# Posts Tagged ‘Clue-by-Four’

## ‘Clue-by-four’ by gwizardry

Posted by Encota on 9 Dec 2016

I think myself fairly careful when filling out numericals but still managed to make two slip-ups this week, resulting in ‘Take 3’ being the first where I hope I have created a correctly completed grid.

The clash at 5d and 15a added to the challenge but hey, even Homer nods!  I understand a correction did appear on the Listener website on Sunday.

So how does one go about solving one of these?  My approach includes creating a ‘nodal diagram’ where letters that are likely to be of higher value are to the left and lower ones to the right, with lines between them showing which lines are certain to be higher than which others (aside: I did the same in the puzzle in Issue 0 of Oyler & Zag’s excellent Crossnumbers Quarterly’s entitled ‘Pentomino Primes by John Gowland’).  Applied to the data in these clues results in the diagram roughly like that below:

I am sure there are better ways but I find this helps me visually spot implications.  Examples:

1. Everything is bigger than D (yes, I know that one is trivial), thus D=0.
2. There are only three arrows terminating on D – those from W, F and T – so only one of these three can be 1 (since all other letters have at least two others smaller than them). In this example, as both 27ac and 3d have at least two digits, then neither W nor F can be 1, thus T=1.  [Note of course that being directly connected to D doesn’t stop W or F being 25.]  The same approach can readily be applied to show X=2.Any ways of improving this?  Comments welcomed!

I also used my usual technique of starting in Red pencil, moving on to Orange and so on through the rainbow as I progressed, to ease backing out if (when) I made an error.
Another aside: if only someone would invent a handheld device where you could capture an image every few minutes then this method could well become redundant 😉
Doesn’t look as pretty though!  My rough version looked like this (though my scanner’s colours are by no means perfect):

Of course one could create an entire dictionary of ‘sum of squares’ for all totals up to 25^2 + 24^2 + 23^2, then pattern match.  That seemed a bit too much like brute force to me though!

My thanks to gwizardry for a clever and enjoyable puzzle – this was great fun.

Tim / Encota

PS I was mildly surprised not to find 8-1-18-5 hiding in the grid somewhere (’nuff said…)

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## Clue-by-Four by gwizardry

Posted by shirleycurran on 9 Dec 2016

I dread the three-monthly numerical puzzles and can’t even console myself by beginning  with a check of the setter’s membership of the Listener setters’ drinkie club unless, like Oyler recently, the setter is into doubles and triples (Oyler who with Zag in December is launching the first edition of the Cross Numbers Quarterly – here’s a plug. It’s the first of their three-monthly magazines containing not one, but eight numerical crosswords – I can’t imagine a Christmas present I would appreciate less, but know that the numericals get a far larger entry rate than all the rest so it’s a gift to the number buffs).

Surprisingly for a non-numerical Numpty, this one didn’t look too bad, except for the carte blanche grid and the lack of clue lengths. Even a Numpty can calculate square numbers. I found an isolated G & T in one of the down clues and decided that we must allow gwizardry his admission ticket to the bar, ‘Cheers gwizardry!’, then we examined letter frequency.

It took no time at all to see that D had to be zero, since it appeared at the end of the majority of the clues. The other Numpty (the mathematical one) worked on the Zipf’s law of frequency, thus establishing that T and X, for example, had to be low numbers,  and with a considerable amount of shall I call it ‘muttering’ when he had to backtrack, produced the semblance of a working grid. Then the air became blue as he attacked the last, top right corner.

Of course, like so many solvers, we faced an impasse: 5d had to be 262 but that clashed with 15ac which was 365. For a frustrated hour we struggled then emails from friends began to appear suggesting that there was an error and prompting us to look at the Answerbank where a few solvers had decided that the clue had to end in TT and not TD. Obviously an error in a numerical crossword will have greater repercussions than one in a verbal one but it was the equivalent of a  clash in any other situation. I wonder whether the editors will simply decide that able solvers should manage to spot this problem, or whether the crossword will have to be discounted in the annual statistics.

Indeed, with that adjusted clue it worked, and we uneasily put the challenge to rest, having established that those four centre digits, read clockwise, gave QUAD. How appropriate! Many thanks gwizardry. That typo was a real shame and I understand that it has now been corrected on the Listener website, though I am told it appeared in the printed version of The Times. We are currently being snowed on in Nevada’s South Lake Tahoe, after crossing the snowy Sierra Nevada so The Times is about 7000 km away and we can’t check.

I know that the ultimate responsibility for accuracy in a crossword is the setter’s but errors can creep in all along the line of editorial checking, vetting, printing etc. I have managed to produce a few horrors in my time but the comedy is that those are the ones we remember, the ones that we are remembered by, and maybe even the ones that produce a smile.

So here’s a smile for gwizardry, who must be just about as sad as Poat who is currently getting a bit of stick from some for hiding his hare in the mud of the pre-ramble. Thank you gwizardry. No, I shan’t look forward to your next – I hate the things, but this was a fair and fine challenge.

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