Hello all. I can accurately say this was the best puzzle I have done by Miles! This is the first EV by this setter, although I found two Listener puzzles and several Magpies listed in Dave Hennings’ database.
The preamble:
Solvers are invited to attempt some ALCHEMY. In each clue wordplay provides an extra letter, which is not to be entered. In clue order these extra letters spell out what to start with (three words) and what to iterate (three words). Following these instructions solvers can reach the conclusion of the trick, to be represented in two ways in the grid: (i) each instance of what a successful alchemist must NOT have used (eight cells) must be located and connected with a line and a circle, and (ii) 11 cells to be found in two straight lines must be highlighted. Chambers Dictionary (2016) is recommended.
I solved largely from the bottom up and used the message to give a little help as I went along. This emerged as:
ANY POSITIVE NUMBER (what to start with), and
RECIPROCATE, ADD ONE (what to iterate)
I thought reciprocate must mean take the reciprocal, but couldn’t initially find any dictionary (or real world) support for this. However, SOED has the required meaning.
To perform the iteration I wrote a quick formula in a spreadsheet. I had a notion that the starting number(s) would be found in the grid (despite that “any” in the message), but it was clear from the moment I changed my starting number to test the formula that all (positive) numbers lead to the same result. As a mathsy person I’m feeling sheepish to admit this, but I just googled the number which immediately led me to the answer. I mean, I could have at least looked in the grid first – if I’d taken a few moments to look for something relevant to alchemy (like LEAD or GOLD) I would have found it. Or thought what mathematical number might be relevant …
Anyway, the number we converge on has a name, and it’s found in those 11 cells to he highlighted:
GOLDEN RATIO
I did remember that the golden ratio is generally denoted by ϕ (phi) and it was useful to bear in mind, because I didn’t have any initial workable thoughts as to “what a successful alchemist must NOT have used.” This time, inspecting the grid got me there as I saw the symmetrical arrangement of Os which could be connected to give ϕ.
It took a bit more thought to see that the Os are 0s. The alchemy is converting our base or LEAD number to this GOLDen ratio by way of this iterative “trick” – and it doesn’t work if we start with 0.
Thanks Miles!
If there is a setter’s blog for this puzzle it will be available after 9am here.
| # | ANSWER | Clue with definition underlined | |
| Explanation, with quoted indicators in italics and ANSWER letters in bold caps | |||
| Across | |||
| 1a | PIT STOP | Public address with its superior circuit breaker? (7, two words) | A |
| P[A] (public address) + ITS + TOP (superior) | |||
| 6a | CASE | Odd character that double 14 reveals (4) | N |
| SeneCA[N] SEnecan (double 14 – 14a twice) reveals the answer | |||
| 9a | AERIE | Visionary of poems lately praised regularly (5) | Y |
| Alternate letters of (… regularly) lAtEl[Y] pRaIsEd | |||
| 10a | NEURAL | Leap and run around this type of network (6) | P |
| LEA[P] and RUN anagrammed (around) | |||
| 11a | GRIFFON | George King and Emperor off riding fabulous beast (7) | O |
| GRI (George King and Emperor) + [O]FF + ON (riding) | |||
| 14a | SENECAN | Understanding to have sufficient power according to philosopher (7) | S |
| SEN[S]E (understanding) + CAN (to have sufficient power) | |||
| 16a | EDOM | Esau’s first with absolute authority overlooking people here (4) | I |
| Esau’s first + DOM[I][nation] (absolute authority) omitting (overlooking) NATION (people) | |||
| 17a | DRACONE | Doctor with opening scenes in play reveals liquid container behind tower (7) | T |
| DR (doctor) + AC[T] ONE (opening scenes in play) | |||
| 19a | ALL-RULING | Lord Lieutenant accepting Burundi is taken in by indisposed sovereign (9) | I |
| LL (Lord Lieutenant) accepting RU (Burundi) is taken in by A[I]LING (indisposed) | |||
| 21a | PRODUCT | Vance and staff tense after capital issue (7) | V |
| [V]P (Vance) and ROD (staff) + T (tense) after UC (upper-case: capital) | |||
| 23a | SOAP | Perhaps EastEnders veteran lives in south-east (4) | E |
| OAP (veteran) is inside (lives in) S[E] (south-east) | |||
| 25a | IGUANAS | Antiguans leaving Thailand upset residents of Mexico perhaps (7) | N |
| An anagram of (… upset) A[N][t]IGUANS removing (leaving) T (Thailand) | |||
| 28a | ROADIES | Crew briefly stood up welcoming farewell (7) | U |
| Without the last letter (briefly) ROSe (stood up) taking in (welcoming) ADIE[U] (farewell) | |||
| 29a | ENDRIN | Staff unceasingly take control of pests (6) | M |
| [M]EN (staff) + DRINk (take) without the last letter (unceasingly …) | |||
| 30a | RESIT | Times abandoning UK departure for special test after failure (5) | B |
| X (times) is leaving (abandoning) [B]RE[x]IT (UK departure) for S (special) | |||
| 31a | ASHY | Pallid husband restrained by command to go gently (4) | E |
| H (husband) in (restrained by) [E]ASY (command to go gently) | |||
| 32a | GODETIA | Trail reflected state of rest, not in flower (7) | R |
| DOG (trail) backwards (reflected) + [in]E[R]TIA (state of rest), not IN | |||
| Down | |||
| 1d | PAGLE | Decayed cowslip leaf split by extremes of rainfall (5) | R |
| PAGE (leaf) split by the outer letters of (extremes of) [R]ainfalL | |||
| 2d | TRICOLOUR | Standard to scowl receiving Irish blood-fine (9) | E |
| TO LOUR (to scowl) receiving [E]RIC (Irish blood-fine) | |||
| 3d | SIFT | Closely examine what poser does around football club (4) | C |
| SIT (what poser does) around F[C] (football club) | |||
| 4d | TEFS | Grasses of Ascot, say, with fences at borders (4) | I |
| T[I]E (Ascot, say) + the edges of (… at borders) FenceS | |||
| 5d | PENNAL | Friendly correspondent controls number getting fresher at Heidelberg once (6) | P |
| PEN[P]AL (friendly correspondent) surrounds (controls) N (number) | |||
| 6d | CUSEC | Engineering unit to utter abuse over mathematical constant! (5) | R |
| CU[R]SE (to utter abuse) above (over) C (mathematical constant) | |||
| 7d | SALANGANE | Flying around sea Angolan is swift (9) | O |
| An anagram of (flying around) SEA ANG[O]LAN | |||
| 8d | ELANET | Medical journal, forgetting Thursday’s flyer (6) | C |
| [th]E LAN[C]ET (medical journal) omitting (forgetting) TH. (Thursday) | |||
| 12d | RADAR GUNS | Irish police officer reversing in tracks adopts American speed trap devices (9, two words) | A |
| G[A]RDA (Irish police officer) going back (reversing) in RUNS (tracks) takes in (adopts) A (American) | |||
| 13d | ECONOMIST | Frugal person wasted time on cost (9) | T |
| An anagram of (wasted) [T]IME ON COST | |||
| 15d | ERUCA | Rocket starts to enter atmosphere after boosting treatment (5) | E |
| Initial Letters of (starts to) [E]nter Atmosphere after reversing (boosting) CURE (treatment) | |||
| 18d | SPIREA | Eagerly desire Australian rosaceous plant (6) | A |
| [A]SPIRE (eagerly desire) + A (Australian) | |||
| 20d | RUNRIG | Progress, rule and approve Scottish landholding system (6) | D |
| RUN (progress), R (rule) and [D]IG (approve) | |||
| 22d | DAIRY | Old man elevated younger one in processing company (5) | D |
| DA[D] (old man) + the reversal of (elevated) YR (younger) and I (one) | |||
| 24d | PASTA | Father’s way to be followed for Italian food (5) | O |
| PA’S (father’s) + TA[O] (way to be followed) | |||
| 26d | SARD | Italian islander having drinks dry up when out of island (4) | N |
| DRA[i][N]S (drinks dry) reversed (up) when missing (when out of) I (island) | |||
| 27d | IDÉE | Pascal’s notion that is of French eccentricity (4) | E |
| I[E] (that is) + DE (of French) + E (eccentricity) | |||
I enjoyed the crossword very much – the clues were excellent and a pleasure to solve – but I was unable to fully resolve the theme. The main instruction, formed from the extra letters, was clear and meaningful. By choosing 2 as the ‘positive number’, I got a sequence of terms that I recognised (2/1, 3/2, 5/3, 8/5, 13/8, …) – one that has a strong connection with the Fibonacci series and the golden ratio. I duly found and highlighted GOLDEN RATIO, but I could make no sense of the references to ‘Alchemy’ and ‘trick’. Knowing next to nothing about Alchemy, I looked it up, but as that didn’t help I decided to come here for enlightenment.
Thanks Kitty for said enlightenment, and thanks to Miles for the well-crafted puzzle. (Incidentally, the SOED may well be the only dictionary that has that meaning for ‘reciprocate’.)
(Kitty
With reference to your ‘best by Miles’ remark in your introduction, I am reminded of a superb Listener puzzle by this setter published some six years ago, which he named ‘Well-spoken’. I can say this was for me one of the best Listener puzzles by Miles!)