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Posts Tagged ‘Four and a half …?’

And now for something completely different…

Posted by Encota on 11 August 2017

OK.  We’ve done the sums.  The answer could be either 4 1/2 or 72.

Inspect the grid.  There are only five pairs of unambiguous letters B (hereafter known as Bs, or Bees) in the grid not separated by a Bar.  Convert these pairs of Bs from Bs to five Bees.  [And obviously 72 is way too big so can be ignored 🙂 ]

That leave minus Half A Bee to be found.  The Preamble talks about one ambiguity: clearly this is the possibility of the third letter of 25 across – is it an O or an E?

Use your favourite means for picking O(dd) or E(ven).  I keep a six foot insect-carved version of the 18th Century gambling game known as E-O in the billiard room for exactly this purpose.  The ball falls in Even, so E it is.  Row 7 now contains ERIC (the half a bee).  For those that need reminding, try https://www.youtube.com/watch?v=MlrsqGal64w

Finally subtract half a bee using the usual accounting convention of placing it in brackets. We now have five bees, less half a bee: 4 1/2 bees now found.  Simples.

2017-07-23 13.54.06

Tim / Encota

P.S. And the ‘Eric The Half A Bee’ Python song’s lyrics include, if I heard them right:

Half a bee, cruciverbally
Must either sail, or rival 3…

[Good grief!  Ed.]

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‘Four and a half…?’ by Sabre

Posted by Encota on 11 August 2017

The nine hidden words in this puzzle spell out, I think, the beginning of a well-known early problem in algebra, namely: “The square root of half a number of bees...”, perhaps made more famous in the Scheherazade series of puzzles.

In the original, it goes on to say that, ‘The square root of half a number of bees in a swarm leave a jasmine bush, as do two others (I paraphrase); 8/9ths of the swarm of bees have remained in the bush.  What is the total number of bees in the swarm?’

As many of us will have had drilled into us in maths at school when converting word-based questions into algebra, “First let the number of bees be ‘b’ ” (of course, what else would you choose?)

Then the above translates into:  8b/9 + sqrt(b/2) + 2 = b                      Equation (1)

Re-arrange with the square root by itself on one side, such that both sides can be squared without pain: sqrt(b/2)=b/9 – 2.  Whether it is that squaring process itself has introduced an additional solution is another matter!

So it leads to (b – 72)(2b – 9) = 0.  To make such a product of two numbers =0 then clearly either the left hand or right hand bracket must be zero, so b=72 (or b = 4 and a 1/2, hence Sabre’s Title with the QM, a somewhat strange number of bees in a swarm – especially as it requires minus 1.5 bees to leave the jasmine bush originally – apart from the obvious Monty Python reference – see below).

To check your answers, you might now have tried putting each answer back into equation (1): b = 72 slots in easily, as 64+6+2 does equal 72.  However, putting b = 9/2 back in only works when you recall that the square root of a number can be + or -, such that (1) becomes 8/9 * 9/2 – 3/2 + 2 = 4 1/2.

Other Monty Python fans might mention the new role for ‘Eric the Half A Bee’ in the alternative solution.  [Aside: how does anyone think to write a song called ‘Eric the Half A Bee’?]

But wait a minute.  Has Sabre been reading our site’s ‘About The Bloggers’ section to note that I am an avid Steven Wilson fan?  Coincidence that SW’s most recent release (at the time of writing: roll on 18th August!) is the mini-album 4 1/2 ?  Surely not…

Steven_Wilson_4_and_a_half_cover

[Steven Wilson: 4 1/2.]

So we’re after 72 bees in the final puzzle. Or, literally, should I say Bs.  I can find 21 definitive Bs and 51 cells where the clashing letters are two apart – and if one squints a bit then B=2 – so perhaps I should be changing each of those to a letter B, too – that would end up with 72 of them in place.  It feels like it must be the right thing to do, especially given the quantities of each, but I am sure I’m missing something subtle in the Preamble.  And is the ambiguous entry 6a’s BOBBLY /BLOBBY for L in BOBBY, or have I missed something else entirely (very likely).  Hmm.

My choice of clue for the week is 11 across, the superb all-in-one clue [with extra word bracketed out]:

  11.  Disease in parts of [the] garden, tips of each turnip affected (12)

…reveals the disease of turnips, FINGER-AND-TOE, that affects the taproot, combined with the wordplay including ‘parts’ as a Container-and-Contents indicator (as in ‘parting the Red Sea’), ‘tip’ as a first letter indicator and ‘affected’ as an anagram indicator.  In all,
putting IN inside {OF GARDEN E(ach) T(urnip)}*  Delightful.

This clue got me thinking: I wonder how often a clue has all the hallmarks of a serious convoluted (I’m hesitating in using the word cryptic) clue but is all a bluff and is actually a near-enough straight clue?  A simple example would be the above clue but with ‘each’ changed to ‘any’, for example.  We’d all be scrabbling around trying to make the wordplay work, when actually it was all definition.  Perhaps they should be encouraged just a little more by crossword editors? Or would that simply help those who favour the ‘bung in from definition’ approach, rather than savour every intricacy of each clue?  I may have answered my own question!

cheers all,

Tim / Encota

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Listener No 4460: Four and a Half… by Sabre

Posted by Dave Hennings on 11 August 2017

One of the advantages of looking after Listen With Others is that you get to see setter’s blogs before pretty much anyone else. This will possibly include background into how the idea came about, how difficult it was to set and what input the editors had to the preamble and/or some of the clues.

One of the disadvantages of running Listen With Others is that you get to read something in a setter’s blog that makes you discover sooner than otherwise that you’d buggered the whole thing up! Depression sets in, and you realise that another all-correct year has slid down the plug-hole.

To start with, Sabre’s clues are tricky enough. When it comes to the endgame, they can be fiendish. Last year’s had Tristram Shandy as its theme and the “As sure as I am I — and you are you” quotation. This week, we had to solve the puzzle, find a riddle in literature, solve the riddle, and then do something appropriate… like throttle Sabre!

In fact, the clashing technique, which I identified after only a few clues, helped with getting a lot of the grid filled. They were always two letters apart in the alphabet.

The riddle began The square root of half a number of bees… was from a long work by Longfellow. Including the words the, of and a as obvious extra words certainly needed a craftsman’s touch. 11ac in particular Disease in parts of [the] garden, tips of each turnip affected (12) took me ages to unravel — IN in (OF GARDEN ET)*. The riddle continued “…and also eight-ninths of the whole, alighted on the jasmines, and a female bee buzzed responsive to the hum of the male inclosed at night in a water-lily.

The riddle itself was easy to unravel, taking me only four attempts (the square root of 81/4 is not 9/4). Bizarrely one of the solutions I came up with was 4½, but surely Sabre wouldn’t be so helpful with the title. Eventually 72 won through.

I next tried to find the ambiguous entry, and luckily got there fairly quickly. 3dn Spot bachelor, look, one of two in bathtub (4).was either BLOT or BLOB. I had opted for BLOT.

It took me about half an hour to suss out what was required with the clashes. It wasn’t the letter between the two letters, but just the letter B, of which there were already a fair few in the grid. A quick tot up of the number of that I had gave me 70 because, in the euphoria of solving a couple of clues, I had forgotten to pencil in a clashing letter or two.

Checking the grid thoroughly, I needed BLOB at 3dn to make 72!! I remember thinking at the time “Wouldn’t it have been more cunning for BLOT to be required?” Apparently, it would have been… and was. I haven’t checked my grid to find where I went wrong, but I have read Sabre’s setter’s blog. Surely I hadn’t miscounted the number of Bs. I must have done that a fair few times as it was.

Oh well, c’est la guerre. It doesn’t stop me being full of admiration of Sabre’s puzzle. An excellent riddle, and so well implemented. Many thanks.
 

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