Nov 09 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R8C4 can only be <4>
R8C6 can only be <2>
R2C4 can only be <1>
R7C5 can only be <6>
R5C4 can only be <5>
R7C2 can only be <5>
R9C5 can only be <7>
R8C5 can only be <9>
R7C3 can only be <2>
R7C7 can only be <4>
R7C8 can only be <8>
R1C5 is the only square in row 1 that can be <5>
R2C9 is the only square in row 2 that can be <9>
R3C3 is the only square in row 3 that can be <5>
R8C9 is the only square in row 8 that can be <5>
R3C5 is the only square in column 5 that can be <2>
R5C7 is the only square in column 7 that can be <2>
Squares R2C5 and R2C6 in row 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <48>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R2C1 - removing <4> from <3467> leaving <367>
Intersection of column 7 with block 3. The value <7> only appears in one or more of squares R1C7, R2C7 and R3C7 of column 7. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R3C8 - removing <7> from <147> leaving <14>
Squares R2C1 and R2C7 in row 2 and R8C1 and R8C7 in row 8 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in columns 1 and 7 can be removed.
R1C1 - removing <3> from <134> leaving <14>
R9C1 - removing <3> from <136> leaving <16>
Squares R1C1 and R5C1 in column 1 and R1C9 and R5C9 in column 9 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in rows 1 and 5 can be removed.
R1C2 - removing <4> from <134> leaving <13>
R5C2 - removing <4> from <14679> leaving <1679>
R5C5 - removing <4> from <1348> leaving <138>
R5C6 - removing <4> from <48> leaving <8>
R1C8 - removing <4> from <1234> leaving <123>
R5C8 - removing <4> from <3479> leaving <379>
R2C6 can only be <4>
R2C5 can only be <8>
Squares R5C5 (XY), R6C5 (XZ) and R5C9 (YZ) form an XY-Wing pattern on <4>. All squares that are buddies of both the XZ and YZ squares cannot be <4>.
R6C8 - removing <4> from <49> leaving <9>
R5C2 is the only square in row 5 that can be <9>
R9C2 is the only square in column 2 that can be <6>
R9C1 can only be <1>
R1C1 can only be <4>
R8C3 can only be <7>
R8C1 can only be <3>
R2C3 can only be <6>
R5C3 can only be <1>
R5C5 can only be <3>
R6C2 can only be <4>
R5C8 can only be <7>
R5C9 can only be <4>
R4C5 can only be <4>
R5C1 can only be <6>
R4C8 can only be <3>
R6C5 can only be <1>
R4C2 can only be <7>
R8C7 can only be <1>
R2C1 can only be <7>
R3C7 can only be <7>
R2C7 can only be <3>
R3C2 can only be <1>
R1C9 can only be <2>
R3C8 can only be <4>
R1C2 can only be <3>
R9C8 can only be <2>
R9C9 can only be <3>
R1C8 can only be <1>
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