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Listener 4162: Carte Blanche with a Twist by Mash

Posted by erwinch on 25 November 2011

A second Listener from Mash but it is his two contributions to the free issue of The Magpie (60½) that have left by far the stronger impression on me – they were simply superb.  As it happens, the first of these was also carte blanche, Sixty (Carte Blanche et Noire), with the second an E-grade numerical!  In his editorial introduction, Mark said that the two puzzles had apparently taken Mash at least two years to compile.  So, the level of anticipation here was at an all-time high and I must say immediately that we were not disappointed.
 
Well, we have seen some formidable preambles but this one was positively intimidating with its talk of mirror symmetry on both diagonals and that ominous note at the end – a specialist source may provide more information.  And then there were those strange down entries – we were told that they were to be jumbled only to be given the exact order of this jumbling.  What on Earth were we getting into?
 
However, construction of the initial 30 × 10 grid was not too troublesome.  In fact, at one stage I experienced that rare feeling of exhilaration when you believe that you have the puzzle broken and the entries are going in thick and fast.  We had three pairs of clues across and down where entries started in the same cell and it was one of these (19) that provided a starting point.  I was able to build on amaurosis across and aismsabte (metabasis) down to complete the initial grid showing across entries in alternate rows and down entries in alternate columns.  I faltered at just the one clue:
 
17ac Spot a feature of Guinness? (9) whitehead – Cryptic definition I originally had blackhead.
 
 
 
The order of the columns was not yet fixed as above.  Columns 2, 3 or 10 could equally be column 1 and the grid numbers would still fit.
 
We now had to transfer the contents of this initial grid to the supplied 15 × 10 submission grid.  It did not take too long to realise that if we cut the grid in half then the across entries in the lower half fitted nicely in-between those in the upper half except that now they read from right to left.  In addition we had Klein bottle appear on two diagonals (presumably the 11 cells to be highlighted) but no clash as far as I could see.
 
It took an hour or so of juggling this grid to resolve the matter.  The key to the solution was the preamble stating that the ideal form of the grid (a Klein bottle) would be visible starting in the top row and reading partly from right to left.  Is there a single solver who did not interpret this as Klein bottle being visible and reading from right to left in two parts?  The problem was that there was still no clash to be seen.  My thoughts at this time were that we were producing a section from a Möbius strip and just to get things straight in my mind I made one out of a till receipt and, going round, marked it N, S, E and W in segments.  I wanted to make sure that things would not be upside-down on the opposite side.  Here is half of it unfolded:
 
 
 
The remainder was plain sailing – the bottom half of the initial grid was to be entered with the letters reading from right to left so that Klein bottle had two letters (was partly) reversed:
 
 
 
 The clash came from two esses at the bottom of column 8:
 
 
 
There did however remain the matter of the hidden message.  Although this was not needed for successful completion I nevertheless felt duty-bound to find it and in the end the search took even longer than the puzzle itself.  I see now that it does not really fit the preamble but I was expecting the message to mention part or section of a Möbius strip and possibly glassblower.  I saw the theme as one-sided objects and the key to the message, the figure 8, resembles a Möbius strip viewed from certain angles.  It seemed reasonable to presume that the message would have been concealed within the clues since to have added this further constraint to an already highly complex grid construction would surely have been unthinkable.  Here is how the search progressed:
  1. I looked first at the 8th letter of each clue.  We started with FUN (well the grid was certainly that!) but I gave up after FUNEAEENTAL was revealed – this was to prove costly.
  2. I looked at every 8th letter in all the clues.
  3. Remembering Nod’s recent Caesar Cipher puzzle, I then shifted the first letters of clues forward and back by eight letters.
  4. I similarly shifted the last letters and the first letters of every 8th word in all clues (too few individual clues reached eight words in length).
  5. I then had to resort to the unthinkable and looked at the initial grid reading every 8th letter in normal order, from top to bottom and then again in the boustrophedon manner.
  6. I shifted the letters of the entire grid both ways and repeated 5 above.
  7. I repeated 5 and 6 with the completed grid – after literally hours I had found nothing but nonsense since starting the search.
  8. It was getting ridiculous when I superimposed a figure 8 over the completed grid (with all letters the right way round for ease of reading):
  
 
I got quite excited when spotting FOUNT at the top but there is another word highlighted that is more appropriate as to how I should have been feeling.  Here I was right back in the same territory as when looking for volution the other week.  Then I went back to the beginning to eventually solve the puzzle and I did the same here except that I first looked at the 8th letter of down clues.  Would you believe it – at last something almost coherent appeared:  GON4THDIARNSION.  When POLY was extracted from the final four across clues I was home and dry – it was every 8th character in each clue that held the message:
 
Fundamental Polygon 4th Dimension
 
Well, the first part meant nothing to me so it was time to look at that specialist source Wikipedia.  A fascinating article, especially the fact (if true) that Klein had originally referred to the Klein surface (Fläche) rather than bottle (Flasche).  The mathematics is of course totally beyond me.  However, the message added little to a puzzle that had already been completed so I wonder if Mash had once intended that we write Fundamental Polygon in a box beneath the grid.
 
As frustrating and ultimately unhelpful as the search for the hidden message was, my enthusiasm for this puzzle was not dampened and I would vote it my pick of the year to date.  I did not find it the hardest (Jumping to Conclusion by Sabre) or the trickiest (Number or Nummer by Ruslan) but it was quite definitely the most fun.  Many thanks Mash and I sincerely hope that you will find the time to return to the Listener in the not too distant future.
 
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3 Responses to “Listener 4162: Carte Blanche with a Twist by Mash”

  1. borealis said

    “I looked first at the 8th letter of each clue. We started with FUN (well the grid was certainly that!) but I gave up after FUNEAEENTAL was revealed – this was to prove costly.”

    Snap!

  2. shirley curran said

    Strangely, I had ‘blackhead’ for that answer too, until somebody told me that Guinness is proud of its ‘whitehead’.

    You sorted out the reversal of the second half of the grid far faster than I did! I love your illustrations.

    Shirley

  3. erwinch said

    Thank you Shirley, occasionally you will get lucky and crack the tricky bits early on.  To this end it would help if I could learn to consult Chambers properly.  The other week I said that Ivy m. and f. looked like a mistake in Chambers (1983) but had I looked in the 11th edition more closely then I would have seen that Ivy is used as a diminutive of Ivor in Scotland.  In my defence, I could not find any examples on the Net.

    Then again, it was a far different story with the hidden message.  From your account you seem to have made fairly light work of it but the majority were certainly with me and Borealis above.  Had we just continued for a few seconds longer looking at the 8th letter in clues then we would have spotted POLYGON and the search would have been over.  As it was, I spent four or five hours looking for the thing between Saturday and Monday evening.  I shall never forget that trick again (nth character) and shall be on the lookout for spaces being added to the count.  It would also be good practice to check all angles before rejecting any idea.  However, I know of one solver who found the message very early on by listing the 2nd to 10th letters in columns on MS Excel – the 8th stood out but he did not find it of much use when it came to completing the puzzle.

    I thought 17ac a better clue for blackhead – on top of the black stuff.  With whitehead as the answer it was virtually a simple double definition clue since the head on Guinness is so evidently white.

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