Listen With Others

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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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2 Responses to “‘Four and a half…?’ by Sabre”

  1. TonyC said

    Tim,

    I have never even attempted a Listener crossword, but I’ve been following Listen With Others for a while now. Nothing I have read in these pages gives me the slightest confidence that it’s time to start trying to solve them, either, but I do love to marvel at their cunning intricacy

    I do solve more straightforward cryptics, though (the Guardian Genius is about my limit), and I have recently been pleased (as ‘Whynot’) to have my own first effort at setting published for a general audience at Big Dave’s Rookies’ Corner. I mention this because my very favourite clue in that puzzle is very much in the mould of your description of a ‘bluffing’ clue in your last paragraph.

    The puzzle is at http://crypticcrosswords.net/puzzles/rookie-corner/rookie-corner-173/ . I won’t give the game away by saying which clue it is, because you might like to find it yourself. I imagine that for anyone who regularly solves the Listener, the whole puzzle can be finished in about ten minutes. I hope that you can find a few minutes to run through it and that it might give you some pleasure, especially when the penny drops on the clue in question.

    Regards
    Tony / Whynot

  2. TonyC said

    Re the above comment, I have noticed since writing it that you follow the Guardian blog so will have been made aware of that clue anyway. Hope you liked it.

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