I fell on this thread by chance and I felt interested by the example.
AI's collection of "hardest puzzles yet":Searching the web, I found that AI has published (here:
http://www.aisudoku.com/en/AIsudoku_Top10s1_en.pdf) a series of 10 puzzles (including his escargot). As he says they are copyrighted, I don't write them explicitly here and I'll refer to them by the number and name he gives them (his pdf is still online). Copyrighting a puzzle seems a little absurd to me, but maybe he only meant that he didn't want his puzzles to be re-published without his name, which I could understand more easily.
More recently, he has published a new puzzle in the Sun:
http://www.thesun.co.uk/sol/homepage/news/3102272/Maths-whiz-Dr-Arto-Inkala-creates-hardest-Sudoku-yet.html, in a dithyrambic article. As he didn't give it any name, I'll call it here #11 and AI Sun-2010-08-19.
He claims #11 is harder, which is true according to SER, but not according to nrczt-braids theory (see below).
Everywhere here, braid means nrczt-braid.
Obviously, considering their SER, none of these 11 puzzles is close to the hardest known as of today, and the last one (and #11, SER 10.6, is published much after SER 11.6 were known).
This doesn't imply that they are not interesting.
Below, I put the number assigned to them in the original pdf, their name, their SER and the simplest type of extended braid they can be solved with (for ease of reading, I re-order them according to their braids classification).
Remember that extended braids are a way of using classical patterns as right linking objects instead of only candidates as in ordinary braids. For precise definitions, see the "abominable T&E and lovely braids" thread
http://forum.enjoysudoku.com/abominable-trial-and-error-and-lovely-braids-t6390.html - unfortunately half of it has been lost in the 2008 disk crash, but the definitions are still there and for the rest you can find a summary on my web pages.
Extended braids are a way of including patterns in braids according to the general zt-ing principle. They subsume both braids and AICs. Remember also my T&E(FP, 1) vs braids(FP) theorem: a candidate zzz can be eliminated by the T&E(FP, 1) procedure if and only if it there is a full braid(FP) with target zzz (where FP is any family of patterns).
Notations:
NS+HS = Naked+Hidden Singles
BI = Basic Interactions (row/block and column/block) - equivalent to whip[1]
Subsets2 = Naked+Hidden+SuperHidden Pairs (SuperHidden=Fish)
Subsets3 = Subsets2+Naked+Hidden+SuperHidden Triplets
Subsets4 = Subsets3+Naked+Hidden+SuperHidden Quads
Subsets= Subsets4
Finned2 = Finned X-Wing
Finned3 = Finned2+Finned Swordfish
Finned4 = Finned3+Finned Jellyfish
Finned=Finned4
Results:
#7 AI squadron, SER = 9.4, Braids(NS+HS) i.e. ordinary braids
#4 AI worm hole, SER = 9.5, Braids(NS+HS) i.e. ordinary braids
#10 AI broken brick, SER = 9.6, Braids(NS+HS+BI), i.e. grouped braids
#2 AI killer application, SER = 9.8, Braids(NS+HS+BI), i.e. grouped braids
#9 AI tweezers, SER = 9.8, Braids(NS+HS+BI), i.e. grouped braids
#8 AI honeypot, SER = 9.9, Braids(NS+HS+BI), i.e. grouped braids
#5 AI labyrinth, SER = 10.0, Braids(NS+HS+BI), i.e. grouped braids
#3 AI lucky diamond, SER = 10.4, Braids(NS+HS+BI+Subsets2+Finned2)
#1 AI escargot, SER = 10.5, Braids(NS+HS+BI+Subsets2+Finned2)
#11 AI Sun-2010-08-19, SER = 10.6, Braids(NS+HS+BI+Subsets2+Finned2)
#6 AI circles, SER = 10.5, Braids(NS+HS+BI+Subsets3+Finned2)
Conclusion: the whole family forms a nice set of increasingly hard puzzles, but the types of braids needed to solve them rely on patterns no more complex than Triplets and finned X-wing. I was disappointed to find no case with quads or even finned Swordfish.
Compared to these hand built puzzles, eleven's automatised method (
http://forum.enjoysudoku.com/the-making-of-a-gotchi-a-simple-way-to-find-extreme-sudokus-t30150.html) allows to create lots of much harder ones, that can be solved by no braid(NS+HS+BI+Subsets+Finned). Why doesn't he get an article in the Sun?
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