Listener 4075 - Square bashing by Arden

[Philoctetes]

Hoorah - numbers. Again one must marvel at the construction. There are some fairly obvious approaches, but I have not ventured into the hinterland much. I do hope the required clues give a satisfactory payoff.

[Aloysius535]

Once this particular Listener puzzle is no longer "live" is there a site anywhere that will show some method for how it should be solved. I have looked at it since yesterday morning and can make weak guesses at some of the letters but not with any certainty. Alternatively is there anyone who would let me know their method (again once the puzzle is no longer "live")?

[Alekhine]

I'm with you, bonefixer. I found the arithmetic to the puzzle fairly easy, but I am struggling to make a sensible word out of the factors of the right hand sode of 23a.

Has anyone cracked it?

[midazolam]

if anyone is wondering, i got one of my replies removed by the editors as I gave away one of the answers by mistake. not sure what i was thinking as i am quite strict on help by hints only. here is what i replied to bonefixer with a change:

Perhaps you have not realised (forgive me if i am wrong) but there are 2 possibilities for 1 across depending on which way round the last two letters solved are. This could make 1 across a positive or a negative number before squaring. By solving 23 across into 2 common words (remembering what 1 equals) resolves this issue and so 1 across can be entered without ambiguity. If we didn't have to worry about 23 across we could never know which way round the grid's halves would be. Very clever from Arden to spot this.

[Mysterons]

I have to confess, once I'd discovered the first possibility for 1 across (using the table at http://www.naturalnumbers.org/psquares.html) I didn't look any further, so the fact that values for F and H could be interchanged went completely over my head ! Thanks to midazolam for pointing that out, and to Arden for such a brilliant puzzle.

Aloysius - this Listener solution will be published in The Times in 3 weeks, and usually gives a fairly good idea of how to start the puzzle, if not a complete solution. Different solvers use different routes to the end, and I found using the tables for the 12-digit square speeded things up for me. With 1 across in place, and half of the 20 numbers allocated to letters, the rest of the grid fill was very straightforward.

Tristram - take a look at 8 Ac (MR/S), 11 Ac (M/R) and 20 Dn (MR) which together will give you a single value for R.

Alekhine - see above and double check you have the correct values for F and H

[midazolam]

aloysius535 - i can give you a run down when it is not live. the listener site / times will post with the solution how to get started rather than a full run through.

alekhine - remember what 1 was

[Clamzy]

Aloysius535 Regarding blow by blow explanations of Listeners no longer live, you may find the blogs at http://listenwithothers.com revealing.
Our very own ruthrobin does one most weeks but you will find the numerical ones by Erwin Hatch give all you could possibly need.

[daagg]

I like the numbers puzzles, but I can see why people who want to do crosswords don't like them. This one has a lovely end which made it all worthwhile for me. I find that some general rules always work (eg start with the shortest clues, find clues which use common letters). The worst aspect of number puzzles is that you can go a long way down a blind alley if you make a single error. I always feel relieved when the first cross-check falls into place.

[Alekhine]

Thanks, Friends ... all is clear. I confess that the notion of squaring a negative number offended the purist in me, but the extraordinary mathematical symmetry which resulted more than made up for it.

[jacinth]

The start of this one was very tough. I was forced to make a guess with T when it was down to a 50/50, but after that it fell into place easily (but not quickly!). It accelerated in a very satisfying way towards the end, which was very clear and unambiguous, so overall I was quite pleased with it (and I'm looking forward to a more logical way to get T in a few weeks' time). Errors were quickly revealed in this one too (unlike 4049 which was a horror for me).

[Mr Crossy]

I promised myself I wouldn’t look at a live puzzle thread in here this year, but Arden has left me with a dénouement dilemma that I think is a bit unfair. I’ve solved the grid and found two ordinary words to make the clue to 23. My difficulty is, which is the “correct” order in which to write the two words? Should each go beneath its respective answer? At first, that seems the obvious choice. But it is at odds with the presentation of all the given double clues, in each of which the alphabetically earlier half comes first.

To put it another way, if 23 had been a given clue, Arden certainly would have presented the two halves in alphabetical order from left to right, which is the reverse of the order of their answers. So is it “correct” to follow that pattern, or is it “correct” instead to write each half-clue directly beneath its answer?

Arden says that the two clues in each clue are presented “in no useful order”. The given order is of no “use” during solving, but that is not to say that 23 need not follow that order if it is to be deemed “correct”!

Am I being silly?!

[x_word_fan]

Mr Crossy

Re. your middle paragraph. Both are correct! Suggest you read some earlier posts (Midazolam on this page)

An excellent puzzle, much enjoyed. An amusing link between the words needed for 23a and the title.

[Mr Crossy]

Thanks, x_word_fan. Got it now. Bang goes my New Year's resolution. Cheers!

[catstail]

I enjoyed solving this. The two word answer does remove any ambiguity.
Excellent puzzle.

[Eril]

My rule isn't to look here till I have completed the puzzle - however I am I glad I looked once 'done'. I couldn't understand x_word_fan's comment at all given my 23s - and then I remembered about 1... A very pleasing puzzle from Arden, and I am still trying to work out how he found a suitable 1ac. I've tried creating my own examples, but with no success so far.

[Deviant]

Didn't really start this until Sunday evening having been helping at the Who Do you Think You Are? fair all weekend (17 hours standing up!).

Thought I was nearly finished (10 letters found) and then found I'd made a mistake somewhere & so will have to start again. I really don't take sufficient care for these numericals :(

[jamesah]

I usually manage to get stuck on these! I've got a set of 6 different 2-digit answers which seems all right but when I enter the relevant numbers into 5dn (LITIST) I get a 6-digit answer with a 7 as the third letter, which is impossible. Is anyone able to tell me if there is more than one set of possible 2-digit answers before I finally give up? Roll on Friday for a proper crossword!!

[Mysterons]

No, there is only one set of answers jamesah - are you sure of your value for L ?

[Philoctetes]

I found this an excellent number job. One problematic letter at the start (and that is a cryptic hint, Jamesah) and then, as each stage progressed, the need to work out new approaches to get over the next hurdle. Several PDMs in one puzzle, in other words.
This is why I like the numbers (though I think the proportion of 1-12 is about right!). Just given the material and the sort of basic arithmetic you learn by the age of 8, you can solve any of them. It is simply a question of clarity of logic. I love language, and the tussle with a good verbal clue is one of life's great pleasures. But that is like eating a good fillet steak - this is a glass of iced spring water on a hot day.

[Clamzy]

Hear, hear.

[catstail]

Jamesah. I had to restart 3 times after making silly errors - esp. with S M and I. Once I got these sorted it was OK.
Have you included E in 5 dn (E + LITIST)? You could try plugging your known numbers into other clues with these letters e.g.18ac etc to see if these fit.
Best of luck and come back to this site it you need to. It is worth plodding on. Honest!