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The outcome would be obvious using the "Mandatory Pairs"
method - and resolved probably much earlier!
The digits '8' in row 8 in the candidate profile would instead be a
mandatory pair of 8's in region 8 (which encloses cols 456 of row 8).
When a mandatory pair form a straight line in a row or column they
"close" the line to any other occurrence of the same digit AND they
eliminate any pre-existing possibility of that digit in any cell on the
same line (here ensuring that r8c2 is NOT 8 - leaving 2).
I have found that use of Mandatory Pairs as the starting technique
obviates the need for seveal "advanced" techniques as the "gain of
information" occurs much earlier - certainly before resort to the
tedious task of compiling the candidate profiles. The challenge for
the human solver is to resolve the difficult or harder puzzle using
mandatory pairs as an aid and without using full candidate profiles.
Alan Rayner BS23 2QT
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