# Listen With Others

## ‘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…)

1. ### shirleycurransaid

Don’t worry, Tim. I have found 8-1-18-5! Watch this space on the eve of Christmas.

2. ### Alastair Cuthbertsonsaid

Thanks for the plug Tim.

3. ### Phil Cainesaid

It is there Tim if you go diagonally and then lift and then and then…..no more complicated than some I saw offered on the previous occasion:-)

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