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Listener 4354: Taxi! by Ilver

Posted by Jaguar on 1 August 2015

Oh dear, another long break — but somewhat enforced, perhaps, as I have remained incredibly busy of late. Managing to keep my Listener head just above water, though, and I thought I would surface properly for this one. After all, if a puzzle that appeals to my mathematical background doesn’t prompt me to blog, what will?

Ilver is another of that group of new setters appearing in the last ten years or so, whose first Listener came out just in time for me to have a crack at it (my solving career starting in 2011). Since then, his nine puzzles in all outlets have included themes such as Pig Latin, Doctor Who and Poirot in the Listener, but also a couple of puzzles that have had mathematical elements. As it turned out, this effort belonged to the latter category — the first hint of that emerging when those extra letters revealed something looking like “a very interesting number”. Oh, that quote! I’ve known about it for a while, GH Hardy telling his sick mathematical colleague, the brilliant Srinivasa Ramanujan, about the taxi he had come in (rather than, say, hoping he’s getting better and asking after the family?), and how boring the number 1729 is, and hoping that this isn’t some omen. “But no!” says the young Indian, “for 1729 is the smallest number that can be expressed as the sum of two [positive] cubes in two distinct ways!”

Of course, all numbers are interesting really (there is a ‘proof’ of this, because any smallest uninteresting number would be remarkable for just that fact, and therefore interesting again, and hence there can’t be an uninteresting number!).

At the other end of the puzzle, we are instructed to highlight an identity. And there is some of it, eventually emerging from those odd clue lengths, as “plus one equals zero” emerges below an “i pi”, and all that is missing from Euler’s identity is the initial “e”.

At this point, though, progress came to a juddering halt for a time. 1729 is the key to obtaining a second quote, and then something in the grid that is also related, and fixing the grid will insert that final e in its rightful place. But how to use the key remained a mystery to me (and, it seems, quite a few others) for some time! Perhaps it’s partly because the obviousness of the final highlighting provides something of a distraction. Is there a direct link between Hardy’s work and Euler’s? Much searching of their respective output follows, but isn’t too revealing. Nor does any quote about Euler seem particularly helpful.

But then, of course, this is primarily a word puzzle, rather than a mathematical one, so thoughts should turn to interpreting things a bit more cryptically. It also helps to check other GH Hardy quotes, of which one alone made it into my edition of ODQ. “Beauty is the first test: there is no permanent place in the world for ugly mathematics,” he said as part of a book filled with other gems. Interpreting 1729 as four separate numbers 1,7, 2, 9, and then taking the 1st, 7th, etc letters of across clues revealed the first part of that quote after all. Phew! (after much grid-staring and head-scratching).

To get to the second part, though? Another bit of grid-staring, although at least with the final E in mind thoughts turn to the 1st, 2nd, 7th, 9th columns of the grid (not rows, because we need that e in the second column/ sixth row). Towards the bottom of the 9th column is the Y of “Hardy”, a bit further above is the H, and the rest emerges if you take 1st/7th and 2nd/9th letters in alternating rows. Follow it up and an anagram of “mathematics” is sandwiched between “the world”. And rearrange that to its proper form and you see the e fall in its rightful place, to complete arguably the pinnacle of what is meant by mathematical beauty. “e to the power of i times pi plus one equals zero, where e is the base of natural logarithms, i is the square root of minus one, and pi is the ratio of the circumference of a circle to its diameter”.

What makes it so beautiful is what this identity brings together. In the first place, the numbers above are fundamental to mathematics in a way few other numbers are. And then the operations (exponentiation, multiplication, addition) are also fundamental to all arithmetic, each being used exactly once, as is the equality relation. There’s a certain elegance in everything being used exactly once, too.

But also, it is where these numbers come from that contains the real beauty. pi is a number from the classical Greek mathematics of geometry (and then Trigonometry, its offshoot developed in the Arab world in the 7th-9th Centuries). i has its origins in algebra, developed mainly in the 12th-14th centuries. And the number e emerges naturally from Newton and Leibniz’s development of calculus in the 17th Century. Even 0 is quite special, representing the abstract concept that took a long time to develop, that you can even quantify and work with nothingness. We can thank the Indian mathematicians for that one.

Thus it is, then, that the entire history of mathematics from the Ancient Greeks up to Euler himself can be contained and summarised in just five numbers and four operations. There can never be a purer and more beautiful result.

4354

 

 

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Taxi! by Ilver

Posted by shirleycurran on 31 July 2015

Taxi 1729 001Ilver! Renowned in the Magpie for the D and E level ‘Child’s Play’ crosswords that his children have put together. What are we in for? A first glance at the grid reveals almost two grids with just two gaps in that vertical line that separates them. There is going to be something fairly dramatic in the grid for that to get past the editors. Otherwise all seems to be normal, just a couple of open lights and a fine average word-length. I wonder what Ilver is up to!

Of course, we check the answer lengths and spot that there are four clues that seem to require answers longer than the space allowed in the grid – but we can’t solve any of those clues, so store the information for later.

Naturally I check Ilver’s membership of the Listener Setters’ Oenophile Club and am initially disconcerted to find ‘To humiliate oneself brew tea with cold rag (7 two words)’ [TEA C* + ROW = EAT CROW] That doesn’t sound like Ilver. Reading on, I come to ‘Essential acid is left in Edmund’s underwear (6)’ [IS< in LYNE = LYSINE – it’s an essential amino-acid isn’t it] – he must be on a health kick. I’m into the down clues before I find ‘Book stay here – exotic drinks (8, two words)’ [B + STA(Y) HERE* giving HERB TEAS] – clearly Ilver is on some sort of tea trip!

A very interesting number!

A very interesting number!

These clues are tough indeed. We struggle with the down clues until a familiar phrase seems to be emerging from the extra letters and the other Numpty tells me about the Hardy Ramanujan number – how Prof. Hardy went to visit the dying Srinivasa Ramanujan in his hospital bed, and, short of conversational openings, commented that the taxi he had come in had a very dull number. Ramanujan’s response is famous. “No, it id A VERY INTERESTING NUMBER; it is the smallest number expressible as the sum of two cubes in two different ways.” (I wonder how he would have coped with the three-monthly Listener numerical puzzles – ten minutes? It isn’t the fact that he was able to see that 1729 was the sum of those two cubes in two different ways, so much as the fact that he was able to instantly state that there was no other smaller figure that fitted the requirement).

1729. Clearly that is the ‘key’ we are looking for and as our grid fills, we wonder how we are going to use it. I fiddle with the letters in the grid, taking the first, then the subsequent seventh, move on two, move on nine and get … TOAEHE. Not promising.

Taxi 001The other Numpty has more success, reading the first and seventh of the first line, then the second and ninth of the subsequent line and so on … and it’s rather like the monkeys typing Shakespeare “Look, this one has finally typed something coherent – ‘To be or not to bogzugigubélih8ui*ç%%…” However, with persistence, we find an intriguing HARDY at the end of the grid, so we are clearly on the right lines.

We have also spotted a rather strange version of Euler’s ‘identity’ Ti pi + 1 = 0 when we finally realized that those extra long clues could be resolved by fitting the PI of SNIPING into a single cell, using + as the conclusion of PERIPLUS, 1 for the ONE in CHAMPIONESS, and = as the start of EQUAL SIGN. Obviously the O of GONOCYTE can do double duty as a zero. But there is that odd T where we need an e.

Taxi 2 001We try applying the same method to the clues and Eureka! We discover another familiar quotation: ‘BEAUTY IS THE FIRST TEST’ and suddenly things fall into place. Hardy again! ‘Beauty is the first test and there is no permanent place in the world for ugly mathematics’.

What do we have in our grid? An anagram of MATHEMATICS (so ‘ugly mathematics’) and, as the preamble told us, its author, HARDY. Oh but this is brilliant; it is almost on the Hardy/Ramanujan level! We unscramble MATHEMATICS and, of course, Euler’s identity receives its missing e, which we are told to write in lower case. I have just a small doubt here. Instinct tells me to use the π sign and that is a lower case letter – but what will happen if I use lower case pi?

That slight doubt doesn’t detract from our admiration of a stunning compilation. Thank you, Ilver!

 

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Journey to the Centre by Ilver

Posted by shirleycurran on 13 December 2013

Journey to the Centre 001There was an immense whoop of relief from at least one Numpty when we realized that a numerical Listener was not being inflicted upon us this week (or was it? All those little numbers scattered around the grid had us wondering!)

Of course, we have been saying, all week, that with so many anniversaries this weekend, (the Gettysburg address, the Kennedy assassination, Benjamin Britten’s centenary and the fiftieth anniversary of some weirdo scientific fellow who flew through time and space in a police phone box) the editors would be mad to give us a numerical. What good sense to step out of the straitjacket and honour or commemorate at least one of those!

The preamble told us fairly clearly which of those we were celebrating but we were a long and winding road from our destination in this journey to the centre. At first, this involved cold-solving, and we are never very good at that. The only gift was that, when we had a few clues solved, and some were generous, we had the length, first and last letters of the adjacent ones. However, the ‘winding’ aspect of the journeys flummoxed us in a few cases – even my very last clue, where I needed to insert EMOTED in order to get to the centre, but had already placed the I of SLID in the second E cell – so easy to go wrong. It was fun though!

Full grid 001Fun? As usual, I gave a speedy troll through the clues to check that Ilver was still a member of the Listener Setters’ Imbibing Association and he just qualified, with his ‘Fermented juice on French afternoon (4)’ SUR + A and, later on, ‘Research frothy ale and decide again (6)’ RES + ALE* giving RESEAL. I have seen him being far more discerning about his choice of beverage (well, we are part of a team of setters) but I imagine, on this occasion, the need to find an O in the fifteenth of his 26 left-over clues made him descend the path of choosing ale with far too big a head on it. Such is the downside of compiling!

In truth, with that constraint, his clues were of the usual high Ilver standing and, for once, generous on the whole so our grid was filled after a few hours of flailing, with the task becoming far easier when only the fourth journey was left to complete and a number of cells were left vacant, clearly indicating the route.  What’s more, the message hidden in the first 34 clues was emerging: COUNT A LETTER IN EACH OF REMAINING CLUES.

1st try  haha 001OK, time for a confession. Rather a long time ago, we test-solved this puzzle. Friends say to me ‘No doubt you have done this already and you’ll be sitting like a Cheshire cat watching us struggle’. Well, this is perhaps the place to disillusion them. First about a test-solve: there is often an immense difference between the original creation and the one that goes off to the Editors. There is then another time-shift to the polished product that appears one, two or even five years later. So what changed? Well, that instruction about how to complete this was nowhere near so clear in the original version (and there was a miscount in how many sides of one of the letters had to be adjacently coloured) and I thought it might be amusing to insert here what I produced on my first attempt to suss out what was going on. It is perhaps better to relegate that one to the bin!

I had realized that there were 26 remaining clues and that I needed to count the frequency, for example, of G in the G clue,  or Y in the Y clue and somehow apply that to the letters in the grid, but even that led to more than the usual Numpty head scratch.

Journey to the centre 001Secondly, clues change, too becoming, on the whole, far easier, and this time, the changes made a slight difference to the instruction. Anyone who thinks ‘The Editors must have made a mistake’ (as I occasionally hear) needs to submit a crossword and experience the detailed to-and-fro dealings of compiler and editors that produce what we finally see.  All that to say that vetters and test-solvers – and there are two or three, probably, for almost every submission before it even reaches the Editors, are not really being privileged to get an early glance – they have to re-solve anyway when the puzzle appears.

Back to the point! Fortunately, once the penny had dropped and I realized that some graphic depiction of the Tardis was not going to emerge from the grid, I was able to be a little more rational in my shading of letters, beginning with those around that centre cell. The device became clear, as did DOCTOR WHO.

What was left to do? We needed to understand how putting an L in the centre cell to reflect the fiftieth anniversary was ‘thus completing a representation of the transport in that row’.  All setters have to occasionally resort to that crosswordese use of EM and EN as ‘spaces’ and there was EM surrounding T and REL DIM. That, it seems, says ‘Time and relative dimension in space’ which gives TARDIS (Wow!). Dare I admit, that I don’t know much about the Doctor Who series but I’m happy to go with that.

Criticism, though. We are going to watch the fiftieth anniversary special broadcast this evening and we are looking forward to those anguished elephant trumpeting noises that accompanied every movement of the Tardis. Ilver has missed the chance to require a recorded message as his final endgame. ‘Solvers must send JEG  a recording of a relevant sound accompaniment to demonstrate that they have found a way out.’

What is left to do? Congratulate Ilver on an astonishing compilation. I have seen what must be hundreds of hours of work that have gone into that polished production. Quite something!

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Listener 4269: Journey to the Centre by Ilver

Posted by Dave Hennings on 13 December 2013

SCENE: The Editor’s office early in 2013. There is a desk in the centre of the room. There are two chairs either side of the desk, a big one and a small one. Editor sits in the big chair, Sub-editor sits in the smaller one with a laptop. Editor puts a piece of paper on the desk. The piece of paper has a crossword puzzle printed on it.

Editor: Well that’s 16th November sorted. What have we got available for the 23rd? It’s the last mathematical of the year.

Sub-editor: Hmmm… why does that date ring a distant bell. Let me google “Anniversaries November 2013”

Sub-editor types furiously on his keyboard.

Sub-Editor (reading off screen): “The first episode of the science fiction television series ‘Doctor Who’ was broadcast in the UK. It is the longest-running and most successful science fiction TV series in the world.” Well, we could commission a special mathematical around the equation of space-time and the twelve dimensions. Elap could write a computer program to work out the interspatial vertices.

Editor: OK, I’ll send him an email tomorrow.

Sub-editor: What are those two envelopes doing in the in-tray?

Editor: That’s odd… I didn’t think we had an in-tray.

Editor takes the two envelopes out of the in-tray and opens the first one.

Editor: It’s a mathematical puzzle from Oyler.

Sub-editor: Well that’s lucky. What does he have to say?

Editor (reading a letter): He says it’s the 600th anniversary of the founding of the University of St Andrew’s, this year and he’s enclosing a puzzle he’s done to celebrate it. He’s also suggesting that publishing it on 30th November would be good as that’s St Andrew’s Day.

Sub-editor: That wouldn’t work… everyone’s just got used to the mathematical moving to the penultimate Saturday of every third month.

Editor: You’re right. I’ll reply that it would be too confusing.

Sub-editor: What’s in the other envelope?

Editor: It’s a puzzle from Ilver. He says it’s the 50th anniversary of Doctor Who on 23rd November this year and he’s enclosing a puzzle to celebrate it. (He pauses.) Oh well, it looks like we’re destined to confuse everyone. I’ll schedule them for the dates they’ve suggested. Sorted!

Sub-editor: Where’s the in-tray gone?

Any similarity to actual events is in the realms of science fiction.

Fast forward to November 2013.

Listener 4269Well, they weren’t going to surprise me this week… I was ready for the quarterly mathematical puzzle. It was just a shame that it fell on 23rd November, the date of the anniversary of Doctor Who that the BBC had been flagging for most of the year! Never mind, I got to blog Stick Insect’s EV puzzle, Distortion, and Nimrod’s IQ, combining the 50th anniversary of JFK’s assassination the day before.

Upon opening the paper, I had the same sort of feeling as I did with Mr Magoo’s domino puzzle, except that had a grid that seemed too small for a normal puzzle and here it seemed too big for a mathematical. A quick read of the preamble, ending as it did “thus completing a representation of the transport in that row”, and I realised we were indeed in Doctor Who country, the transport being the TARDIS.

The unfortunate thing was that I probably had a lot of cold solving in front of me. Moreover, certain clues (as seems common these days, we weren’t told how many) had an extra wordplay letter, but they shouldn’t be too daunting.

Luckily, the clues, all good, were pretty straightforward, but it took me about an hour to finish my first pass through them. Not that that bothered me… I had solved over 40 of them, and the grid was coming along nicely. I’d even managed to get the message spelt out by the extra letters: Count a letter in each of remaining clues. All that was in the first run of clues, with the rest not having any extra letter at all. How wonderfully sneaky! Moreover, the clues without an extra letter numbered 26, so it was obvious that something needed to be done with them, one for each letter of the alphabet.

It wasn’t much later that I had a full grid, and the instruction had to be interpreted. My initial thought was that we had to count the occurences of each letter of the alphabet in the clues in order. Unfortunately, the F in row 2 column 1, had to be surrounded by four shaded cells and that conflicted with the W in the top left corner which would be surrounded by none.

I tried various other possible interpretations, including trying to find one particular letter whose appearance in each clue indicated how many shaded squares there were. Nothing worked out.

It wasn’t too long before I checked my four word chains and discovered that I hadn’t finished the top left corner correctly. Indeed, the end of stage 6, REALTER didn’t appear properly at all. Stupid boy! My first instinct about counting each letter of the alphabet in order proved correct, and I built a new grid containing the numbers 0 – 4 and corresponding to the number of shaded squares that should surround each one.

Listener 4269 My EntryThis stage proved a little bit tricky, but was very rewarding when it all worked out correctly, and there in front of me in large letters was DOCTOR WHO. Obviously L, for 50, needed to be slotted in the central square to reveal ETRELDIMM, ie T (time) & REL (relative) DIM (dimension) in EM (space), which is what TARDIS stands for.

Thanks, Ilver, for a superb (and not too tricky) implementation of a wonderful anniversary.

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Easy Win by Ilver

Posted by clanca1234 on 21 October 2011

Friday evening – best night of the week. Work’s finished for a couple of days, and we get a new Listener to look at. On the plus side, I’m home pretty early (6 o’clock). On the minus side, I’m still trying to shake off a bad cold and cough I’ve had for over a week, and my brain is working at a fraction of its normal power (no jokes, please).

So what do we have? A new setter, which is good. Strange pseudonym, though – Ilver. I’m going to have to make a conscious effort not to type Elver throughout this blog (which, co-incidentally, I’ve been asked to write as one of the normal bloggers tested this for Ilver). Anyway, enough wriggling about, and let’s read the preamble.

Even before reading the preamble, whilst waiting for the printer to do its stuff, I can solve a few clues. 1ac is a simple anagram – I SHUT A* = HIATUS, and 11ac must be ALBUMS (A + L + BUMS). I can do 16ac straight off, as I recently clued YAPP myself for a puzzle, and 20ac is obviously TART< in SA. Hmm. I’m not sure how much of a challenge this is going to be, as the clues seem pretty straightforward so far. Right, print off complete, let’s read the preamble.

Well the obvious thing to do is to try to find the 8 DLM+1 down clues. I can see one straight away – “Kara’s large vessels” at 21dn must be ARKS + A. Hmm. I think the key thing here is the wording of the preamble. Normally DLM clues CONTAIN a definition of the answer and a jumble of the answer. Here the DLM clues CONSIST of a definition of the answer and a jumble of the answer + one letter. Whilst it’s good to see DLM clues, I fear that these will be too easy to spot. And yes, some of them have to be the shorter clues, so rather leap out of the page.

40 must be ASCI, 43 REA, 32 ENTERA, 30 TRAINER, 35 SORDA and 10 UNESCO. Not sure about the other one. So what does that give us as the extra letters? LAIINGT. So the hint is a jumble of LAIINGT?. Let’s have a scan at the other clues and see if we can find the 8th DLM clue. Ah yes, there it is – A TERRE at 4dn. So it’s a jumble of LAIINGTP. Ummm… PIG LATIN? That certainly fits. Let’s remind of ourselves of the definition of PIG LATIN in Chambers… okay, so move the initial consonant to the end, and add ‘AY’. So PIG = IGPAY. Fair enough. I’m pretty certain that PIG LATIN is what’s going on here, as having slotted in the 12 or 13 answers I already have, I can see that the penultimate letter of four of the perimeter entries is A, which fits in with a pattern of *A?. Surely it’s all downhill from here! I do hope that I’m wrong about the theme, though – otherwise I’ve cracked it in about ten minutes, which surely can’t have been what the setter had in mind.

Anyway, that’s a good time for a break. Time for  a lemsip and to see if can open the cough mixture. No, that’s not because I’m too feeble to do so (although I suppose I can’t entirely rule that out). You’d have thought I’d have learned the lesson when it comes to buying Sainsburys own brand cough mixture by now. Every year I buy it (as it’s about a third of the price of other branded names), and every year I get about a third of the way down the bottle, and then find that it’s impossible to open the childproof cap anymore. I don’t know if this is a design fault or a Chris fault, but suspect the former, as Emma also can’t open this bottle. I’m sure there’s some Benylin somewhere. Quick break whilst I go to find it.

Hmm, that took longer than I planned. I made the mistake of going upstairs to change, sitting on the bed to do so, and somehow fell asleep. I can’t be well. So back on with the puzzle. Let’s concentrate on a corner or two, and try to work out the Pig Latin entries.

Right, twenty minutes later, and I’m obviously missing something, or Pig Latin isn’t actually the theme. For the two entries in the bottom row, I have ?I?TAY and ?ADLA?. Taking the latter of these, the entry could be either the pig latin form of LEAD or LOAD. But which? That seems like a massive ambiguity. And the left hand entry could be anything with the pattern T?A?, of which there are MANY possibilities. And we also have ?RDHA?, which could be H?RD…. Oh, hats off to Ilver for that one. That must be HERD, the LEAD/LOAD one must be LEAD, as both of those are words that can follow PIG – PIGHERD and PIGLEAD. Which makes the other one PIGTAIL. I like that idea a lot. Well done to Ilver! Should be plain sailing from now on….

As indeed it is. Another twenty minutes and the grid is complete. There’s a handy looking PORC down the centre of the grid, and if I dust off my Latin, I can see that one changes ESSAY to USSAY, giving a pig latin form of SUS, and that reveals PORCUS to highlight. Lovely! Good stuff from Ilver, and a nice interpretation of the theme.

I do have a few moans, however. The unching in the puzzle is very, very generous to say the least. I know that the perimeter entries effectively add unches, but even treating those as unches, there are still many fully checked entries – 9ac, 15ac, 17ac, 41ac, 44ac, 47ac, 24dn, 27dn, 10dn, 28dn, 12dn, 21dn. That makes the whole fill very easy indeed. I also wasn’t a fan of the DLM clues, as they were just too easy to spot and solve, thus giving the theme away far too easily. But yes, I recognise that the Listener series does need easier puzzles as well as harder ones, so I’ll chalk this up as a good one for newcomers to the series.

And one minor clueing query… in the down clue for KIPP, is the final P really ‘on’ KIP? Surely ‘under’ would have been more accurate here?

So, a good puzzle, that I enjoyed. With a few more unches, and a less obvious clueing gimmick, it would have been very good. Hats off to Ilver though, for a  nice idea.  I particularly liked the Latin part of the endgame (SUS, PORCUS), and the linked nature of the Pig Latin entries. Very good stuff indeed. I look forward to the next Ilver!

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