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Listener 4131: Carte Blanche en Tore by Ten-Four

Posted by erwinch on 22 April 2011

Ten-Four is one of the many new setters to have appeared in recent years, some of which seem to be burnt-out after just one or two puzzles, but here we have a fourth.  From the first three of these, I had him classed as being on the easy side but might that be about to change?
 
Any upset to my usual routine and I can’t do the Listener.  I find them impossible say when travelling or when alcohol is involved to the slightest extent.  Well, my brother was down from Edinburgh, visiting for a long weekend.  Here he is (left) in a recent photograph of us with our sister and pet dog:
 
 
Consequently, it was the following Thursday before I had a proper look at Carte Blanche en Tore and this a type of puzzle that is notoriously difficult to get started on.  However, Ten-Four was kind to us in this case and gave us an immediate entry point.  There being an odd number of across clues (27) meant that the middle answer (to 26ac) had to be placed in the centre of row 8 in order to satisfy the required 180° symmetry.  Two further rows would contain just the one entry and also two columns but not the centre one.  Remaining rows and columns would contain two entries each.  26ac was straightforward:
 
Sharper Winter Olympian perhaps pockets prize (7) spikier – PI[E] in SKIER
 
Passkey at 27dn looked good starting from the P of spikier and, somewhat later, oak tree (5dn) to finish at the E.
 
1ac (retrial + Y) was an obvious anagram (of LITERARY) as was 1dn (of MIRABIL(IT)E) but remblai + I took considerably longer to winkle out of Chambers – the definition (earth) was perhaps a little vague here.  I confidently placed these starting in the top left-hand corner of the grid but nothing else seemed to fit with them there.  With hindsight it all looks so obvious now that remblai must be found in the centre column and not 3dn (scarper) but I was held back by the difficulty of the next seven across clues after the first – these were all among the last to be solved.  I had tentatively placed remblai in the centre column when trying to fit rawhide (20ac) and tassets (24ac) together in row 7 but it was quite a while before this was confirmed as correct.  Only one other pair started at the same cell: breasts (47ac) and begored (47dn).  Eventually the grid was completely filled:
 
 
 
Extra letters in the wordplay spelled out the following message:
 
You can do up to seven.  Join each pair of K’s with lines that don’t cross.
 
So, on to the second part of the puzzle, which I sensed would be the more time consuming.  I had never heard of graph theory and Wikipedia didn’t really help but it appeared to be a simple logic problem that we had to work out here.  The preamble’s use of straight (line) in the two-dimensional case was redundant since you cannot increase the number of dots connected beyond four by using curved or angled lines:
 
 
 
I did briefly entertain the idea that we were to connect the K’s on the surface of the torus using straight lines that could pass through the body and across free space.  Since the five K’s were on two separate planes then some lines would only appear to intersect when viewed from above – but this idea was totally unsatisfactory.  It is possible that straight was mentioned in the preamble only to suggest to solvers that we should use straight lines in our solution.  However, a solution using curves should not be marked wrong provided that they exit and re-enter the grid at the correct points.
 
My first attempt at joining the K’s was by placing them on a large toroid.  The idea was that green would indicate hidden and red in view so that a green line could cross red lines but not another green line and vice versa:
 
 
However, this was far too confusing, as can be seen.
 
I then joined nine completed grids in MS Paint and made all the connections that crossed the centre grid:
 
 
 
Cutting out the centre grid then presented the required solution:
 
 
 
A mirror image of these connections will give a valid alternative.
 
Well, I thought this a tremendous puzzle and really enjoyed it.  It was a difficult theme to translate into a crossword and I am grateful to the Listener Editors for taking a bit of a chance here – Ten-Four has certainly gone up in my estimation.  If I have any quibbles then I might have questioned the need to show the bars in the solution although indicating both the bars and numbers were a great help when solving.  Since my bars are offset, they only appear on one side of the perimeter.  Had I made an entry then I think that I might have shown them on both sides.
 
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