Fifteensquared

Never knowingly undersolved.

Independent 7317/Virgilius

Posted by John on March 30th, 2010

John.

Typical brilliance from Virgilius. At first I thought, after predicting confidently that the long word across was going to be SYMMETRICAL, what’s the big deal? All crosswords are symmetrical. Then I saw it (not immediately, having got so used to Virgilius using the across answers to illustrate his theme): all the down answers use only the letters A, H, I, M, O, T, U, V, W, X, Y, so that they all have a vertical line of symmetry (not the rotational symmetry of the crossword grid).

Across
7 A LA CARTE — (a claret a)*
8 FOR A
10 BI(ST)RO
11 MEALTIME — I think this is simply saying that two is not the usual time for tea, and playing with “Tea for Two”, but perhaps this isn’t the whole story
12 F{airly} A{wful} C{ontract} TO TUM
15 ADOPTS — 2 defs I think
17 SYMMETRICAL — refers to the Nina, with two meanings of ‘down’
21 FINISH — to perfect something is to finish it, but I can’t see the rest
22 OP OP AN AX — not a plant I was familiar with, but it clearly begins OPOP
24 YOGHOURT — yo{u} (trough)*
27 TROJAN — 2 defs, one of them referring to Paris and the Trojan War
29 HEAR{t}
30 PACIFISM — if in (camp is)*
 
Down
1 TAXIWAY — tax I “weigh”
2 TAUT — “taught”
3 WAY OUT — 2 defs
4 A TOM — a queen (= female cat) needs a tomcat if she is to produce a family
5 MOO T
6 MAM MOTH
9 HAW A II
13 unhealTHY MIce
14 M OTTO
16 tOMAHAwk
18 MAHOUT — (ham)rev. out — a mahout is an elephant’s keeper and driver, a word I first came across in George Orwell’s brilliant essay ‘Shooting an Elephant’
19 TIMOTHY — (myth I)* about OT
20 MA(HAT)MA
23 O (U) TWIT
25 HO A X
26 THAW — (what)*
28 O MIT

22 Responses to “Independent 7317/Virgilius”

  1. IanN14 says:

    Thanks John.
    I think 21ac. is also IN (present) inside FISH (school).
    Another fantastic obliquely hinted theme from the most brilliant setter.
    Please keep them coming…

  2. Mick Hodgkin says:

    Yes, great stuff. I noticed a limited set of letters coming up, but didn’t fully grasp the them until I had the whole grid filled. I don’t draw Y symmetrically myself, but that’s probably just for speed of completing crosswords.

  3. Eileen says:

    It’s been said so often but how does he keep doing it? Many thanks again, Virgilius / Brendan. We’re really being spoiled this week.

    [I'm with you re the Ys, Mick!]

  4. Richard Palmer says:

    Virgilius is brilliant as always.

    On my first pass through I wrote PALINDROMIC at 17 across thinking it is quite within Virgilius’s capabilities to come up with such a grid.

    I’m not sure about 24 across how “you cut initially” gives YO – shouldn’t it be “you cut finally” or just “you cut”?

  5. Gaufrid says:

    Richard
    In 24ac it is just ‘you cut’ to give YO. The ‘initially’ indicates that YO goes before the anagram of ‘trough’.

  6. Richard Heald says:

    That’s how I interpreted 24 Ac too.

    Like Richard P, I confidently entered PALINDROMIC at 17 Ac, thinking that the rest of the puzzle would be a piece of cake – how wrong I was! And how clever of Virgilius to use the crucial discovery that every second letter of SYMMETRICAL falls within the required subset. The only (extremely minor) flaw for me is that the letter V is not included in any of the down answers to complete the subset. Otherwise, full congrats to the V-man on yet another work of genius, hot on the heels of Brendan’s masterpiece yesterday.

  7. nmsindy says:

    Thanks for the great blog, John. Yes, more wonderful stuff from the master – I too thought first of palindromes tho was not too confident.

    Quite apart from the theme, some of the clues were really great esp liked MEALTIME (I agree with yr explanation of this, John), WAY OUT and ATOM. I read 15A (ADOPTS) as a cryptic definition.

    And, while not wanting to get too deeply into the symmetry issue, on which many know more than me, aren’t crosswords, like those chosen letters, symmetrical about a vertical axis ie the eighth column?

  8. Peter Biddlecombe says:

    Took a quick look at this and enjoyed it.

    nmsindy: No! The type of symmetry used in standard crossword grids is rotational symmetry, which is all about turning the puzzle 90 or 180 degrees about around a central point – the middle of the eighth square of the eighth row or column, i.e. the midpoint of the grid.

  9. nmsindy says:

    Thanks, Peter, that makes sense all right.

  10. Brendan says:

    I was thinking of doing something relating to symmetry, and was amazed when I noticed that all the even letters, when capitalised, of SYMMETRICAL are (and only one of the odd letters).

    Finding possible down words was easy with Crossword-Compiler by entering a bunch of A’s, a bunch of H’s, and so on, then asking for partial anagrams.

    On Richard Heald’s comment, I somehow just forgot about V, consequently kicking myself.

  11. Kathryn's Dad says:

    Rats! Nearly finished it but got stuck in the NE corner. Even with most of it done, couldn’t twig the symmetry theme. But what a clever theme and a very stretching puzzle for me. I can feel a glass of red coming on …

  12. Uncle Yap says:

    Sorry I come in one day late (if only Eimi can arrange for the Indy puzzle to be in printable form so I do not have to wait for someone to type out all the clues and solve on paper).

    I must be dense today and after happily solving the delightful puzzle, I do not seem to understand what this “vertical line of symmetry” is all about. Can someone be very explicit in describing the symmetry. Thank you.

  13. SimonG says:

    Thanks, Uncle Yap – I thought it was just me being thick…

  14. Kathryn's Dad says:

    Uncle Yap and Simon, it’s that all the down clues are symmetrical about their vertical axis, because all the letters that are used in them are similarly symmetrical. So if you draw a line down the middle of all the down clues, they’ll be the same shape on the left and right hand sides.

    If it’s any consolation, it took me ages to realise this as well.

  15. jmac says:

    Re # 12 & 13.
    As well as vertical symmetry, there is also horizontal symmetry (from mathforum.org):

    VERTICAL SYMMETRY: if you draw a vertical line |
    |

    down the middle of an object with vertical symmetry, the two sides will be mirror images of each other. Examples of capital letters that have vertical symmetry are:

    A H I M O T U V W X Y

    HORIZONTAL SYMMETRY: if you draw a horizontal line ______________

    across the middle of an object with horizontal symmetry, the top will be a mirror image of the bottom. Examples of capital letters that have horizontal symmetry are:

    B C D E H I K O X

  16. jetdoc says:

    Like several others, I completed this without spotting the theme — in my handwriting, several of those letters are far from symmetrical; if I’d been completing it on-screen, maybe it would have been more obvious. I do wish I had spotted it, because it’s very clever.

    Can someone explain the significance of ‘in exercise’ in 5d?

  17. SimonG says:

    @Kathryn’s Dad – thanks for the explanation which, belatedly, now makes sense to me… I must say I find it challenging enough to complete the Grauniad & Indy crosswords without trying to spot symmetries (vertical and/or horizontal) as well! Having said that, I do now appreciate why most of the above comments are so complimentary to the setter…

  18. Uncle Yap says:

    Ah ! So!
    Kathryn’s Dad, thank you for the explanation. My esteem for Brendan / Virgilius has gone up a couple of notches this last few days.

  19. Eileen says:

    Hi jetdoc

    A moot is an exercise for law students, a discussion of a hypothetical case.

  20. John says:

    Having taught about symmetry for years I found all the symmetry ideas here very straightforward, but I shouldn’t have assumed that this was the case: if you haven’t thought about it before it’s not at all obvious.

    Basically there are two types of symmetry, line symmetry (also called reflection symmetry or mirror symmetry, exemplified by the letters A, T, W etc, which have a vertical line of symmetry, and B (perhaps), C, E etc, which have a horizontal line of symmetry; also L, if carefully drawn, which has an oblique line of symmetry) and rotational symmetry (exemplified by S, N and Z). The order of rotational symmetry is the number of different ways in which a shape can be rotated to fit into the original shape. Thus S, N and Z have rotational symmetry of order 2.

    But these are not exclusive. A shape (like H) can have two lines of symmetry and also rotational symmetry. No letters have rotational symmetry of order 4 (unless X is very carefully drawn, or O is extremely carefully and rather artificially drawn), but the swastika has rotational symmetry of order 4 and no lines of symmetry, while the square has rotational symmetry of order 4 and 4 lines of symmetry.

    Crossword grids usually have rotational symmetry of order 2 and no lines of symmetry, but there are other types: I think (but am not sure) the Daily Telegraph often carries grids with four lines of symmetry and rotational symmetry of order 4. Quite often you will see rotational symmetry of order 4 and no lines of symmetry.

    Phew.

  21. Colin Blackburn says:

    Excellent puzzle. Like the Richards I entered PALINDROMIC far too quickly. Once I had the Y I quickly saw SYMMETRICAL realised what was going on. Studying M336 Groups and Geometry paid off, if only in lodging symmetry in the accessible part of my brain.

  22. Kathryn's Dad says:

    I’m starting to feel slightly humbled by my explanation at no 14 …

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