by **Binarius** » Thu Feb 15, 2007 2:05 pm

Hi Dudzcom,

Regarding the website you refer to, reductions 1 and 3 are equivalent under the exchange of digits and rows/columns. It may be helpful to visualize the grid as a 9x9x9 cube (with digits changing along the third axis) -- you will see that Naked Pairs, Hidden Pairs, and X-Wings are exactly the same shape, just rotated through the three dimensions. The same goes for Naked/Hidden Triples and Swordfish, and Naked/Hidden Quads and Jellyfish. Note that we don't actually care about Squirmbags or n-Gronks for the same reason we don't care about naked or hidden subsets for n>4 (i.e., they each have a complementary subset of order <=4). Finally, I think the site may be mistaken in the statement that "Symbol Reduction is only valid when applied directly after Subset Reduction"; the way I see it, that would only be true if one updated one's candidates only after applying the Symbol Reduction rule -- a forgivable lapse of thoroughness on the part of a human player, perhaps, but less so on the part of a computer.

As for reduction 2, it is also equivalent to reduction 1 under the exchange of boxes and rows/columns. This situation is not as straightforward to visualize, since the intersection of a box and a row/column consists of either 0 or 3 coordinates for each digit, compared with the simpler value of 1 coordinate for each digit for the intersection of a row and a column; equivalently, any consideration of the effects of box constraints will break the three-fold symmetry we enjoyed with our 9x9x9 cube from above.

One more thing to note. While it is true enough that these rules will be sufficient to solve the vast majority of puzzles (specifically, those with ratings lower than "Hard", "Tough", "Fiendish", etc.), it is also true that they constitute a subset of the Simple Sudoku Technique Set, which has become standardized by convention in the advanced solving community as the realm of complexity only beyond which it becomes useful to formulate the "dozens of solution strategies" I presume the website is referring to. (It is true that many of these strategies are themselves special cases of more comprehensively overarching rules on which work remains ongoing, but this only becomes clear on levels that, while not necessarily higher, strike the solving community as more complex. We're only human, after all.)