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Listener 4049: The Domino Effect by Googly

Posted by erwinch on 18 September 2009

I thought Googly a well established numerical setter so was somewhat surprised to see that this was only his fifth Listener since 1995.  My records show that I had successfully solved the previous four with the most memorable being Verity Hill’s Dice-Box (No.3737) in 2003.  I remember being sidetracked by a poet of that name, which only goes to show the power of the Internet to mislead.
Well, a return to polyominoes after just six months with the domino, the shape that inspired the nomenclature since do- was deemed close enough to the Greek for two.  However, not an inspiring shape so this is going to be a very different puzzle from Pentomino Factory.  The preamble gave nothing away as to the positioning of the dominoes – would they be placed in a symmetrical pattern, would adjoining numbers match, etc?  It is generally fatal to make assumptions with these things and the only thing that we knew for certain was that the double zero would appear in adjacent blank cells – any one of dozens of positions in the grid.
For the opening I considered OO (2dn) and O + OH (1ac).  The latter is a multiple of O and its final digit must be able to match the first of OO: O = 7, 8 or 9.  Only 64 consists of two domino numbers but make no assumptions!
On to DODO (6ac): D = 2, 3 or 4.
Then CO + OP (11ac) and COP (29ac), which gave a number of possibilities for C and P.  From AA – DO (28dn), A (32dn) has a maximum value of 31 meaning that P, in PA (35ac), must have a minimum value of 4.
And then, well, nothing really.  I could get no further and having no firm grid entries after two days was unprecedented for me.  I started to entertain some pretty fanciful ideas: were there certain domino clues that had to be worked in base 7?  The non-domino numbers would fit nicely into a 5×5 square in the centre with the dominoes arranged around the edge.  We could see 6:6, 6:5 and 6:4 arranged vertically in the top two rows from the left – 666 fits for 1ac but could not continue to 3ac and 6:0 could not start 6dn.  All this was utterly futile.  I had been away on holiday the previous week and had barely looked at Poat’s Listener let alone finished it so could be looking at two blanks in a row.
Seasoned number puzzlers are accustomed to ignoring the longer clues until near the end but in desperation I did look at them and then kicked myself for having missed the following:
COAL + CARP – CARD – COP (33ac) + COP (29ac) = COAL + CARP – CARD (23dn)
The entry lengths meant the following:
29ac = ?0
33ac = 9??
23dn = 100?  At last I had my first grid entries.
Looking at COP (29ac) = ?0 gave C = 1 or 2; P = 5 or 10
After that progress was fairly rapid although I did use BBC Basic quite a bit to help with the donkey work, avoid omissions and minimise errors.  The following grid is as far as I could get without considering the dominoes:
4049 Interim Grid Fig 1
Confirmed values were: A=11, B=13, C=1, D=3, E=2, F=9, H=31, L=5, O=7, P=10, R=8, S=43, T=21 and V=41.
Placing the dominoes was fairly straightforward starting in the SE corner.  We couldn’t have two 1:0’s so double zero and double one were positioned and crossed off the list.  Eventually all were placed, the remaining clues solved and the final values assigned:
4049 Dominoes Placed Fig 2
G=17, I=35, K=95, N=34, Q=25, U=29, X=44 and Y=19.
So, no symmetrical pattern and no matching of numbers except by chance such as with the double five.  I have never seen them but Wikipedia tells us that there are commercially available sets up to double 9, 12, 15, 18 and possibly 21.  The higher values become difficult to distinguish with so many pips so perhaps they should use numbers like Googly.  However, might our instruction be to replace the numbers with pips?  The puzzle had no M so domino and number were out but we could see something like dot all tiles.  But enough of the speculation, the first two missing clues were soon unravelled:
8ac = 87978 = 2×3×11×31×43 = EDAHS reversed gives shade although I had heads at first.
31ac = 79170 = 2×3×5×7×13×29 = EDLOBU or double.
Finding the third missing clue and placing the final domino (5:2) was a delightful puzzle in its own right.  We were at the following stage:
4049 Final Three Cells Small
Ignoring the clues, 18ac could be either 426, 456, 476, 486 or 496.
426 = 1×2×3×71 = CEDI or dice (if I=71)  I checked in Chambers to see if dice might also cover dominoes to give shade double dice but it doesn’t.
456 = 3×8×19 = dry
476 = 2×7×34 = EON or one  Giving a clear favourite for the instruction: shade double one.
486 = 1×2×3×81 = CEDI or dice again (if I=81)
496 = 2×8×31 = ERH or her
However, once the clues were considered 18ac could only be 476 and IQ=35×25.  There was one other fit for IQ (=11×75) but 11 had already been assigned to A.
So, shade double one it was to give our final grid:
4049 Solution Fig 3
Someone once wrote that they didn’t like the number puzzles since they couldn’t be multilayered unlike the word ones.  Well Googly has certainly proved that wrong.  We had the concealed entrance, the number fill, the domino fill and a dénouement.  Granted, not as exciting as a felled cherry tree but really, what more could you ask for?  This was simply superb and you have to feel sorry for those unable to appreciate it as such.
Well, only one more number puzzle to come this year, due at the end of November, and we have not heard from Elap so far…

5 Responses to “Listener 4049: The Domino Effect by Googly”

  1. shirleycurran said

    The beautiful presentation of your blogs (blood-free) awes us every time and this is no exception!

  2. Verity Hill said

    I am said “minor poet.” How were you distracted, exactly?

  3. erwinch said

    Dear Verity,

    Apologies, I certainly had no wish to be disparaging and have now edited the blog.  I am in no position to judge your merits as a poet in any way.  Sometimes we come to an impasse with these puzzles and in desperation will use any means as an aid to further progress.  At least it was the case seven years ago but googling Verity Hill came up with references to your work.  However, this turned out to be a total red herring.  Verity Hill’s Dice-Box by Googly was a numerical puzzle where numbers were randomly assigned to each letter of the alphabet.  The clues were made up of real words but two words were missing, each used in several clues.  The missing words turned out to be fact (Verity) and barrow (Hill).  The nets of three dice were to be found in the completed grid – dice unfolded into six connected squares and containing the numbers 1 to 6 once only.

  4. Verity Hill said

    I’m not offended. I prefer being minor. “Major” carries with it a burden of productivity, and I’m glad to be a puzzle for many of the same reasons.

  5. […] this puzzle was first available online.  None other than Verity Hill commented on my blog The Domino Effect by Googly. […]

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