Dec 14 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C6 can only be <3>
R4C5 can only be <9>
R6C5 can only be <3>
R1C4 can only be <1>
R9C6 can only be <4>
R4C9 can only be <4>
R4C1 can only be <6>
R6C9 can only be <7>
R5C5 can only be <8>
R9C5 can only be <1>
R5C4 can only be <4>
R6C1 can only be <4>
R8C5 can only be <7>
R9C4 can only be <3>
R5C6 can only be <6>
R9C1 can only be <5>
R1C1 can only be <2>
R1C5 can only be <5>
R2C5 can only be <2>
R2C8 is the only square in row 2 that can be <7>
R3C2 is the only square in row 3 that can be <9>
R3C7 is the only square in row 3 that can be <5>
R2C2 is the only square in row 2 that can be <5>
R7C2 is the only square in row 7 that can be <7>
R5C2 can only be <3>
R5C1 can only be <7>
R8C8 is the only square in row 8 that can be <2>
Squares R2C1 and R3C3 in block 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <13>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R2C3 - removing <13> from <1346> leaving <46>
Squares R3C3 and R3C8 in row 3 and R7C3 and R7C8 in row 7 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in columns 3 and 8 can be removed.
R8C3 - removing <3> from <1346> leaving <146>
Squares R1C2 and R1C9 in row 1 and R9C2 and R9C9 in row 9 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in columns 2 and 9 can be removed.
R2C9 - removing <6> from <136> leaving <13>
R8C2 - removing <6> from <468> leaving <48>
R8C9 - removing <6> from <1368> leaving <138>
Squares R2C1 and R2C9 in row 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <13>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R2C7 - removing <1> from <146> leaving <46>
Intersection of column 7 with block 9. The value <1> only appears in one or more of squares R7C7, R8C7 and R9C7 of column 7. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R7C8 - removing <1> from <134> leaving <34>
R8C9 - removing <1> from <138> leaving <38>
Squares R1C2 (XY), R1C8 (XZ) and R9C2 (YZ) form an XY-Wing pattern on <8>. All squares that are buddies of both the XZ and YZ squares cannot be <8>.
R9C8 - removing <8> from <89> leaving <9>
R5C8 can only be <1>
R5C9 can only be <9>
R3C8 can only be <3>
R3C3 can only be <1>
R7C8 can only be <4>
R2C9 can only be <1>
R7C7 can only be <1>
R1C8 can only be <8>
R1C9 can only be <6>
R1C2 can only be <4>
R9C9 can only be <8>
R2C7 can only be <4>
R2C3 can only be <6>
R2C1 can only be <3>
R7C3 can only be <3>
R8C1 can only be <1>
R8C7 can only be <6>
R8C3 can only be <4>
R9C2 can only be <6>
R8C9 can only be <3>
R8C2 can only be <8>
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