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The sky is the limit, but you need wings to reach it.
http://www.rcbroughton.co.uk/sudoku/forum/viewtopic.php?f=5&t=96		 Page 3 of 3
Author:  mhparker [ Wed Jun 04, 2008 12:32 pm ]
Post subject:  Re: The sky is the limit, but you need wings to reach it.
rcbroughton wrote:
Just implemented it in SudokuSolver...

Wow, that was impressively quick! Great work, Richard! ;clapclap;

Look forward to getting my hands on the next version and seeing it in action!
Author:  mhparker [ Thu Jun 05, 2008 5:54 pm ]
Post subject:  Re: The sky is the limit, but you need wings to reach it.
Jean-Christophe wrote:
mhparker wrote:
Incidentally, that's why I mentioned Aligned Pair Exclusion, because (although I haven't analyzed it in detail yet) I thought it may be one of the few remaining mainstream vanilla techniques that stands a chance of catching some eliminations that might currently be missed.


Not quite true... APE are already caught by ALS-XZ as explained in Sudopedia.

Thanks for pointing that out, J-C. I had not read this Sudopedia article before, and had mainly learnt about APE from Andrew Stuart, who describes it (in his book "The Logic of Sudoku") as a "beautiful strategy", with no mention of its equivalence to ALS-XZ (which, rather strangely, he chose to discuss before APE). However, in his online Scanraid solver, he checks for APE first, which (in the light of what you say) is probably just as well...

The Sudopedia article, however, just mentioned the equivalence of simpler cases of APE to ALS-XZ, although in practice all 5 or 6 examples of APE eliminations I've examined in the last couple of days (including a couple of more complicated scenarios) are also catchable via ALS-XZ. So I'm wondering whether APE really is a true subset of ALS-XZ. If so, I'd love to see a proof (assuming I could understand it, that is! :) ).

BTW, I didn't realize until recently just how powerful ALS-XZ is. For example, the most "recent" Daily Nightmare (from February 17, 2008) can be done with just basic techniques (singles/intersections/naked+hidden subsets) plus ALS-XZ. I expect this applies to many other Nightmares, too. The bad news is, how does one "spot" these beasts?
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