# Fifteensquared

## Guardian 25,044 – Brendan

Posted by Andrew on June 23rd, 2010

Another clever themed puzzle from Brendan, this time based on (mostly elementary) mathematics. Amazingly, just about every clue and answer has mathematical connections – a brilliant feat. Maybe my mathematical background helps, but I found it not too hard, though it took me a while to understand 25ac.

 Across 5. CHORDS Double definition – chords can be geometrical or musical 6. PASCAL PA[y] SCAL[e] 9. CURVES V in CURES (preserves) 10. QUADRANT Double definition 11. STAR ST[atistics] + AR[ithmetic]. Apparently “the artist formerly known as Prince” has been known as Prince again since 2000. 12. PRIMORDIAL PRIM[e] + ORDI[n]AL 13. DENOMINATOR N in MODERATION* 18. HUNDREDTHS TH[em] in HUNDREDS 21. PAIR A in PI R – the circumference of a circle being 2*pi*R 22. PLUS SIGN The shape formed by 8dn and 13ac in the grid. 23. BISECT B + I SECT – the answer is mathematical, even if the clue isn’t 24. DEGREE Double definition – one degree (the angle) is 60 minutes 25. CENTRE Double definition – moderates are the political centre, and players 12 and 13 are “centres” in Rugby Union (which has teams of 15) Down 1. CONVERSE Double definition 2. ADDS UP Double definition 3. PARABOLA PARA + LOB< + A. The parabola is the shape of a trajectory (in idealised conditions) 4. SCORED CORE in S D 5. COUNTS Double definition 7. LINEAR Double definition – Linear A and Linear B were scripts used in ancient Crete, and a straight line is the shortest distance between two points. 8. EQUIDISTANT D in QUANTITIES* 14. ONE-SIDED Double definition – “partial”, and reference to equations having 2 “sides”, separated by an equals sign. 15. OPPOSITE Double definition – “one kind of side of triangle” is perhaps a bit vague, but it’s used for example in the definition of the sine of an angle: Opposite over Hypotenuse. 16. EUCLID CLUE* + I’D 17. CIRCLE L in CIRCE 19. DESIGN S in DEIGN 20. SUBSET (US BEST)*

### 53 Responses to “Guardian 25,044 – Brendan”

1. Richard says:

Thanks for the early blog, Andrew.

I really enjoyed this. Beautifully crafted. I must admit however that I couldn’t fully see how 3, 7, & 21 worked until I read your explanations.

2. Bryan says:

Many thanks, Andrew, this was very enjoyable and I was amazed at how Brendan worked the theme.

Like Richard, I had failed to see how some of the clues worked, particularly 25a and 7d.

Well done, Brendan, my Irish great grandparents (who popped out of Cork) would have been proud of you.

3. Ian says:

Thanks Andrew. Thanks to Brendan too for yet another excellently themed crossword.

As a result of the flawless clueing and a good maths knowledge I was able to shift this one in 19′.

4. Dave Ellison says:

Thanks Andrew and Brendan. Needed the explanation for 25a (I contemplated SETTLE but couldn’t reconcile that with the S on MODERATES, so plumped for CENTRE, as it would be part of the theme).

Also being a lapsed mathematician, I found this quite easy – 21′, or so (about 16′ but the last two, 18a and 25a, held me up; we have had HUNDREDTH before recently – why is this one so hard to complete given all the checking letters?)

5. Martin H says:

I’m not a fan of these through-themed puzzles. The setter, obediently following his own inner daemon, is obliged to shoehorn thematic material in wherever he can. We solvers then say, ‘Oh how clever’, and dutifully fill in the resulting unsatisfactory clues.

Ten out of twenty-six clues here are dd’s, of which 2, 14, 15 and 24 are weak and 25 limited in its appeal. In 7, ‘linear’, except in certain particular cases, does not imply ‘straight’. ‘Arrangement of lines or shapes’ (19) is a feeble definition of ‘design’; 21, piR is not the circumference of a semicircle – it’s half the circumference of a circle, which is not the same at all; nor is ‘+’ (22) an ‘additional symbol’ – it’s a symbol for addition (although the rest of that clue was very nice). All careless clueing. There are three good clues at 8, 12, and 17, but the rest are routine stuff, unremarkable except for their role in the theme.

6. Eileen says:

Many thanks for a great blog, Andrew.

Well, not being a mathematician, lapsed or otherwise, [more at home with Linear A and B and Circe] I might have expected to be foxed by some of these answers, but, thanks to the aforementioned flawless cluing, I didn’t have any problems.

I particularly liked PRIMORDIAL, DENOMINATOR, PAIR and PLUS SIGN.

Once again, I have to say, ‘How does he keep on doing it?’ Thanks for a super puzzle, Brendan.

7. duncandisorderly says:

I have to agree that 21ac is not strictly accurate.

but is martin h playing the role of “angry maths teacher”?

d.

8. mhl says:

Thanks for the post, Andrew. I thought this was very enjoyable throughout – a great theme and it’s always pleasant to have a puzzle that’s doable on the way into work :) In my opinion the cluing was first rate.

Martin H: obviously I disagree with your comment on the whole, but on one particular point: “additional symbol” to mean “symbol indicating addition” is surely an example of a standard type of cryptic device.

9. sidey says:

Thoroughly enjoyed this although the rugger reference in 25 meant nothing to me.

10. Richard says:

duncandisorderly @7

Whilst Martin H’s views might be at variance with most of the others today, that doesn’t excuse you going of on a tangent….

11. liz says:

Thanks for the blog, Andrew. I thought this was a lovely puzzle and enjoyed having to dredge up my maths knowledge from long ago. I wouldn’t want every puzzle to be themed, but Brendan does it so well…

I needed the blog to see the wordplay at 25ac.

12. Stella Heath says:

As often happens, I find my feelings reflected perfectly by Eileen’s comments – and thank you for answering my query yesterday.:-)

I was quite perplexed to begin with, and got to the last half of the across clues without solving anything, but once the penny dropped, the puzzle was quickly polished off, with not a few smiles on the way.

Thank you Andrew, and Brendan

13. Pat says:

I loved this. Another tour de force from Brendan, and I can happily forgive any slight technical inaccuracies. Primordial was brilliant.

14. pendred says:

i read 22 as additional=plus and symbol=sign so perfectly fair to my mind.

15. EdUS says:

Re Martin H’s criticism: While I agree some of the clues were weak, even obvious for those of us with a mathematical background, I fully approve of setters’ use of imprecise clueing as it makes divining the answer more challenging while leaving no ambiguity regarding its correctness. Perfect blog BTW.

16. Lopakhin says:

A meal can take hours to create and be wolfed down in minutes – to the chagrin of the cook. I wonder how long (days? weeks?) it took Brendan to concoct this little marvel that I raced through with gobsmacking ease. Thanks, anyway, to him for getting me to burp up deeply buried – and in my subsequent life, totally useless – information.

17. Jobs says:

This is brilliant. Possibly the best Brendan offering yet.

Thank you Andrew for explaining 7D

18. Little Dutch Girl says:

This took the House Elf and I 15 mins – he’s an engineer and I’m a scientist. However it didn’t detract from the enjoyment – except when the House Elf slipped into anorak mode and I had to endure a rather tedious explanation of what a conic section is. I shouldn’t have asked and I won’t bore anyone with the explanation.

Perhaps we had the edge on Dave Ellison with 18a because I was born on the Hundred of Wirral.

We like the themed ones but not too often. But the blog as always was good to read. Thank you Andrew.

19. Derek Lazenby says:

Damn! Right up my street and y’all beat me to the comments. Didn’t get the rugby one though.

20. John says:

If it’s indeed a dd, can anyone explain why “playing with” = OPPOSITE?

21. Bryan says:

John @ 20

John Travolta was ‘playing with’ (or ‘opposite’) Olivia Newton-John.

22. Martin H says:

hi mhl (@8) – your cryptic device is presumably along the lines of: as ‘personal’, among many possible examples, means ‘related to the person’, so ‘additional’ can be nudged into meaning ‘related to addition’. I find the real meaning of additional too strong to bear this shift, and even if pendred’s explanation @14 does work, and I’m not convinced, we are left with ‘additional symbol…….(4,4)’ – so obvious that the subsidiary element becomes redundant.

23. iDIYot says:

Hi John,

Does it mean “OPPOSITE” as in “OPPOSITION” ie “OPPONENT”?

24. John says:

Thanks IDIYot and Bryan:
I suppose there is always a way in which some sort of explanation can be dredged up, (I thought someone might bring up bridge as well), but “opposite” is literally “in opposition” or “against” and thus “playing against” would have been more appropriate and also resulted in a quicker solve of the clue for me.

25. Kathryn's Dad says:

Okay, for seasoned mathematicians there might have been one or two ‘well, that’s not quite right, now if you’ve got 10 minutes I’ll just explain why’ moments (and I have studied maths and I love you all in a special way, before you – and England – kick off …)

But I’m with Jobs at no 17. This was one of the best Brendan/Virgilius puzzles I can remember. The mutt’s nuts, imho.

26. FumbleFingers says:

I love it when Brendan goes for broke on a themed puzzle! Any newbies here who like this one should check out his equally relentless 24,521 in Guardian archives.

I thought no clue was so weak as to merit criticism, especially in this “uber-theme” context. PRIMORDIAL particularly tickled my fancy. The only bit where I needed Andrew’s help was understanding 25a, since I know little about rugby.

@iDIYot – per Bryan @21, OPPOSITE in the sense “Travolta starred [with | opposite] Olivia Newton-John in Grease”.

27. FumbleFingers says:

btw – I always used to think “starred opposite” was only applied to male and female lead actors, alluding to their being opposite sexes.

But Google tells me lots of people are happy with, for example, “Meg Ryan starred opposite Diane Keaton in Hanging Up”. Maybe they’re “opponents” in the sense of fighting to be the main star. I just don’t know.

28. Richard says:

Is it simply the case that a star performs opposite a co-star irrespective of gender? Presumably one does not play ‘opposite’ anyone lower in the cast?

29. muck says:

Thanks for the blog Andrew, and others for further comments.
Brendan’s puzzles are always a treat, and I thought this one of his best.
I guessed 25a CENTRE and 7d LINEAR, but needed the explanations here.

30. FumbleFingers says:

OED defines opposite [number] as “…a partner, a counterpart…”

31. Lopakhin says:

Hence army slang: oppo – for one’s khaki compadre

32. jerb says:

Hang on a minute Martin H and duncandisorderly – isn’t the clue at 21a “Circumference of SEMIcircle….”? Surely that makes PI R alright.

33. Andrew says:

I think Martin’s (valid) point is that a semicircle’s perimeter includes the diameter of the circle, so its length would be pi*R + 2*R.

34. Median says:

If you’re looking in, Brendan, thanks very much. I thought this clever puzzle was the most entertaining Guardian cryptic for quite a while.

35. FumbleFingers says:

Quite agree, Median. If you’re looking in, Brendan – you are the bee’s knees, mutt’s nuts, cat’s whiskers, & various other unmentionable doggy bits. Maybe one wouldn’t want it every day, but this has been a real treat, thank you!

36. Scarpia says:

I struggled with this,as maths is not my strong point – I passed at O level in 1970 and have probably forgotten it all since then – except for how to count!
Some answers were part guesses e.g. I didn’t know conic sections were curves(or vice versa?).
Was chuffed to work out “pair”,so some of the old knowledge must have stuck – an excellent clue.
Nice bit of misdirection in 12 and 25 across,kept trying to fit themed words as answers.
Saying all of which,I agree with Martin H @5 – a themed puzzle doesn’t really impress me,it’s the quality of the clueing that counts.
I guess I must be missing something because,yet again,I am perplexed as to why Brendan’s puzzles are so highly praised;I’m not saying they’re bad,but for me they lack “sparkle”.

37. snigger says:

duncandisorderly – “angry maths teacher”???????

do they teach maths nowadays??

Never mind worrying about the mathmetical accuracy of 21ac – i have spent most of today, not on the crossword, but trying to explain “pi” to “the lad”. He makes a good cup of coffee so for now his employment is secure !!

the good news is, the brickies are right up there with pythagorus – 3,4,5 and you have a right angle.

38. Davy says:

Thanks Andrew,

An interesting puzzle from Brendan although I failed, as yesterday, to complete the NW corner. I thought that STAR was too obvious so I didn’t put it in. Also, I was convinced that 5a had a double ‘O’ (circles) in it.
I didn’t know about the other meaning of CHORDS but I should have got it from ‘harmonious combinations’ especially as I play the guitar. The DD is definitely my least favourite clue format and the only way to solve
it is to think of the correct word. These days my memory is about as good as an amoeba so I struggle with DDs.
My favourite clues of today were 12a and 22a.

Thanks to Brendan and I think his puzzles should be more frequent.

39. brr says:

As yet another lapsed mathematician I really enjoyed this – especially PRIMORDIAL.

40. monica says:

simply superb.

41. Mr Beaver says:

What a lot of lapsed mathematicians there are among us !
A delight for me therefore (apart from 25a – though I guessed it had some Rugby connection…) but I felt sorry for those without such a background.

42. Scarpia says:

All these “lapsed mathematicins” remind me of the old joke about the constipated mathematician.

43. Dave Ellison says:

Scarpia @42 A mathematician worth his salt wouldn’t need a pencil In any case it was “lapsed” not “prolapsed”!

44. FumbleFingers says:

Gaufrid – do you keep stats? My guess is Brendan might be a serious contender for “highest number of different people posting”. Hardly any of whom are finding fault.

As I hope he knows (biology notwithstandsing) I would love to have babies with Brendan. When it comes to kick-ass crosswords, he da man!

45. eimi says:

Of course, I couldn’t possibly comment, for fear of showing favouritism, and I’m very lucky to have such a superb group of setters over at the Indy, but I can’t deny that, as setters go, Mr Greer is indeed apian patellae, and I look forward to his next puzzle as keenly as the solvers.

46. Hornbeam says:

A short, belated well done from me also.

47. scarpia says:

Dave Ellison @42.
Very good!

48. Geoff Chapman says:

Yeah, Brendan is da man. The new Araucaria. Or possibly the first Brendan. Only quibble, 25ac would have been fairer if it was “12 or 13 in XV” rather than ‘fifteen’.

But who am I to argue? Give the man more and more opportunities.

49. Huw Powell says:

This was fun. I noticed the interesting grid when I printed it the other day, and sat down to it today. It’s always nice when one gets the first clue one looks at (CHORDS). Then I rapidly noticed the math theme, and fairly ripped through the puzzle, slowing down for the last 4 or five that I got. Thought 22 and 25 were very amusing, the self-references were nice. Was it a bit easy? Sure, some clues were very easy, but I think that Brendan managed to tie every single word to the theme more than makes up for it.

One little problem, I doubt I ever would have got 18, not knowing or having a way to get to “hundreds” from “old parts of county”.

Also also, once I saw the theme I decided I ought to be able to do it without any aids because I like math. Shame about what I can only assume is a Britishism preventing completion.

Thanks Brendan, and Andrew!

50. Huw Powell says:

PS, 21 was the second clue I got, and I almost fell off my chair laughing.

51. Huw Powell says:

Hi Martin R,

At 22A, “additional” = “plus” + “symbol” = “sign”. The reference to the diagram is the literal definition. The clue is flawless.

And as far as being easy, that is more than made up for it not just being “heavily” themed, but by *every single entry* being themed. Oh well, different strokes for different folks.

52. Huw Powell says:

One more commment. 25 doesn’t have to have anything to do with rugby. It is based on the grid – answers “numbered” 12 and 13 are both in the CENTRE of a 15 square row or column. So that part of the clue is actually a double definition using the same words! Wow.

53. Jan says:

I’m ages behind but what the h***.

As a retired teacher of mathematics I loved this crossword although 25 stumped me. I thought it was a rugby reference but didn’t think of the obvious position.

I can assure the doubters that my students would recognise all the references. I was quite happy with the semi-circle clue – it’s a cryptic crossword, for goodness sake! Where were the mathematicians complaining about ‘splitting the difference’ for the mean in a recent Genius crossword?

This was a superb puzzle. Thank you again Brendan.

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