Qaos provides the March Genius challenge
The preamble told us that the letters in 16 squares are not allowed for in the wordplay of the clues involved. Taken as a group, when encoded these 16 letters magically lead to a number that is to be entered in the box at top of the entry form.
The symmetry of the unclued letters in this puzzle became fairly obvious early on which was a help in identifying the wordplay. Some crossing letters and the definitions were often enough to identify the down entries and the symmetry pointed the way to the necessary wordplay.
The unclued letters were always unchecked letters in the down entries, so all the across clues were normal.
If I’d been more on the ball when solving the clues I might have noticed sooner that the unclued letters were the first sixteen letters of the alphabet. I didn’t notice that until I got to the endgame and thought about encoding. I put the unclued letters in order and found A to P inclusive.
At that point I reckoned that the encoding would be a simple A=1, B=2 … P=16 so I mirrored the square pattern of the unclued letters in the grid with a square of numbers. Then the meaning of the word ‘magically’ in the preamble became clear as the numbers formed a magic square with all the rows and columns adding to 34.
However, this is not just a simple magic square, it is a ‘most perfect magic square’ in that multiple groups of four numbers add to 34. For the technically minded, a ‘most perfect magic square’ is defined as follows – a square of doubly even order n = 4k is a pan-diagonal magic square containing the numbers 1 to n2 with three additional properties: Each 2×2 subsquare, including wrap-round, sums to s/k, where s = n(n2 + 1)/2 is the magic sum. In our case k=1, n=4 and s=34.
In the diagrams below I have found 54 possible groups of 4 numbers that add to 34. I am not sure if that is all the possible groupings. I am sure someone reading the blog will be able to say how many groups of 4 numbers there should be.
The clues were very fair with some cleverly linked pairs of clues included. There was also an allusion to one of the major figures of the crosswording world in 13 across where Afrit got a mention. Afrit was A F Ritchie, who spent much of his life in education and religious circles. It is worth reading about him online by clicking here
Qaos must have been constrained in the construction of the puzzle by the position of the unclued letters. I believe there are 48 possible non-symmetric most perfect magic squares, so Qaos had a few choices, but even so the unclued letters impact on the possible choice of words for the grid.
I enjoyed this Genius very much. Thanks to Qaos.
The filled grid looked like this.
MAGIC NUMBER: 34
| No | Clue | Unclued Letters |
| Across | ||
| 1 |
The Queen abandons regular tradition (6) CUSTOM (tradition) CUSTOMER (person who usually frequents a certain place of business; a regular) excluding (abandons) ER (Elizabeth Regina; Queen Elizabeth) CUSTOM |
|
| 5 |
English politician in exam storm (7) TEMPEST (storm) (E [English] + MP [Member of Parliament]) contained in (in) TEST (exam) T (E MP) EST |
|
| 10 |
Acting school returns for Jewish month (4) ADAR (in the Jewish calendar, the twelfth month of the ecclesiastical year, the sixth of the civil year [part of February and March]) RADA (Royal Academy of Dramatic Arts; acting school) reversed (returns) ADAR< |
|
| 11 |
Those moving with skill? Reversing learners during turns (10) TRAVELLERS (people who moved around; those moving) ART (skill) reversed (reversing) + ([L {learner }+ L {learner} to give learners] contained in [during] VEERS [turns]) TRA< VE (LL) ERS |
|
| 12 |
Hard to treat end delivered (8) STUBBORN (hard to work or treat) STUB (end) + BORN (delivered) STUB BORN |
|
| 13 |
Afrit cryptic following 1s (6) TARIFF (a list or set of CUSTOMs [1 acrosses] duties) Anagram of (cryptic) AFRIT + F (following) TARIF* F |
|
| 14 |
Allegedly wants massages (6) KNEADS (massages) KNEADS (sounds like [allegedly [cited in quote or discussion]) NEEDS (want) KNEADS |
|
| 16 |
Jailor frees northern bird (6) TURKEY (a bird of the pheasant family) TURNKEY (under-jailer) excluding (frees) N (northern) TURKEY |
|
| 18 |
Hit by small vehicle … (6) STRUCK (hit by) S (small) + TRUCK (vehicle) S TRUCK |
|
| 20 |
… and another tug? (6) STRAIN (stretch; draw tight; tug) S (small) + TRAIN (vehicle) created by using the ‘small vehicle’ word play of the previous clue again [another] S TRAIN |
|
| 22 |
Guard in Lord of the Rings, perhaps, assists leaders in trouble (6) PATROL (guard) Anagram of (in trouble) LOTRPA (first letters of [leaders] each of LORD, OF, THE, RINGS, PERHAPS and ASSISTS) PATROL* |
|
| 23 |
Science of law: no money for a quiet defence (8) NOMOLOGY (the science of law) APOLOGY (defence; justification) with (NO + M [money when used in the money supply designations M0, M1 etc) replacing (for) (A + P [quiet] NO M OLOGY |
|
| 25 |
Off-road licence not accepted — it’s made up (10) RECONCILED (restored back to friendship; made-up) Anagram of (off) ROAD and LICENCE excluding (not) A RECONCILED* |
|
| 26 |
Biden, for example, wins hearts with style (4) CHIC (with style) CIC (President Biden is Commander-in-Chief [CIC] of the American military forces) containing (wins) H (hearts) C (H) IC |
|
| 27 |
Foreign body eaten by goose? Oddly, that signals the end (7) GOODBYE (form of address at parting; a word that signifies the end of a meeting or get-together) Anagram of (foreign) BODY contained in (eaten by) GOE (letters 1, 3 and 5 [oddly] of GOOSE) GO (ODBY*) E |
|
| 28 |
Demand can cut capital, shilling first (6) INSIST (maintain very firmly; demand) TIN (can) excluding (cut) T (the first letter [capital]) + S (shilling) + IST (first, if you read the first character as a 1) IN S IST |
|
| Down |
Unclued letters |
|
| 2 |
University a little upset with no good revising (8) UPDATING (revising) U (university) + TAD (small amount; a little) reversed (upset) + NG (no good) U DAT< NG |
P I |
| 3 |
Heath Robinson component produces deep, rhythmic sound (5) THROB (beat or strong pulsation; deep rhythmic sound) THROB (hidden word in [component] HEATH ROBINSON) THROB |
|
| 4 |
Procedures might initially get shot to pieces (7) METHODS (procedures) M (first letter of [initially] MIGHT) + an anagram of (to pieces) SHOT M THOS* |
E D |
| 6 |
Type of seat to build, right on the floor (7) EJECTOR (reference EJECTOR seat [a seat in an aircraft, etc that can be shot clear with its occupant in an emergency]) ERECT (build) with R (right) being moved to the end to form EECTR – as this is a down clue, the R is moving to the bottom of the entry EECT R |
J O |
| 7 |
Animal in river to fight back, not with attention (5,4) POLAR BEAR (an animal) PO (river in Italy) + BRAWL (fight) excluding (not ) W (with) reversed (back) + EAR (attention) PO LAR B< EAR |
|
| 8 |
Unkempt person‘s coats are back-to-front (6) SCRUFF (untidy or unkempt person) FURS (coats) reversed (back-to-front) SRUF< |
C F |
| 9 |
Carefully move around Spain with captivating lovely borders (13) PAINSTAKINGLY (carefully) Anagram of (move around) SPAIN + TAKING (captivating) + LY (outer letters of [borders] LOVELY) PAINS* TAKING LY |
|
| 15 |
Rider preparing for trade week? (9) AFTERWORD (epilogue [concluding section]; a RIDER is a clause or corollary added to an already complete contract or other legal document) Anagram of (preparing) FOR TRADE and W (week) AFTERWORD* |
|
| 17 |
Very difficult to promote teacher’s 11 (8) PILGRIMS (TRAVELLERS [entry at 11 across] to a holy place) PIG (something that is very difficult) + SIR (form of address for a male teacher) reversed (to promote; down entry) PIG RIS< |
L M |
| 19 |
Wretched posh girl (7) UNLUCKY (wretched) U (upper class; posh) + LUCY (girl’s name) U LUCY |
N K |
| 20 |
State of meditation is uplifting to suppress being angry (7) SAMADHI (state of super-awareness brought about by profound yogic meditation, in which the yogi becomes one with the object of the meditation) IS reversed (uplifted; down entry) containing (to suppress) MAD (being angry) S (MAD) I< |
A H |
| 21 |
Extremists drain contents of espresso at summerhouse (6) GAZEBO (summerhouse or other small structure giving a commanding view of the landscape) AZ (first and last [extremists] letters of the alphabet) + EO (letters remaining in ESPRESSO when the central letters AZ EO |
G B |
| 24 |
Hair of English philosopher cut short on Sunday (5) LOCKS (hair) LOCK LOCK S |
For the longest time, I was sure that the reference to a “number” in the instructions was the classic cryptic clue for some sort of anesthetic, to go along with the pun “painstakingly” down the middle, but no anagram or cryptogram for the letters A through P seemed to work. I realized what was happening when I highlighted the letters in the grid, and the square pattern was clear. Incredibly ingenious puzzle.
Yes, a very enjoyable puzzle. I think that there was an Inquisitor puzzle a while ago that also exploited this theme, but in a different way.
Many thanks to Duncan for the detailed blog and for everyone’s comments – they’re always appreciated.
I normally write programs to help set my Genius grids, but for once, this idea didn’t need one. The first attempts tried 5×5 magic squares (using A-Y) but I found it impossible to fill without needing far too many obscure words (as well as too high a percentage of unclued letters). I intend my puzzles to be fun first and foremost, not dictionary crawls. But 4×4 fitted perfectly, removed the difficult crossing letters V/X/Z and led to very few obscure entries. It even allowed me to use a “perfect” magic square, as Duncan has noted.
The only other tweak was to the preamble. I’m indebted to my test solvers, who tackled this without any hints as to the final “number” needed. From their feedback, it was clear a small hint was needed to help solvers complete the last step.
I’ve not seen a previous Genius puzzle use this idea, but as I don’t solve many other crosswords I’m not surprised it’s been done before elsewhere. I suspect it would be more elegantly implemented using a barred grid, but I like the Genius series’ restriction of using blocked grids.
Thanks again and Happy Easter!
Absolute magic!
I thought the final revelation as to the meaning of “magic” was quite beautiful here. Many Genius crosswords seem to be constructed so as to prevent the use of word-searchers and the like, but this seemed to be set more like an “enigmatic variations” where the trick was to solve a final puzzle after doing the crossword itself. There was a really neat moment of realisation which then led to further realisations of just how beautiful the magic square was.
There are lots of ways to measure the pleasure of a crossword, and no single one is correct. Sometimes it is the difficulty, sometimes it is how a puzzle unravels bit by bit, and sometimes it is the smile it brings to ones face as more becomes clear. This fell into the latter category and was over too quickly…but was a lot of fun nevertheless. Thank you Qaos – I don’t think you are cruel enough to set really really hard puzzles but you have a sense of humour and fun that aligns with my own.
If you like puzzles that take time to unravel and are really word-based, do try the GCHQ Turing puzzles – most satisfactory solving and a nice twist at the end before you can enter the answers into the Enigma machine. Very crosswordy.
We would have said – Absolute magic! – but kenmac beat us to it.
The best Genius puzzle for ages.
Thanks Qaos for the enjoyment and for dropping in with some background to the puzzle. Thanks also to Duncan for another comprehensive blog.
A feature of this type of magic square is that complementary pairs are always in the same relative position ( two diagonal steps apart).
I found this helpful in completing the solution, as the mention of ‘magic’ in the preamble put me on the right track pretty soon.
Thank you very much for this comprehensive, interesting and colourful blog duncanshiell, would you believe that i hadn’t even twigged that the “missing” letters all appeared in magic square positions in the grid? Luckily the info of missing letter count plus the word “magically” was enough to tell me what was going on and helped to put me right on a couple of the trickier entries (eg SAMADHI, new word, wonder if I will ever use it?).
This revelation raises my appreciation of Qaos’ work even higher than it had been at the time of solving (for me this fell into each of TheZed@5’s categories at various times and I appreciate that it would probably have been beyond me without the 2 key hints). I thought CHIC was clued really nicely with a different use of BIDEN to those seen elsewhere lately, NOMOLOGY also new for me but very fairly clued, with overall favourite GOODBYE. Thanks Qaos.
A very enjoyable puzzle – right up my street. I wish I’d thought of it! Nice one, Qaos.