Comments on: Independent 8,081 / Phi

By: allan_c

allan_c — Sat, 08 Sep 2012 18:05:30 +0000

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″

By: Phi

Phi — Sat, 08 Sep 2012 01:21:21 +0000

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).

By: Wil Ransome

Wil Ransome — Fri, 07 Sep 2012 23:02:02 +0000

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.

By: allan_c

allan_c — Fri, 07 Sep 2012 22:28:37 +0000

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

By: Bertandjoyce

Bertandjoyce — Fri, 07 Sep 2012 20:34:43 +0000

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!

By: Paul B

Paul B — Fri, 07 Sep 2012 20:03:44 +0000

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.

By: Kathryn's Dad

Kathryn's Dad — Fri, 07 Sep 2012 18:47:29 +0000

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.

By: RatkojaRiku

RatkojaRiku — Fri, 07 Sep 2012 17:30:20 +0000

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

By: Kathryn's Dad

Kathryn's Dad — Fri, 07 Sep 2012 15:11:17 +0000

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.

By: nmsindy

nmsindy — Fri, 07 Sep 2012 11:43:34 +0000

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.