## ‘Four and a half…?’ by Sabre

Posted by Encota on 11 Aug 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 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

## 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

## 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.