of course it's a matter of semantics whether such chains are "guessing".
personally, i would not consider them to be guessing, rather more
advanced rules than "this column must contain a 5, which must be in
this square".
how about something like "if a=1, then b=2, and then c=3 ... which
forces a contradiction. so a =/= 1." is that "guessing"?
i would say "no".
> be y" really doesn't change its nature to my view. And so I'm still not
> convinced that that particular grid can be solved without guessing..
the response from the automated system(?) seems cleaner than the
chains i found ... but requires translation into humanese, or better
yet, mathematics.
) I tossed it at Sudoku Susser, which is excellent at defining
) logical steps. Turns out this is an XY-wing example.
)
) * Squares R4C1 (XY), R6C3 (XZ) and R4C9 (YZ) form an XY-Wing pattern on <9>.
) All squares that are buddies of both the XZ and YZ squares cannot be <9>.
)
) R4C2 - removing <9> from <39> leaving <3>.
) R6C9 - removing <9> from <49> leaving <4>.
i'm not familiar with "wings", "buddies", etc. but can surmise their
meaning by examining the grid:
+-------+-------+-------+
| 3 6 7 | . 4 . | 5 9 2 |
| 9 5 2 | 3 7 6 | 4 1 8 |
| 8 1 4 | 2 5 9 | 6 3 7 |
+-------+-------+-------+
| e h 8 | 6 2 . | 7 5 g |
| 5 . 6 | 4 9 . | 2 8 1 |
| . 2 f | . 8 5 | 3 6 i |
+-------+-------+-------+
| 6 4 3 | 9 1 2 | 8 7 5 |
| . . . | . 3 4 | 9 2 6 |
| 2 . . | . 6 . | 1 4 3 |
+-------+-------+-------+
we have e in {1, 4} , f in {1, 9} and g in {4, 9} .
since f =/= e =/= g , we have 9 in {f, g} .
(note the duality between squares and values.)
then from f =/= h =/= g , we have h =/= 9 ,
and similarly i =/= 9 . that determines the values
h = 3 and i = 4 , and the remaining values are easy to
fill in from here.
is that "guessing"? my opinion is "no", but noone has ever
cared about my opinion anyway!
mike
