# Fifteensquared

## Independent 8,081 / Phi

Posted by RatkojaRiku on September 7th, 2012

It was no surprise this Friday morning to find that I had a Phi puzzle to grapple with.

As is customary, I sailed through about half the clues before grinding to a halt and spotted the makings of a theme about halfway through but couldn’t fully appreciate the relevance of it.

I realised that a number of the across entries contained numerals (italicised), but it was only when checking the name of the mathematician (whom I didn’t recognise) at 2 that I realised the connection, see below. Of course, the solver doesn’t have to spot it in order to complete the puzzle, but it heightens one’s pleasure when one does. Thanks, Phi, for expanding my general knowledge yet again!

I struggled most in the SE quadrant and eventually “cheated” on the anagram at 12 to get me going again. My favourite clues today are 6, for the clever split between the definition and wordplay (and its Olympic/Paralympic topicality?); 15, for playing with the meanings of “long”; and the & lit. at 14. The source of berries at 13 was new to me, as was the stone at 3.

*(…) indicates an anagram

 Across 1 AFRO A (=article) + *(FOR); “working out” is anagram indicator; the definition is “combination of locks” i.e. hair 4 COMPONENT COM-M-ENT (=observation); [P (=power) + ON] replace M (=core, i.e. middle letter of “com-m-ent”) 9 ABALONES ALONE (=sole) in ABS (=sailors, i.e. able seamen) 10 ACUMEN CU (=copper) in AMEN (=indication of agreement) 11 KNOTWORK [NOT + WOR (ROW=dispute; “backing” indicates reversal)] in K K (=Kings, i.e. letter “k” x 2) 12 BRIGHT R (=River) in BIGHT (=bay, e.g. the German Bight) 13 ACACIA [C (=caught) in AÇAÍ (=source of berries, i.e. a Central and South American palm)] + A 14 THREE-PLY E (“ultimately” means last letter only) in   [TH (“mostly” means last letter dropped) + REPLY (=answer)]; & lit. 16 FIVEFOLD *(LIVED OFF); “scrapped” is anagram indicator 18 ULLAGE E.G. (=say) + ALL (=every) + U (=university); “clawed backed” indicates reversal; ullage is the quantity by which a vessel is holding less than its full capacity, hence “shortfall” 20 EIGHTY EIGHTY (=important); “to shun women (=W)” means letter “w” is dropped 22 PANCETTA PAN (=dish) + *(ETC) + TA (=thanks); “cooked” is anagram indicator; pancetta is an Italian variety of cured pork 23 SPINAL SPIN (=twist) + AL (=entirely; “almost” means last letter is dropped) 25 THIRTEEN [T (“last of” means last letter only) in IRE (=passion)] in THEN (=subsequently); the definition is “supper attendees”, referring to the Last Supper, attending by Jesus and his twelve apostles 26 TWENTY-ONE 21 used to be the age of majority in the UK, before it was lowered to 18, hence “no longer for majority”; twenty-one (or vingt-et-un) is a card game, pontoon 27 SURF SURF (=flaky skin, i.e. on scalp); “cold water (=C, i.e. the marking on a cold water tap) displaced” means letter “c” is dropped Down 2 FIBONACCI FIB (=unreliable statement) + ON (=supported by, as in The book is on the table) + ACC (=account) + I (=one); the reference is to Italian mathematician Leonardo Fibonacci (c. 1170 – c. 1250), who is best known for having spread the Hindu-Arabic numeral system in Europe, hence the theme of this puzzle 3 OOLITIC OC (CO=company; “upset” indicates vertical reversal) in *(OIL IT); “processed” is anagram indicator; oolitic means pertaining to a kind of limestone (=oolite) with grains resembling fish roe 4 CONSOLATORY *(SOLAR TYCOON); “after vandalism” is anagram indicator 5 MUSAK A in MUSK (=perfume); musak is typically background music played in supermarkets, etc 6 OVA O V A; “taking premier placings” means first letters only are used; the definition is thus “eggs”, with the break between the definition and wordplay coming between “eggs” and “on” 7 ERUDITE E (=English; “little” indicates abbreviation) + [IT in RUDE (=primitive)] 8 TEETH TEE (=support, i.e. in golf) + TH (“only half of” means half the letters only are used); the definition is “effectiveness”, as in The law had no teeth 12 BARQUENTINE *(BANNER QUITE); “unfurled” is anagram indicator; a barquentine is a three-masted rigged vessel 14 TAD TAD (=subdued); “having polished off Phi (=ME, i.e. the setter)” means the letters “me” are dropped 15 LIGHT YEAR LIGHT (=insubstantial) + YEAR (=long, i.e. crave; “not entirely” means last letter dropped) 17 ENHANCE *(HEN) + ANCE (=frolic; “topless” means first letter dropped) 19 LAERTES SET (=stage effects) + REAL (=genuine); “upturn” indicates vertical reversal (of everything) 21 INPUT P (=positive) in [I (=one) + NUT (=crazy (person))] 22 PATIO PATI (I + TAP (=knock); “up” indicates vertical reversal) + O (=old; “little” indicates abbreviation) 24 LIT Double definition: LIT means “burning”, on fire AND “books etc”, lit(erature)

### 12 Responses to “Independent 8,081 / Phi”

1. Thomas99 says:

I didn’t notice the Fibonacci series hidden in the grid, but it’s absolutely brilliant! It also explains some of the harder clues (it’s always fair enough to make thematic clues a bit tougher, I think, and some of the words are a little obscure, presumably to accomodate the numbers in all the rows, and in the right order). Many thanks for pointing it out and for the blog. A harder than average Phi, and one of his best.

2. aztobesed says:

Thanks for the blog and to Phi.

Tongue in cheek, I suggested on the Guardian site that one day a setter would set a clue using a Fibonacci sequence to indicate letter choices but using them to fill a grid is next to genius. Wish I’d spotted it as I was doing it but it’s a testimony to the quality of the puzzle that such a technical thing is going on without you even noticing it. Full of admiration for this setter. (And I can’t wipe the grin off my face. )

3. nmsindy says:

Yes, excellent themed puzzle – Fibonacci numbers are pretty well known in the maths world and quite a few themed puzzles have been based on them. Did not find this too difficult with the precise clueing leading me to answers that were new (or forgotten) words. Favourite clue AFRO – many thanks, Phi, and RR.

Brilliant puzzle. I got FIBONACCI early on (once I’d remembered how to spell it …) and then saw the numbers and went off looking for the sequence, which I did know about. Since nobody’s spelt it out overtly, can I explain for non-mathematicians that the FIBONACCI sequence is 0,1,1,2,3,5,8,13,21 … Each number is the sum of the previous two.

And in this puzzle we have 0 (in OOLITIC, say), compONEnt, abalONEs, knoTWOrk, THREE ply, FIVEfold, EIGHTy, THIRTEEN and TWENTY-ONE. And as Thomas says, in order. There may be other subtleties, but that’s how I saw it. The Fibonacci numbers are fascinating, reflected in the natural world in all sorts of stuff, from the spirals of snail shells to growth in animal populations.

One of my favourites of Phi recently; thanks too to RR for the blog.

5. RatkojaRiku says:

Many thanks to fellow solvers for spelling out the point about the sequence, which was wasted on me, since I knew no more about Fibonacci than that he was associated with numerals; as such, I had wrongly assumed that Phi’s choice of numbers was purely random – I should have known better, of course.

I had tried to pick out the numbers in a different colour when writing the blog, but to no avail, so thanks to Kathryn’s Dad for doing half my job for me 😉

Sorry to hog the blog, but just to say that a bit more research into the FIBONACCI sequence shows that it’s related to another mathematical concept, the ‘golden ratio’. And guess which Greek letter is used to represent said ‘golden ratio’? I’ll give you a (not very cryptic) clue: it’s got three letters and starts with P …

I’m going to pour a glass of red and have a lie down now. Good weekend to all.

7. Paul B says:

Had my suspicions raised by the grid to start with, so dim light flickered on after seeing THIRTEEN and TWENTY-ONE sitting there.

Fine puzzle, perhaps today’s best one.

8. Bertandjoyce says:

As per usual we started this one late on. We noticed the numbers but completely missed the theme though both of us know the Fibonacci series quite well.

As others have said, the makings of a good themed puzzle is when you don’t have to spot the theme to finish the puzzle.

This was briliant Phi – we should have been more patient or started it earlier to give us time to look at the numbers more closely.

Thanks RR for the blog. You had a good one today!

9. allan_c says:

Like B&J I started this late on and obviously wasn’t at my best as although I completed the puzzle I missed the theme, despite knowing about Fibonacci. I too struggled in the SE corner even though I got 12d straightaway.

Incidentally, a Fibonacci sequence can be built up starting with any two numbers you like and soon each consecutive term will be the previous one multiplied by the golden ratio. For example: -7.82 and 5.9 will give you -7.82, 5.9, -1.92, 3.98, 2.06, 6.04, 8.1, etc; by the time you get to the 14th term the ratio of each term to the previous one is close to the golden ratio, approximately 1.618

Thanks, Phi and RR

10. Wil Ransome says:

Yes, quite delightful. But I think Phi is beginning the Fibonacci sequence with 1, since 1, 1, 2, 3, 5, 8, 13, 21 appear in successive rows. It seems a bit of a stretch to include the 0 — there is no row to contain it except the first, which provides 1.

11. Phi says:

I deliberately started from ONE because ZERO is not so easy to fit in! On the other hand, I could then have got away without having to resort to more than one answer as the full number – I was rather keen on hiding them wherever possible.

I’d forgotten the link to the golden ratio (though I’ve used that as a theme before, for obvious reasons).

12. allan_c says:

Oops! I won’t get top marks in maths for saying the golden ratio is “approximately 1.618″ – it should of course be “approximately 1.618:1″

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