clashing with O, or CALL with ISTO.

Now that I have this idea, it’s easy to spot SCALLOP clashing with BISTOURY in the lower left to give CALLISTO, and MASSEUR clashing with OPACITY in the middle to give EUROPA.

And the disconnected cell in the very centre of the grid must be JUPITER. I’ll draw it a bit bigger.

(So the question I asked at the beginning remains unanswered: why have the bars been omitted from the grid? It turns out that I can just draw them in based on the numbers after the clues. I suppose the intention was to not reveal the disconnected central cell right away, but I think it was an unnecessary and somewhat misleading complication, because of the doubt it created as to how the numbers and clashes worked.)

After solving a couple more clues I consider 27 across, “Corrupt ~~Idaho~~ satirist”, the answer to which has to fit into _V_ _AL. It looks like it ought to be •VENAL with the dot representing JU. And yes, the clashing answer at 15 down (“Capital ~~ombu~~ tea”) is CHAPITER.

So this clash is JUPITER, and so the dot in the middle must instead be IO, which can be understood to represent a clash between GALILEO and GALILEI. How delightful!

And now that these dots are in the right place, their arrangement looks much more satisfactory, because the dots for the moons that I’ve found so far look as though they are in positions that are approximately to scale. Let’s check that:

	Semi-major axis		Implied scale (10⁵ km / cell)
Moon	(km)	(grid cells)	Implied scale (10⁵ km / cell)
Io	421,800	1.4	3.0
Europa	671,100	2.0	3.3
Callisto	1,882,700	7.2	2.6

This seems to be about as good a fit as you could expect from a crossword grid. So GANYMEDE, with a semi-major axis of 1,070,400 km, must lie between 3 and 4 grid cells from Jupiter. If I draw two circles with radii of 3 and 4, Ganymede ought to lie between the circles, in one of the three positions indicated by the red dots.

Are any of those positions right? Yes, 11 down, “~~Good~~ fish? Rather old”, is SOMEDELE, and 17 across, “Gypsy ~~exfoliants~~ blasted zit”, is TZIGANY.

I can see now why the grid is not symmetric: getting the Jovian system to scale must have been a tricky constraint.

The remainder of the crossword is still no pushover. There is one clue I don’t understand. 23 across, “Ratify losing part of ~~Ogilvie~~ clan” is SEAL. “Ratify” is the definition, but how does the wordplay work?*

It was a horribly difficult puzzle to start with, and for a long time I thought I wouldn’t be able to do it, but guessing the quotation saved the day. It all looks straightforward now I understand it, but as the great scientist said,

“All truths are easy to understand once they are discovered; the point is to discover them.”

* Erwin Hatch explains that it’s “clan” ⇒ SEPTAL with “part” ⇒ PT removed.

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The Glady Marsh by Salamanca

Fri, 12 Feb 2010 00:00:00 GMT

Listener crossword 4070: The Glady Marsh by Salamanca (2010-01-23)

This was a perfect lesson in how to hide something in plain sight. The first clue I solved was 14 across, “Become ‘A Study in Scarlet’ (6)” and I thought, what a brilliant clue! as I filled in the answer REDDEN. But it wasn’t until a couple of hours later that I released that this clue had given away the whole theme to the puzzle.

After the misprinted clues and amended entries of the last couple of Listener crosswords, this was a welcome respite, with nothing to do but solve the clues and enter in the answers. And there were some cracking clues this week. “Sleep under church ground thus? (12)” was a great anagram &lit for ENSEPULCHRED. “Terrain is uneven: does this make it _______? (7)” was a very pleasing composite anagram &lit for SIERRAN.

There were some good words too. “Speaker of seditious words causing panic in Greek animals (12)” is a perfectly transparent clue: we’ve got to anagram “Greek animals” to get a word meaning “Speaker of seditious words”. But I needed nearly all the checking letters before LEASING-MAKER was revealed.

Some of the clues were pretty tough. “Hill in SA: one of Scotland’s hill’s round (3)” clues KOP. I could see that it’s a South African hill, but it took a long time to work out that it’s “Scotland’s hill” ⇒ KIP, with “round” ⇒ O replacing “one” ⇒ I. The wordplay eluded me even longer in “One doing piecework who requires time to start off (6)” ⇒ TASKER: the smooth surface had me completely fooled. In fact, it’s utterly simple: “who requires” ⇒ ASKER, with “time” ⇒ T placed beforehand.

Anyway, with the grid filled in except for the four thematic entries, here’s how the rubric stood: “The answers to askerisked clues”—ANGEL, LIND, LAR, SOPH, NEST, PEAR, BETS, WAND—“along with the title are in the fashion of that indicated by the _ _IT_N_O_THE_ALL in accordance with the theories of _ _EGSON and L_S_R_DE (making their first appearance).”

Hmmm, L_S_R_DE suggested LESTRADE, the police inspector from Arthur Conan Doyle’s ‘Sherlock Holmes’ stories. Making his first appearance? That would have been in A Study in Scarlet in 1887, where a key element of the plot is the mysterious message left by the murderer at the scene of the crime:

I have remarked that the paper had fallen away in parts. In this particular corner of the room a large piece had peeled off, leaving a yellow square of coarse plastering. Across this bare space there was scrawled in blood-red letters a single word—

RACHE.

“What do you think of that?” cried [Lestrade], with the air of a showman exhibiting his show. “[... I]t means that the writer was going to put the female name Rachel, but was disturbed before he or she had time to finish. You mark my words, when this case comes to be cleared up you will find that a woman named Rachel has something to do with it. It's all very well for you to laugh, Mr Sherlock Holmes. You may be very smart and clever, but the old hound is the best, when all is said and done.”

Holmes was unimpressed with this theory.

“One other thing, Lestrade,” he added, turning round at the door: “‘Rache’ is the German for ‘revenge’; so don't lose your time looking for Miss Rachel.”

So we are looking at the WRITING ON THE WALL, which LESTRADE and his colleague GREGSON believed to represent an incomplete woman’s name. And sure enough, the asterisked answers might have been interpreted by these policemen as ANGELA, LINDA, LARA, SOPHY, NESTA, PEARL, BETSY, and WANDA.

The final instruction was, “Solvers must show their understanding of the theme by writing the full title for the puzzle in the space at the foot of the grid.”

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Conversion by Samuel

Fri, 05 Feb 2010 00:00:00 GMT

Listener crossword 4069: Conversion by Samuel (2010-01-16)

“All answers must be amended prior to entry.” It’s the kind of rubric that sends a shiver down my spine: misprints (but only in some of the clues), answers to be amended, and mysterious references to “professions”, a “workplace”, and multiple “conversions”. But these things usually become clear in the end, so let’s get started.

28d FEASTED
27a Feel upset confining female sailor allowing relation in wards ⇒ EFFABLE (misprint O)

These two would intersect if EFFABLE were amended (e.g. by jumbling or by rotation to the right by one or two letters) so that one of the “F”s was in the fourth cell.

21d Tamed canine, deeply disturbed ⇒ YCLEPED (misprint N)
38d OLEOS
37d KNOUT
19d INYALA
6d OPIUM
3d SEASHORE
2d SEBAT
1a ASSET

ASSET intersects with the first letters of SEBAT and SEASHORE, but only if the two letters “S” are in the third and fourth cells. Let’s suppose that every across answer is rotated by one cell to the right, so that its last letter moves to the front. That would make 5 across, “Bowled out for 7, Boycott’s ruptured earholes?” O_ _C_ _ _ _. I don’t fully understand the clue but it seems to be an anagram of BOYCOTT with B (“bowled”) replaced by something clued by “7”. Maybe a reference to 7 down? Anyway, the definition must be “earholes”, so maybe it’s OTECTOMY, with the question mark indicating a punning definition (the holes are the ones left by the removal of the ears).

Let’s fill in what I’ve got so far, assuming that down answers are amended by deleting one letter. See right.

4d See Tory base reeling having lost tense, ugly election perhaps ⇒ EYESORE (misprint R).
31a CLASP
24a REPLACEABLE
25d Polite strike is broken by a drunken sot ⇒ PEASTONE (misprint O)
44a Desirable bachelor lost out relaying to the stars ⇒ SIDEREAL (misprint T)
12d Nurse king, perhaps, caputured by dyed-in-the-wool Afghans ⇒ OLAF (misprint O)
23d Every diamond’s a sham ⇒ ALLICE (misprint D)
32d Spicy plant hoards he leaves for you in Paris ⇒ CACTUS (misprint K)
36d NACRE
39a Showing revolution is all over in France ⇒ STOUT (misprint S)
41a Little Larry’s more sexually attractive naked ⇒ UTE (misprint O)
35d Letter’s eaten by that old bear’s head ⇒ YEST (misprint E)

So far, all the down answers that I’ve been able to enter have had their second letter removed. Also, I have across misprints *O*DS*O*T* and down misprints *R*O*NDO*KE. The across misprints could start SECOND. Is it SECONDS OUT ROUND OKE? That can’t be right! The misprint at 32 down must be N: a cactus is a “spiny plant”, not a “spiky plant”. So the misprints spell SECONDS OUT ROUND ONE. The subject of the crossword must be a boxer (maybe ALI that I can already see at 23 down?), and his “workplace” mentioned in the rubric must be the boxing ring.

So I’m instructed to take SECONDS OUT of the down clues, and move the across clues ROUND ONE. Let’s apply the instructions to everything I’ve got so far. See right.

43a UPON
10a T-BAR
17a FAT FARM
16d Student chased by onion seller, initially he wallows in regret ⇒ RUSHEE (misprint U)
21a HERESY
18a STORTING
11a Lame deer gets in for the onset of estrus ⇒ ILK (misprint S)
1d TORAH

7 down is OUTCASTE and 5 down is ST KITTS, but neither fits. It must the case that OTECTOMY is wrong, which is a relief because I didn’t understand how the clue works. Aha, “7” clues the obscure Roman numeral S, and the answer must be OTOCYSTS. This word is missing from the 2003 edition of The Chambers Dictionary. (FAT FARM too.) Maybe it’s time to buy the 2008 edition?

13a I start to see conveyance returning from trek ⇒ CASSIA (misprint E)
14a Bank owners without a pound must be targets for firing ⇒ CLAYS

I don’t fully understand either of these. In 13 across, it looks as though I’m supposed to reverse “I”, “start to see” = S, “conveyance” = SAC, but where does the A come from? In 14 across, the definition is “targets for firing”, i.e. CLAYS in the sense of “clay pigeons”. But the rest? Either “bank owners” = CAYS and “without a pound” means “around L” or else “bank owners” is something like CALLAYS from which “a pound” = AL has been removed. But neither possibility seems right.*

Nonetheless, both of these answers must be right because they reveal CASSIUS CLAY across the middle of row 3. And there appears to be a BATTERFLY in column 3—indeed much of Ali’s famous quote FLOAT LIKE A BUTTERFLY, STING LIKE A BEE can now be seen going anticlockwise in a square, with a couple of errors where it intersects with CASSIUS CLAY. I guess we’re going to end up fixing those errors in the final step of the puzzle.

20a AEDES
22a Sexy rector’s inside with a lot of berks ⇒ STREAMY (misprint C)
9d SPAYAD
12a ADO

15 down is FOREMAN. Here is one of the “professions that was found wanting”. The other must be COOPER, and sure enough, it slots in at 40 across.

26d ANTLIONS
45a STOSS
29d SANGRIA
29a When queen gets out, special tail section tilts ⇒ STAINS (misprint N)
33a ANALECTA
42a I am on the trail of river otter band ⇒ RIM (misprint U)
30d SEALCHS

In 30 down, ‘divers?’ (even with a question mark) seems a very weak definition for such an obscure word.

Now the grid is complete, what about the final step?

The rubric says, “On locating the subject of the puzzle in the grid, solvers must carry out a conversion (the source of which was itself a conversion). This completes, in the shape of the subject’s place of work, a thematic quotation that must be highlighted.”

So what do I do? A further application of ROUND ONE to CLAY would get the L into the right place, but it looks as though I would need to apply ROUND THREE to CASSIUS to get the U into place, and there’s no justification for this. Maybe I need to apply the instruction SECONDS OUT in a different way, by removing the letters “S” from CASSIUS CLAY before rotating. That doesn’t work either.

Maybe I need to pay attention to the repetition of the word “conversion”? Cassius Clay was a convert to Islam, and when he converted, he famously converted his name to MUHAMMAD ALI.

* Derek Arthur and John Grimshaw explain that “from” clues À (“as in Thomas à Kempis” confirms Chambers), and that “bank owners” are BARCLAYS, from which “pound” = BAR is to be removed.

Update 2010-02-06. On the Listen With Others blog, Samuel describes the setting of this puzzle.

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364 263 by Xanthippe

Fri, 29 Jan 2010 00:00:00 GMT

Listener crossword 4068: 364 263 by Xanthippe (2010-01-09)

It’s a carte blanche puzzle, with one letter to be removed from a word in each row and each column (and moved to the margin), just to make things a bit more difficult. At least all the grid entries are real words. So let’s get started.

I have to confess that I’m no great shakes at cold solving. A first pass through the clues yields only five answers: COERCED (from which the only letter that can be removed is the D, leaving COERCE); EASTER (which could yield ASTER, EASER, EATER, ESTER); BAIRN (⇒ AIRN, BAIN, BARN, or BIRN)*; SARIN (⇒ SAIN, SARI); PLEAT (⇒ LEAT, PEAT, PLAT, PLEA).

* I might have been able to make faster progress had I checked all these words in Chambers, since this dictionary is lacking BAIN (OED: “A quantity of water or other liquid placed in a suitable receptacle, in which one may bathe”) and BIRN (OED: “The portion of a clarionet or similar musical instrument into which the mouth-piece is inserted”).

By good fortune all the deletions from EASTER yield _ _ _ER, and it looks as though it’s possible that COERCE intersects with the E. With nothing else to go on, let’s guess that this is right, and put in as many bars as I can deduce from the answer lengths.

It seems likely that the long down answers cross through the C and O of COERCE, and sure enough, they are ESPECIALLY (⇒ SPECIALLY) and PREORDERED (⇒ REORDERED), and this make it possible to get the long across answers, ENQUIRIES (⇒ ENQUIRES) and ERADICATE (⇒ ERADIATE).

The digraph QE in column 3 looks very unlikely, so I put in bars around the Q. I solve a few more clues: COUPLET (⇒ COUPLE), TOMCAT, APROPOS, NOODLE (which has a very nice triple clue, “Simpleton spent dole on some pasta”).

There’s four-letter down clue (“Greenish, endlessly twitching, eyes”), that from its position in the list of clues (comes after NOODLE but before the last two five-letter clues), I can deduce must have its first letter on row 5. So it’s either URP_ or EI_ _. It’s EINE (“Greenish endlessly” = EENI and “twitching” is the anagram indicator). And the symmetric answer is SLUR.

Putting in SLUR and EINE forces some more bars. Because no letters were removed from either SLUR or EINE, there must be other words in columns 4 and 7 (so that some letters can be removed from these columns), and that means there can’t be a four-letter word at the top of column 8 (because there aren’t enough clues to have a four-letter word at the tops of both columns 7 and 8).

Then I make a mistake. Somehow I’ve decided that there’s a three-letter answer on row 4, to the left of COERCE, so that on row 3 there’s a five-letter answer on its own. This allows me to put some more bars in. Wrongly. Next I get REAM (⇒ RAM, REM) and since this lacks an L it can’t intersect with SLUR. So I can put more bars in, but this leaves the grid rather poorly connected.

Surely a respectable setter like Xanthippe wouldn’t set a grid like this? It’s beginning to look as though I have gone wrong.

Yes, I’ve definitely gone astray. I need to put BAIRN at the top of column 2, and REAM at the left of row 4. But there’s no way for these to intersect, no matter which letters I remove. So I was wrong about the location of REAM. It must be on the right of row 3 instead. So backtracking, I get this:

The thematic word at the left of the grid is _ _[EA]DICT_ _ _ which looks like it could be PREDICTION or PREDICTIVE. I wonder if the theme is PREDICTIVE TEXT? Yes, TEXT goes at the lower left (“Tense UK retailer shunning new lines”).

Let’s decode the title using T9’s online translator:

364 263 DOG AND

and the instructions:

5646 2368737 63 2667328848359 68623733 23557 9484 287837 263 26675383 JOIN CENTRES OF CONSECUTIVELY NUMBERED CELLS WITH CURVES AND COMPLETE 843 74273 87464 896 78724448 54637. 2 84733 9673 75264 747273 6878 23 THE SHAPE USING TWO STRAIGHT LINES. A THREE WORD SLANG PHRASE MUST BE 9748836 86337 843 4743. WRITTEN UNDER THE GRID.

The slang phrase must be DOG AND BONE, with the lines we’re instructed to draw forming a picture of the BONE.

So could the other thematic entry be MOBILE PHONE? That fits with BAIRN (⇒ AIRN), EASTER (⇒ ASTER), PLEAT (⇒ PEAT) and SARIN (⇒ SARI). That’s good enough for me, let’s fill it all in.

I find it can be a bit of a slog when I’ve worked out the code and the theme and know what I have to do, but I still have big blank areas of the grid, knowing that the remaining clues are the most difficult ones. But duty calls: back to the grindstone.

ECLAT appeared twice in Saturday’s Times: it was also in crossword 24,430.

SADIST seems quite sadistic, using two obsolete words, “no longer save” = SA and “old poem” = DIT.

“Judge acquitting Frenchman after one French impression” eventually yields IDEE (⇒ DEE) after much thought. I think it’s “judge” = DEEM, “acquitting” = removing, “Frenchman” = M, “one” = I, and “French impression” = IDEE.

“Guide with base moved down on printer’s plate” must be STEREO (⇒ STERE). I get “printer’s plate” (short for STEREOTYPE) but the wordplay eludes me for a long time. Eventually I figure it’s “guide” = STEER, “base” = E, “on” = O.

But one of the clues is beyond me. “Prop primarily supporting one edge of hide” must be SHORE (⇒ SORE). “Prop” = SHORE, “primarily supporting” = S, but how does “one edge of hide” = HORE? Someone, throw me a bone here.*

* Dave Hennings explains that “one edge of hide” is H OR E.

(Listen With Others | comment)

Packing the “S” tetracube

Sun, 17 Jan 2010 00:00:00 GMT

In my previous article on packing tetracubes, I finished by noting that the problem of packing 54 “S” tetracubes into a 6×6×6 cube looked as though it was going to be pretty challenging.

And so it proved.

In particular, I couldn’t find any way to break up the puzzle into sections that I could solve by hand. For a while I had the idea that you could start with a packing of the 4×4×2 cuboid:

And then use this technique to expand the packing from 4×4×2 to 6×4×2:

I tried for a long time to repeat the expansion to get a 6×6×2 slab, as I did for the “T” tetracube, but with no luck. Every attempt came to nothing, with this ring-shaped structure being a typical result:

A solution

In the end I gave up and wrote a computer solver (using Donald Knuth’s “Dancing Links” technique, of course), from which I learned that there is no way to pack 18 “S” tetracubes into a 6×6×2 slab.

Here’s a 6×6×6 solution, courtesy of the computer:

Estimating the number of solutions

In my previous article, I linked to Keiichiro Ishino’s solutions for the “T” tetracube problem. Ishino also gives 11 solutions for the “S” tetracube problem. (Ishino’s puzzle website is well worth a browse. He gives solutions, and in many cases solution counts, for hundreds of polycube packing problems and interlocking burr puzzles. There’s a staggering amount of work on display here.) For both of these 6×6×6 packing puzzles, Ishino claims only that there are “20,000+ solutions”; presumably he stopped his computer search at that point.

An aside: at creativecrafthouse.com Dave Janelle sells versions of these puzzles called “Monster T” and “Monster Z”. The blurb for the former reads, “The 54 ‘T’ shaped pieces will make a 6×6×6 cube 20,000 different ways [...] I found the design for these Monster Puzzles from a mathematician’s website and thought they would make fantastic puzzles.” I guess the anonymous “mathematician” must be Keiichiro Ishino.

There are of course many more than 20,000 solutions to these packing problems. In a few minutes my computer finds hundreds of thousands of solutions for both problems. So how many solutions are there altogether?

Well, one very rough-and-ready way to estimate the number of solutions is to see how the number of solutions grows as a function of the number of pieces to be placed. If I instrument the solver so that each time it backtracks it reports the number of solutions found so far, then this is what I get:

Pieces to place	2	3	4	5	6	7	8	9	10	11
“T” solutions	1	2	2	2	2	4	4	4	4	4
“S” solutions	2	2	2	2	2	2	6	14	32	33
Pieces to place	12	13	14	15	16	17	18	19	20	21
“T” solutions	8	8	8	16	16	16	16	16	16	16
“S” solutions	107	369	379	379	758	1516	3032	3032	6064	6064
Pieces to place	22	23	24	25	26	27	28	29	30	31
“T” solutions	16	32	32	64	64	64	360	646	1102	1102
“S” solutions	37082	54592	54592	93208	93208	672142	1189974	1189974	4289574	5291538
Pieces to place	32	33	34	35	36	37	38	39	40	41
“T” solutions	1102	1102	8094	38694	59126	235693	235693	235693	235693	471386
“S” solutions	12179980	43909804	87819608

Notice that contrary to my hand-solving experience, it looks as though there are a lot more ways of packing the “S” tetracube than the “T” tetracube. But this is a single run of the solver, and it might just be the case that it has lucked into regions of the search space with more “S” solutions than average and/or fewer “T” solutions than average.

In order to extrapolate from this data, I need a model that I can fit it to. Here’s a very naive model: the n pieces are distributed roughly evenly within the region to fill, with each piece taking one of m orientations, and there is then a probability p that a piece doesn’t overlap with any of its neighbours. If no piece overlaps with any neighbours, then there’s a solution. In this model the number of solutions is about (mp)ⁿ.

So let’s use Gnuplot to fit exponential curves to the data:

set key left
set logscale y
set yrange [1:]
set xlabel "Pieces"
set ylabel "Solutions"
s(x) = b * a ** x
t(x) = d * c ** x
fit s(x) 'sol.data' using 1:2 via a,b
fit t(x) 'sol.data' using 1:3 via c,d
plot 'sol.data' using 1:3 title "S solutions", \
     s(x) title "S best fit",                  \
     'sol.data' using 1:2 title "T solutions", \
     t(x) title "T best fit"

Eyeballing the graph, I’m not altogether convinced by the goodness of fit for the “S” tetracube, but in the absence of a principled change to my model, fiddling with the curve equation is not going to improve matters. Here are the best-fit parameters that Gnuplot finds:

Final set of parameters		Asymptotic Standard Error
a	1.76546	± 0.08082	(4.578%)
b	3.47972×10⁻⁵	± 6.62×10⁻⁵	(190.3%)
c	2.28617	± 0.06749	(2.952%)
d	5.48797×10⁻⁵	± 5.561×10⁻⁵	(101.3%)

And extrapolating to the puzzle with 54 pieces yet to place, there are about:

10⁹ solutions with the “T” pieces.
10¹⁵ solutions with the “S” pieces.

This suggests that with about a week of computer time I could get an exact count of “T” solutions, but counting the “S” solutions is well beyond my resources.

Improving the estimate

As I noted above, the solution counts generated from a single run of the solver might be unrepresentative. It would be better to get a more representative sample of the solution space.

Something for another post, perhaps.

(LiveJournal | comment)

Rentokil by Jago

Fri, 15 Jan 2010 00:00:00 GMT

Listener crossword 4066: Rentokil, by Jago (2009-12-26)

The rubric describes five unclued entries that give the theme to the puzzle and which indicate the “main object” to be found. It also mentions, in passing but rather ominously, “the grid’s final construction”, which suggests that a tricky transformation will be required after solving the clues.

So, what about trying to guess the theme of the puzzle from the title? “Rentokil” suggests pest removal, which suggests the Pied Piper of Hamelin. Perhaps rodents and children would have to be removed from the grid in some way? According to Brewer’s, the Pied Piper’s second appearance was on St John’s Day. And St John’s Day is December the ... 27th. That’s tomorrow, not today. Is that close enough for the Listener crossword? I’m not sure it is.

(If only I were a regular Listener solver, or had thought to check the Listener Crossword website, I would have seen that this theme had already appeared in July 2009 — number 4041, “Motley Collection” by Merlin — and so was vanishingly unlikely to appear again so soon.)

Anyway, let’s solve some clues, which are all in the form of a definition and letter-mixture. Normally I find these very hard to get started on because of the large number of possibilities to consider. But today 40 across leaps out at me: “a holiday: now we can put our feet up” ⇒ FETE. The intersecting words fall quickly: “giving their anger against Christians” ⇒ IRE; “Eventually fed guests with sweet” ⇒ FUDGE; and in what seems like no time at all I have the bottom half of the grid.

My Pied Piper theory seems briefly promising as I solve “Donations go toward animal charities at Xmas” ⇒ WOODRAT. But it’s demolished when it becomes possible to guess that two of the unclued entries form the thematic phrase ON THE FEAST OF STEPHEN. And of course St Stephen’s Day is December the 26th. So is the theme Good King Wenceslas? Let’s not be too hasty, now, and consider other possibilities. I’m away from home and only have the Concise Brewer’s, which doesn’t have much. The name “Stephen” means “wreath” or “crown”. The British Parliament is sometimes known as “St Stephen’s” after the chapel at Westminster where it used to sit. None of this seems to fit. But Wikipedia’s entry on St Stephen's Day comes to the rescue with a description of “hunting the wren”. In this Gaelic custom, “wrenboys” catch or kill a wren, and parade it around town on a pole, begging for money and singing a song beginning:

The wren, the wren,
The king of all birds,
On Stephen’s Day
Was caught in the furze

Let’s finish the grid and see if this is right. The top half is a bit harder than the bottom half, with a few words that need a visit to the dictionary. “Feast and sup: Yuletide carousal” ⇒ UPSY is new to me, as are SKEG (“I keel over when keg’s empty”) and ETHE (“oh, it hasn’t been easy since the early Christians decided on it”).

The remaining thematic entries are revealed to be TROGLODYTES (the genus of wrens, so named because of their habit of entering small crevices), and HUNTING THE BIRD. It seems to me that the latter ought to say “WREN” instead of “BIRD”. So “WREN” must be the “main object” that we’re hunting for. And the title “Rentokil” should be understood as “wren to kill”!

What about the “instructions given in the set of clues”? I am embarrassed to admit that it is not until this point, with the grid filled in and the theme discovered, that I notice that the initial letters of the clues spell out FOLD GRID TO ORIGAMI BIRD SO ONE IS HEAD. SEE WING. Oops. I had so many clever ideas for doing things with the superfluous words in the clues that I missed the simplest possibility of all.

So it’s out with the scissors and some origami instructions. Taking care that the “1” in the top left of the grid ends up at the head of the bird, I fold a rather dumpy-looking bird — more a plump moorhen than an elegant crane. But sure enough, under the right wing is the hidden WREN, formed from the W of WOODRAT, the R of DESSERT, and most suprisingly and delightfully, the rotated M of SMASHED and the rotated Z of ZION.

Update 2010-01-17. This puzzle did not go down well with some well-known Listener setters.

Don Manley [Duck]: “I romped through the clues, and found them rather simple and dull, but fear that I then lost interest, not wishing to do the origami research. For me crosswords are really all about clues, but The Listener is too often about a a non-crossword puzzle that must be solved after a crossword has been done—one reason why I’m now less inclined to bother with it these days and catch up on reading. Sorry, Jago, ’cos you’re a nice guy!”

Paul Henderson [Phi]: “This fell straight into one of my categories of poor puzzle—about a 5–10 minute solve followed by several hours of trying to work out what form the submitted grid should take, a ridiculous division of labour.”

It helped to know that there’s an origami construction called the “bird base” which forms the basis for many models (and not just birds). When you fold the bird base with Jago’s grid, the WR and MZ are already brought together, so more or less any way of completing the model will satisfy the requirements.

With regard to the difficulty of the grid fill, I think it’s right for the Listener to set easy puzzles from time to time, to encourage new solvers. If you’re failing to complete the puzzle week after week then eventually you’ll give up, but even the occasional success can be highly motivating.

(Listen With Others | comment)