# Fifteensquared

## Inquisitor 1275: Divisions by Stan

Posted by kenmac on April 10th, 2013

Preamble: The wordplay in each clue leads to the answer plus an extra letter. These letters, in clue order, suggest how solvers should draw six straight lines, including two for guidance, and highlight 30 cells in the completed grid.

So, not much to do regarding the grid fill though I found identifying some of the extra letters a bit tricky.

There were some nice clues with a lot of misdirection. My favourite must be 7d which, for ages, wanted to be JESTER (JUST HERE minus Height; U ignored; anag: flying around) which would have even fitted with ABAT-JOUR in 5a! 11a was also good with its apparent reference to 36d.

Anyway, the extra letters spelled out: FOUR CONIC SECTIONS DIAGONALS DEFINE GENERATORS OF CONE, none of which meant much to me

A search on Wikipedia for Conic Section and I could see that the three conic sections of a cone are hyperbola, parabola and ellipse. And, apparently, circle (a special case of ellipse) is often known as the fourth conic section. Finding CIRCLE (a11,b11,c11,d11,e11,f11), PARABOLA (f13,g12,h11,i10,j9,k8,l7,m6) and HYPERBOLA (d1,d2,d3,d4,d5,d6,d7,d8,d9) were reasonably easy but ELLIPSE (a1,c2,e3,g4,i5,k6,m7) took a little longer given that it’s offset from the normal diagonal.

This left me with the problem of where to draw the six straight lines. My first instinct was to draw lines on the diagonals and next to the conic sections previously identified but I wondered why we needed to prove twice over that we’d identified them! I then wondered if we just had to draw lines around the sides and across the diagonals but that didn’t seem to make any logical sense. I pondered it for a week or more and finally decided that despite the fact that it seems unsatisfactory, we must have been expected to draw lines beside the sections (as shown in my grid.) I’d be interested to see what others thought and I look forward to seeing the published solution.

In conclusion, I enjoyed the grid fill and the discovery of the extra letters but I did not enjoy the end game in the slightest I found it a little too Listener-esque to be enjoyable – sometimes I think The Listener is more like hard work than enjoyment and I’m worried in case The Inquisitor goes the same way.

 Across No. Clue Entry Extra letter Wordplay 1 Party hard for this Eastern European ESTH F FEST (party)+Hard 5 Acoustic device one introduced to a vessel with voice ABAT-VOIX O A BOAT (vessel)+VOIX (voice) 10 Gold and sterling remaining, forming union ALLYING U AU (gold)+L (£; sterling)+LYING (remaining) 11 Revolutionary solvers initially attempt 36D? CHESTY (a reference to a rather large “chest”size) R CHE (Guevara; revolutionary)+S(olvers) (initially)+TRY (attempt) 13 Criminal Records Office anticipates parliamentarian’s caper ROMP C CRO (Criminal Records Office) (before: anticipates) MP (parliamentarian) 14 Behold former weapon LANCE O LA (behold)+ONCE (former) 16 Poser left fashionable sketches MODELLI N MODEL (poser)+Left+IN (fashionable) 17 Ditch fool after learner swerved LEANT I Learner+EA (ditch)+NIT (fool) 19 Satisfy approved end APPEASE C APProved+CEASE (end) 21 Scrubs female chief after suggestions of conflicting answers FYNBOS S Female+YN (suggestions of conflicting answers)+BOSS (chief) 22 Astaire dancing around decorative wooden design TARSIA E ASTAIRE (anag: dancing around) 23 Iberian music: loud with recurring final passage FADO C F (forte; loud)+CODA (final passage; rev: recurring)) 25 Votes for the archaic cliques YESES T YE (the; archaic)+SETS (cliques) 28 To isolate leads to insanity and stress with loss of independent existence ISLE I I(nsanity)+S(tress) (initially: leads to)+LIE (loss of independent existence) 30 Bannister, for one, returning after stupidly solemn entrance examination PRELIM O PO (stupidly solemn)+MILER (e.g Roger Bannister; rev: returning) 33 Native Americans drooping with return of tailless skunk LAKOTA N LANK (drooping)+ATOk/ATOc (skunk; tailless; rev: return of) 35 Fight about very fine old holiday home PARADOR S RADical (very fine)+Old inside SPAR (fight) 37 Occupational therapist inhaling cigarette died OBIIT D BIDI (cigarette) inside OT (occupational therapist) 39 I limited Scotsman’s meal ITALIAN I I+TAIL (limited)+IAN (Scotsman) 40 Cunning, devious person reflected light beam LEERY A EEL (devious person; rev: reflected)+RAY (light beam) 41 Soldier overwhelms imperial warriors IMPI G IMPerial inside GI (soldier) 42 Automaton moving to deserted tree TAMANU O AUtoMATON (TO deserted; anag: moving) 43 Eternal schoolboy missing start of term following autumn’s vacation AEONIAN N AutumN (first and last letters: vacation)+EtONIAN (schoolboy; missing T: start of Term) 44 A palace he demolished for medusa, say ACALEPHE A A PALACE HE (anag: demolished) 45 Poorly paid worker of yesteryear died in open space in town DUNG L Died inside LUNG (open space in town)
 Down No. Clue Entry Extra letter Wordplay 1 Listener’s covering poet’s dry and withered failure EAR-MUFF S SEAR (dry; poetic)+MUFF (failure) 2 Northerners sleepy judgement cunningly made once outside SLOOMY D DOOM (judgement) inside SLY (cunningly made; obsolete: once) 3 They persist, nailing one pulling publicity stunt HYPER E tHEY PERsist (hidden: nailing) 4 Disapproving king finding happiness after glut KILLJOY F King+FILL (glut)+JOY (happiness) 5 Look closely at a stud? Yes, when cycling ANALYSE I A+NAIL (stud)+YES (anag: when cycling) 6 Take pawn in stress ACCEPT N Pawn inside ACCENT (stress) 7 Moth just here, lacking height and flying around VENEER E EVEN (just)+hERE (lacking height; anag: flying around) 8 Indian state welcomes Saints and Hammers, say OSSA G SS (saints) inside GOA (Indian state) 9 Male characteristic leads to exaggerated swaggering through old training ground XYST E XY (chromosome; male characteristic)+E(xaggerated)+S(waggering)+T(hrough) (initials: leads to) 12 Gland’s mucus comes up with nothing TONSIL N SNOT (mucus; rev: comes up)+NIL (nothing) 15 Getting up in afternoon is weird – foolishness! NIAISERIE E IN (rev: getting up)+Afternoon+IS+EERIE (weird) 18 Nothing removed from chubbier subordinate UNDER R RoUNDER (chubbier; O (nothing) removed) 20 Befool once sonata’s played with dropped note ASSOT A SOnATAS (anag: played; Note dropped) 24 Producer of oil and tar accepted with no end to prejudice ARABIA T TAR+Accepted+BIAs (prejudice; no end) 26 Location for shooting – end of gunfire confused part of army base ELSTREE (film studio; “shooting” location) O (gunfir)E (end of)+LOST (confused)+RE (Royal Engineers; part of army)+E (base) 27 Dessert reasonably stirred with no hints of egg and lemon SABAYON R ReASONABlY (anag: stirred; without E(gg) or L(emon)) 29 Making a living at last pay doesn’t feature in desires EARNING S yEARNINGS (desires; without (pa)Y) 31 Secular pub welcoming avid regulars LAICAL O AvId (regulars) inside LOCAL (pub) 32 Create space: at the outset, mode of vanadium electron’s in an excited state MOVEUP F M(ode)+OF+Vanadium+Electron+UP (in an excited state) 34 Endlessly follow and steal back old decoy TRAPAN C TRACk (follow; endlessly)+NAP (steal; rev: back) 36 Fair, accepting one without prior knowledge BLIND O I (one) inside BLOND (fair) 37 Sky unit thanks National Olympic Committee first OCTA N NOC (National Olympic Committee)+TA (thanks) 38 Marie disturbed a different woman IRMA E MARIE (anag: disturbed)

### 28 Responses to “Inquisitor 1275: Divisions by Stan”

1. Joan MM says:

I think you and I(and probably many others) have the same opinion on this Inquisitor – it was all great until it was time to draw the lines! Some of the clues were excellent and it took me a while to winkle out all the extra letters. Once I had the phrase, highlighting was straightforward – but having read up on conic sections, I lost all interest in doing the final step. There was no feeling of ‘oh, that’s very clever/interesting/funny’ – more a feeling of ‘if I’d wanted to do a Listener-type crossword, I’d do the Listener crossword.’

2. starburst says:

Couldn’t agree more. The end bit felt like a particularly difficult and joyless bit of maths homework. Unavoidable when you’re 16. Perfectly avoidable when you’re older and there are trash TV programmes to watch

3. Hi of hihoba says:

I couldn’t agree LESS with the previous two comments. I loved this puzzle, and just because a bit of maths was involved is no reason for people to become all uppity. There is plenty of information to be had by googling “conic sections”, and for those of us with some memory of school maths this was pretty simple. Scientists have an appreciation and knowledge of art and literature, crossword solvers should have a decent knowledge of science and maths, not proudly trumpet their ignorance!!
The lines are to define the four conic sections relative to a double cone stretching to infinity. The cone is actually a solid and the lines represent planes. A parabola is defined by a plane parallel to one of the “edges” of the cone, the circle defined by a plane cutting the axis of the cone at right angles. It’s a bit more difficult to define the hyperbola and ellipse, but if the plane cuts at an angle such that it takes a bite out of both halves of the cone, that is a hyperbola, if only one (and isn’t a parabola), it is an ellipse.
So I drew my lines through the middle of the words from top to bottom, or left to right of the diagram. Hope that was right!

4. kenmac says:

HI.

It’s your very last sentence that sums it up for me. I always feel that the puzzles should be completely unambiguous.

Regarding this puzzle, we (the solvers) had already proved that we’d understood that it was all about cones; we’d identified the three (four) conic sections; that should be sufficient. We shouldn’t have to worry about whether the line should be through the middle of a word, at 48.3 degrees, the right shade of pink, the correct length to the nearest micrometre or anything like that.

Doing a little bit of research on new (or forgotten) subjects is part of the whole Inquisitor experience as far as I’m concerned and I look forward each week to (re)learning something that I’ll probably forget (again) in a couple of weeks.

If I hadn’t been blogging this, I wouldn’t have worried in the slightest and I would have left well alone since I wouldn’t have submitted it.

5. IanN14 says:

I think the point is that the two guiding lines should be drawn from the top right of square c1 to the bottom left of a13, and top left of d1 (ie. the same start point) to the bottom right of square f13.
This forms the cone through which the sections pass appropriately to their type.
Hope this helps.

6. Regalize says:

I too gave up on this one after the grid fill (enjoyable), getting the instructions, highlighting…. and then NOTHING. I was desperately hoping that ‘generators of cones’ might lead to fir trees or even ice-cream. Even googling Conic Sections meant zip. I am one of the proudly ignorant ones Hihoba. Maths like this was always (and still is) beyond me. I can work out the cost of 28 glasses of Pinot Grigio and ten pints of best bitter…. what more do I need?
Nevertheless, I enjoyed the puzzle as I always do.
Well done Stan. And well done kenmac too for the explanation of the lines, zzzzzzzzzzzzzzzzzzzzz!

7. Hi of hihoba says:

Kenmac, I have no problem with where you drew the lines. It is the orientation of the lines that is important, not the exact position.

8. D. Reynolds says:

I hated this. A friend of mine suggested a warning that could be attached to puzzles like this – ‘may contain maths.’ At least we know when the 4 maths Listeners appear and can avoid them if we wish to [although the subject does get smuggled into the remaining puzzles far too often for my liking]. There’s nothing worse than getting mugged by a mathematician after the hard, but enjoyable, clue solving has been gone through. And this was Easter week! Couldn’t we have had something more uplifting?

9. Bertandjoyce says:

What’s with all this hang-up with Maths? We mathematicians (at least we enjoyed Maths at school!) enjoy solving themed crosswords based on language, literature, or whatever. As soon as there is a mathematically based or in this case geometrically based theme people seem to give up on it, complain that the last part spoiled their enjoyment or need a warning(?!!).

Yes, we would agree there is some ambiguity BUT it is the planes of the various sections that define them. The CIRCLE was horizontal so the axis of the cone had to be vertical. The rest was reasonably easily deduced provided you knew the criteria of the other sections. This may be specialist for some but we have had to search literary, musical or other connections to complete Inquisitors in the past so why should this be different?

We loved it even though we did have difficulty finding the ELLIPSE despite knowing it must be there somewhere!

Keep up the good work Stan and thanks to kenmac for the blog!

10. Regalize says:

B&j@9. Well I will admit to an element of sour grapes with this one. I hate not being able to complete an IQ puzzle. However, ‘We mathematicicans…..enjoyed Maths at school’. Ah there’s the rub. I’m not and I didn’t (thanks Sister Eugenius). As the esteemed editor of this series said on the Today programme this morning, cryptic crosswords are about aptitude. http://www.bbc.co.uk/news/uk-22091273 And yes, it can be learned. But its a bit like trying to explain ones addiction to crosswords to friends whose eyes glaze over after two minutes. Sometimes the interest in a subject is just not there.
I am not usually interested in statistics (Listener or otherwise) but I would quite like to know how many entries there were on this puzzle.
Ed?

11. HolyGhost says:

Responses seem to be almost as polarised as reactions to her demise a couple of days ago.

Let me first say a general “Hear, hear” to Hihoba @3 and Bertandjoyce @9 – I’ve had to chase up Schubert’s The Trout Quintet before now, and 36 poets, some obscure, that Schadenfreude dug up four years ago (both fine), and this was fairly bread & butter so-called maths for me.

As to starburst @2 and regalize @5 & 10, I think they could do worse than (re-)reading C.P.Snow’s The Two Cultures – why is it acceptable not to know about the Second Law of Thermodynamics, but unacceptable to be ignorant of Shakespeare’s works?

On The Listener topic … I certainly don’t mind Listener-esque puzzles (I wish I had time for both), but this wasn’t one. And in response to D. Reynolds @8, those quarterly puzzles are numerical, whereas this was verbal with a bit of geometry thrown in. (Sudoku’s aren’t maths either.)

So, having got all that off my chest:
I really didn’t like the lack of clarity right at the end, and like the blogger (thanks go to kenmac) I agonised on and off for a week. The two diagonal lines defining the cone are clear, but what about the other four? For me, the choice seemed to be between from one edge of the grid to the other, or just where those lines intersected the ‘cone’ – I plumped for the latter (tho’ with some misgivings which I won’t bore you with … to do with the precise definitions of a cone and a hyperbola …)

Good stuff from Stan – but, in future, please would he & the editor not leave the rubric with such an ambiguity.

12. D. Reynolds says:

Some people obviously enjoy maths, but do maths formulae ever provide satisfying conclusions to cryptic crosswords? The process of solving is very open ended, most other themes I can think of continue this process – maths formulae are just too finite – there’s nowhere else to go with them. Yes, in the real world there are plenty of other places, but in the real world we tend to communicate what we mean as clearly and directly as possible.
I completed this puzzle, and I’ve done quite a few in this vein, but they leave me cold. I honestly wouldn’t have started any of them if I’d known about the maths element at the outset – all of them disappointed me. Can anyone remember a really good example of a maths themed cryptic crossword?

13. Jake says:

11a made me laugh when the penny dropped!
A brilliant crossword, tough though not that I’m complaining, it had me hooked. And beat me, I had a full grid but could not figure ELLIPSE as regular cell spacing to highlight – I was looking for straight vertical lines, even though PARABOLA is diagonal NE. And I was red herring-ed by ELLI appearing in the grid the P SE on the next lower row!

Thanks for the blog Kenmac and shining light on what I couldn’t see, cheers Stan for an awesome work out. A top puzzle!

14. Joan MM says:

I feel it important to say that I did NOT mind this having a mathematical/geometrical theme – my disappointment is with the final stage, drawing lines. I think this required more knowledge and interest than usual – if you/one didn’t understand the concept, there was no chance you’d be able to finish it off. ‘The lines are to define the four conic sections relative to a double cone stretching to infinity’ and ‘it is the planes of the sections that define them’ seem quite a bit beyond ‘basic’ maths to me.
It’s interesting that there is some ambiguity even among maths-likers re where the lines are to be.

15. twencelas says:

To compare the Inquisitor to the Listener is more than a little harsh, to me it seems wholly unfair.
This is a well constructed puzzle with the various planes at the correct angles within the grid, no mean feat.

The theme may not amuse everyone, but the Inquisitor series shows none of the decline (in my opinion at least) in the quality of amusement compared to the Listener puzzles in the last year or so.

To stay on subject, conic sections are as basic to an education as Shakespeare and a damned sight more useful. And yes my background may be scientific but my breadth of knowledge extends outside this area, often enhanced by these puzzles. Wikipedia (much though I may despise it) can be an aid to educate the under-educated. Personally, I found this fun.

As to the line drawing, personally the diagonals define the cones and the shading the sections through them.

16. D. Reynolds says:

Poor Shakespeare seems to be coming out of this very badly. Considered less ‘useful’ than conic sections in educational terms [but at least on a par with something as basic as the second law of thermodynamics].
it was quite easy to google the solution to this ‘bread and butter’ puzzle, but i was hoping to make a meal of something ‘clever/interesting.’
i think the vocal minority will have their way though – they usually do.

17. Rob H says:

Thanks to Stan for a superbly-constructed puzzle.

I really don’t get all the bluster about the maths/geometry and drawing of lines. The orientation and positioning of the words describing the four conic sections in the grid does give what I thought was a strong indication of the correct orientation of the other two lines, the two diagonals. A quick look at Wikipdeia would have confirmed this. I probably spoent less time ‘researching’ this puzzle than many others.

18. starburst says:

There is a point being missed by the Maths gang.

Firstly, whether you like it or not, crossword puzzles are a WORD-based pursuit, not a mathematical one, and those who approach cryptics from the word go are, by and large, interested in words in my experience.

The second, and perhaps stronger point, is that other themed puzzles (both Listener and Inquisitor) may require the solver to unearth facts or information that is not familiar to them, but no matter how arcane the subject, the solver is still only researching some information. There is a world of difference between me having to look up, for example, the works of Mussorgsky (with whom I’m largely unfamiliar) and having to actually apply mathematical aptitude to a puzzle.

In other words, I don’t need to be a musician or understand musical notation to do a puzzle about Mussorgsky, but the maths puzzles generally require me to know how to DO maths, not just know ABOUT it.

I’ve expressed myself badly but my more irascible self would simply say I don’t think maths puzzles are cryptic crossword puzzles.

19. twencelas says:

I suspect we will all agree to disagree. It’s a puzzle, plain and simple, not one I would describe as mathematical – to me these puzzles are logical, which was my attraction to these in preference to the daily cryptic offerings (which I enjoy as well).
One of life’s beauties is we all see things differently. As to Shakespeare – my apologies to the bard for any offence but Romeo and Juliet did not aid our understanding of astronomical movements.

20. Ross says:

My logic was the same as Hihoba’s, for what it’s worth. So I went right through the middle of the words comprising the sections. But it concerns me a little that, on looking at Kenmac’s solution, I’d agree that it too “works” (with the lines below the words). For a puzzle to be completely solid, there ought to be a single correct solution, and one which once reasoned out is obviously the only correct solution (see e.g. the second Woodchuck, where logic established that you had to highlight the SHADOW). I wonder, therefore, if I’ve (we’ve all) missed something…

I initially decided just to draw the lines through the letters comprising the “sections”, but no further. In agreement with Hihoboa’s theory, though, it struck me that the infinite extension of the “generators” ought to be reflected accordingly. I’m no mathematician, but got that much from (I think) Wikipedia – so I am not myself persuaded that this is a “maths” puzzle requiring the doing of maths, so much as a difficult but not untypical IQ requiring the Googling of the instructions.

Ultimately, I was disappointed with the final step (if I have it right), involving as it did little more than highlighting what was already highlighted (“plus a bit”). The discovery of ELLIPSE, elliptically, was however a joy.

As for the Listener / IQ debate, I remain to be persuaded that the standard Listener is much more difficult than the “top end” IQ. I’ve been doing them both every week for a year, and have found only a few Listeners to be so off the scale that they wouldn’t also make it into the IQ (typically those that require me to get the scissors out and chop up the grid, at which point I leave my toddler to guess with me; seems to work).

Out of interest, for those of you who do regularly submit IQs to the weekly competition, any idea how many entrants there are? I’ve been submitting steadily for a year, and not even a mensh! My girlfriend has reached the conclusion that it would have been much cheaper to “buy the sodding champagne” than spend it on stamps.

21. John Lowe says:

In reply to Ross@20: At one time my mother and I used to submit our two separate entries, and there were five winners each week. At the rate at which we won bottles of Champagne I guessed there were of the order of 300 people submitting answers. Circumstances have changed and we now only submit one entry between us, and I would guess that there are more people submitting answers – or we are on a run of worse luck….

A more official count would be interesting!

22. Hi of hihoba says:

Regarding numbers of entrants, I have corresponded with both the previous editor (Mike Laws) and the present one and so far as I know neither was able to obtain any information about numbers of entries from the Independent Magazine editor.
Has anyone else any source of information? My experience with the champagne has also been one of diminishing returns over the years, so I suppose the entry keeps increasing, which is good!

23. Ross says:

I remember it ‘back in the day’ when you got a choice between champagne and olive oil. The one time I cicled the latter, I won…

24. HolyGhost says:

Further to the number of submissions to the weekly IQ competition:
I recall that a couple of years before he died, Mike Laws (the previous editor) said the production team had informed him it was “bucketloads” – he was left unsure as to how many buckets there were & the size of each of them.

25. Nick says:

I don’t understand all the concern over maths, it is an awful long time since I did any and I can’t claim to have done any here and fail to see how anyone else can. I just looked on the Internet for conic sections in the same way that I would have looked for any thematic content and copied what I found in the same manner. It could have been a verse from a poem and the amount of maths involved would have been the same.

I thoroughly enjoyed the puzzle and my only minor gripe would be why was in necessary to both highlight the words and draw lines as it seemed a bit confusing. Would it not have been better just to draw lines – the words acting as indicators as to where they should be?

26. Fran says:

D. Reynolds@12 asks: Can anyone remember a really good example of a maths themed cryptic crossword?
Many years ago, the Magazine Crossword, as it was then called, featured a series of answers where letters clashed. The numerical difference between letters resulted in Pi (to about 24 digits); clashing letters had to be replaced by these numbers and then the Pi shape highlighted. I recall completing the grid, with the clashing letters, but then coming to a halt. (I’m not sure if the rubric included the hint about replacing clashes with numbers.)
My recollection is that there were no winners that week but the solution, when published, seemed eminently logical and satisfying.

27. D. Reynolds says:

That sounds like a clever idea well realized. I was hoping that someone would provide at least one example [pity I missed the puzzle]. Thank you Fran. And as the theme is pi it can’t possibly be described as finite! The perfect exception that proves the rule maybe?

28. D.Reynolds says:

…..well if you wait long enough!
For me, Kea’s Enigmatic Variations 1125: TRRNRUNxVT of June 1st 2014 is a hybrid cross(maths)word that works incredibly well. Theme and execution are perfectly integrated and I’m amazed that it’s possible to construct something as good as this given the constraints [but then I’m not good enough at maths to know any better].
If I hadn’t hit on the magic phrase ‘Alphametic’ in my frantic wiki searches for a suitable ‘engine’ I couldn’t have finished it off [perhaps this is its one tiny weakness?] Although I’d still have been impressed without actually finishing it.
If this kind of thing cropped up every 5 years or so I’d be overjoyed. Sadly, I’ll probably get an ill conceived maths hybrid every month or so for the next 5 [which seems to be the trend these days].

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