Listen With Others

Are you sitting comfortably? Then we’ll begin

Listener No 4574, Well-spoken: A Setter’s Blog by Miles

Posted by Listen With Others on 20 October 2019

Some years ago I became aware of the 9-point circle, a property of any triangle except isosceles (8 points) or equilateral (only 6), and I thought it involved some really elegant geometry. More recently I wondered if it could be incorporated into a crossword and make a diverting change from the usual verbal gymnastics. After much exploration, I discovered the triangle with vertices at (0,0), (10,0) and (6,12) which had critical points with predominantly integer coordinates. This triggered the 13×11 grid shape. Using O for each point on the 9-point circle and X for each vertex of the triangle seemed a neat idea, and presented a nice challenge for the grid-fill.

However, the Euler line was, for me, just too irresistible to ignore, and for this to feature, extra constraints were imposed, and these pleasingly were not insurmountable. QIGONG was certainly involved at one stage, opposite perhaps NUTTER but other options prevailed. Likewise ELAN and STEP, ALA and TUE, LEO and EEN all had ‘their day’, but, for reasons that I still do not fully comprehend, maximising the average word-length and minimising the number of fully checked entries are paramount nowadays, so they had to be dumped.

As so often happens in a crossword construction serendipity intervened and I spotted the anagram of LONE TEPEE LEANS, which I thought was a pleasing bonus. This was the reason for using a carte blanche, requiring solvers to recognise the four unclued entries by filling in bars, but the editors warned me of the resulting ‘clutter’ interfering with the more significant drawing, so bars were not required and they were (probably) right.

The cluing, for me, usually takes longer than the grid construction. I recall that the clue for ANNEX originally had 22.5 degrees, but with the need for omitted letters, this rather conveniently was adapted to 45 degrees (without roasting alive any Floridans !). The clue with the Man U legend was dedicated to my brother who lives in the Manchester area. I particularly liked the clue ‘Spring: this describes about a quarter of years’ for LEAP, as an example of the same words capable of being interpreted in two distinct ways. I have to give credit to the editors for introducing the de Longchamps reference in the ETEN clue, as, until then, I was unaware of his connection with the Euler line.

As for the title, it was meant to hint at OILER, a well, but I was unsure whether the mathematician’s name sounded like that or more like YEW-LER. However, the editors were happy, checking in Collins and ODE apparently.

The need to draw the line precisely through the centre of the circle was I felt a fair requirement to confirm that solvers were fully aware of what was going on, though I can see that some non-mathematicians may beg to differ. However, mathematicians could check that the 12 points (3 X’s and 9 O’s) were all precisely positioned, centre of cell, as was the orthocentre, also on the Euler line at the G cell in row 11, confirmed by drawing the 3 altitudes through it from each X. Furthermore if (6,12) is called point A and (0,0) is B and (10,0) is C, then tan A = 1, tan B = 2, tan C = 3 and angle A = 45 degrees.

And finally (paying homage to Columbo), here is a challenge to acute observers. 50 is the smallest number expressible as the sum of two squares in two different ways. How is this exploited in the geometrical construction?
 

Advertisements

Posted in Setting Blogs | Leave a Comment »

Listener No 4574: Well-spoken by Miles

Posted by Dave Hennings on 18 October 2019

This was Miles’s first Listener, although he has had a fair few over at Magpie — some of them D graded. I think Ds are slightly more difficult than the average Listener, so I was hoping for a challenge. Mind you we’ve had a couple of those in recent weeks.

A carte blanche faced us here. Nine clues omitted one letter of the answer, and they would spell out the puzzle’s theme. Four unclued entries were the only other difficulty, apart from having to jigsaw the answers into the grid. And yet again, the endgame would involve some drawing, although “shapes” seemed to indicate there little or no artistic skill would be involved.

The clues were solid with some easy and some tricky. My favourite was probably Just about highest point orbiting round earth? (6) — an &lit. for APOGEE. The letters omitted from wordplay gave Euler line. Although I’d heard of him, I hadn’t heard of it, so an enjoyable journey round the Web was educational. I normally paid attention during Maths classes, so I’m sure we didn’t do this way back when!

Identifying the three X’s was straightforward, seeing that they probably gave a triangle, and it wasn’t a giant leap to then look for some O’s. The only O’s in the grid seemed to form a circle. Rather than describe the construction of an Euler line, I hope the animation on the right tells all. (Egg on face if there’s an error somewhere!)

Thanks for a fine puzzle, Miles.
 

Posted in Solving Blogs | Tagged: , | Leave a Comment »

Well-spoken by Miles

Posted by shirleycurran on 18 October 2019



We have already solved fairly challenging compilations by Miles at the C and D level in the Magpie but this is his first Listener and the title ‘Well-spoken’ doesn’t say much to us (it still doesn’t now that we have solved it but I am sure Dave or Tim will  explain it). I quite like a carte-blanche crossword. It is clear that this one is going to have some drawing as the endgame, so bars would probably be an encumbrance and we are given three 11-letter solutions that help us place the remainder of the words we solve. I believe the clues have to be fairly generous in a carte blanche since the solver is starting with a blank grid and no guiding spaces with numbers – and this was a generous set.

We are also given enough alcoholic clues to give Miles admittance to the Listener oenophile setup. ‘Drop bits of egg fermented into French drink; it’s like fizzy yoghurt (5)’ (Well it would be wouldn’t it – what a gross way to handle your apéritif!) We put E(gg) and F(ermented) into our KIR and get KEFIR ‘an effervescent drink made from fermented cow’s milk’. ‘He might generously subsidise upsetting waste on NY bar-room bill locally (10)’ There’s a rather strange surface reading there but we work backwards from BENEFACTOR producing NEB< as the bill, CAFE< as the NY bar-room and ROT< as the waste. ‘Then there’s ‘Sicilian smoker burns alcohol in a saucer (4)’ A bit of an old chestnut, ETNA and the first one we solved but ‘Cheers!’ anyway, Miles, I’m raising my glass to a fine set of clues that soon gave us a complete grid.

The omitted wordplay letters had spelled out EULER LINE. It’s rather an EULER day today. The numerical crossword setters Oyler [sic] and Zag have just issued Number 12 of the Crossnumbers Quarterly where solvers who enjoy numerical puzzles can enjoy about nine of them in each three-monthly addition. Take a look!

We needed to take a look at Wiki in order to understand what half of the preamble was spelling out for us then, when we had joined our three Xs to make a triangle, there was a smile of understanding of that unch phrase for there almost in the centre of our grid A LONE TEPEE LEANS.  Those four small unclued words ELAN, LEO, STEP and EEN would have lowered the median word length considerably had they not originally been split up by bars in our grid and they performed the delightful task of describing what we were drawing.

It must have been quite a challenge to fit words into a symmetrical grid with those Xs, Os, and EULER correctly placed to produce the Euler line and as usual, I learned something new so thank you, Miles.

 

Posted in Solving Blogs | Tagged: , | 1 Comment »

L4574:”Well-spoken” by Miles

Posted by Encota on 18 October 2019

Title: Homophone for an (oil) well => “OILER” => Euler.  Aha!

Well, mine looked like this:

I’d forgotten there was such a thing as a Nine-Point Circle, let alone what all the 9 points actually were. I see it is also known as Euler’s Circle, which is neat.

Tim / Encota

Posted in Solving Blogs | Leave a Comment »

Listener No 4573: Jean’s Stuff by Schadenfreude

Posted by Dave Hennings on 11 October 2019

Schadenfreude’s very last Listener puzzle this week, following on from Falling in Love Again / Sagittarius Rising back in April.

OK, so I’d heard of the Karelia Suite, which provided the theme music for This Week on ITV way back when, but none of the others rang a bell. Hold on! There was Finlandia as well, and that eventually gave me the way in after I finally twigged that 1ac Top sailor overcome by alcohol got stripped (5) wasn’t a sailor but a top, DIABOLO.

Opus numbers no doubt led all of us on a search for the opus numbers of Sibelius’s works for which Wiki provides supplemental JS numbers where appropriate.

15ac Bacon spots Lady Sarah’s auntie (6) brought a smile for RASH + ER, and I never thought I’d find LI’L ABNER in a Listener crossword! As for the title, Jean’s Stuff, Sibelius must be turning in his grave.

For the last time, thanks, Schadenfreude.
 

Posted in Solving Blogs | Tagged: , | Leave a Comment »