Carte Blanche en Tore by Ten-Four
Posted by shirleycurran on 22 April 2011
Graph theory using three dimensions on a torus and starting from a carte blanche! This was a daunting prospect. We were cold-solving till midnight on Friday and through most of Saturday
and, even though some clues quickly yielded a solution (like 1ac ‘Literary broadcast being heard again’ – RETRIAL with an extra Y, and ‘Earth, it’s missing from mirabilite, oddly’ REMBLAI with an extra I) we seemed unable to solve the first and last groups of clues and convinced ourselves that we didn’t have enough solutions to attempt a grid fill.
We had 37 solutions at this point – well beyond the 20 we tend to regard as encouragement to continue and we even had a putative phrase produced by the extra letters YOU CAN DO UP TO SEVEN – JOIN EACH PAIR OF KS WITH LINES THAT DON’T CROSS. What we had to do was fairly obvious but we needed some way to complete our grid.
We had OAK MAST, OAK TREE, SPIKIER, ATTASKT and PASSKEY all flaunting Ks but the problem was how to enter them and a traditional grid with square 1 occupied by RETRIAL and REMBLAI got us nowhere.
That key word in the middle was our saving. Yet again, the Listener crossword has made us think
differently. We started filling from the middle out, putting SPIKIER in the central place that symmetry seemed to allocate to it. By a stroke of luck, we hit on the intersection of OAK TREE with it and the placing of RAWHIDE just above it and we were away.
From here on, this was fun. All our solutions fitted and soon we saw a pattern of Ks emerging. The greatest pleasure was that, as our grid filled, our remaining eighteen unsolved clues miraculously appeared. I wonder how many despairing solvers abandoned, unaware that there was a way to treat this as a conventional solve (Yes, honestly, at one point, I feared that we had to complete the impossible task of cold- solving all 55 clues!)
When REMBLAI finally slotted into place, I was reminded of Phi’s ‘Heart’ where the LEAFBEET started in the centre of the top line of the finally tectonically shifted grid. I wonder whether Ten-Four’s two easy clues at no 1 were deliberately so to mislead naive solvers like me to attempt a grid by fitting them in their conventional place! No, surely no-one would be so devious!
With a full grid, we were faced with the next problem. How were we to demonstrate the seven points connected on a torus by straight lines on this flat, two-dimensional surface? Clearly we could join the points with straight lines, but the lines then had to leave the borders of the grid at the point where they would arrive if the opposite edges joined up.
We found an interesting item on the Internet that demonstrated how this could be converted into a tidy geometrical diagram http://enderton.org/eric/torus/torus2.html but ours was more haphazard. However, it clearly worked and, to prove it, the mathematical half of the numpties amused himself by turning one of the old swimming floats from the box in the basement into the said torus with each K having six lines departing from it (or entering it).
Poor Mr Green. Not only does he have all those lines to check but also the bars we had to enter at both sides of our grid. I wonder whether the entry will be lower than usual this week. This was certainly the most difficult crossword we have struggled with for some time.
However, we have to acknowledge that it was a construction of genius and a superb crossword, so thanks to Ten-Four.