Dec 27 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C4 can only be <7>
R6C5 can only be <1>
R6C8 can only be <8>
R1C5 can only be <6>
R6C6 can only be <3>
R4C8 can only be <9>
R2C6 can only be <1>
R4C5 can only be <7>
R5C9 can only be <3>
R3C1 is the only square in row 3 that can be <7>
R1C8 is the only square in row 1 that can be <7>
R3C9 is the only square in row 3 that can be <1>
R1C1 is the only square in row 1 that can be <1>
R4C6 is the only square in row 4 that can be <6>
R9C8 is the only square in row 9 that can be <1>
R9C1 is the only square in row 9 that can be <3>
R8C1 is the only square in column 1 that can be <5>
R9C9 is the only square in row 9 that can be <5>
R1C3 is the only square in column 3 that can be <5>
Intersection of column 3 with block 7. The value <2> only appears in one or more of squares R7C3, R8C3 and R9C3 of column 3. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R8C2 - removing <2> from <24689> leaving <4689>
R9C2 - removing <2> from <2489> leaving <489>
Intersection of block 8 with row 8. The value <8> only appears in one or more of squares R8C4, R8C5 and R8C6 of block 8. These squares are the ones that intersect with row 8. Thus, the other (non-intersecting) squares of row 8 cannot contain this value.
R8C2 - removing <8> from <4689> leaving <469>
R8C9 - removing <8> from <2689> leaving <269>
Squares R3C3 and R9C3 in column 3 and R3C7 and R9C7 in column 7 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in rows 3 and 9 can be removed.
R9C2 - removing <4> from <489> leaving <89>
Squares R7C1 and R9C2 in block 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <89>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R8C2 - removing <9> from <469> leaving <46>
Squares R2C2 and R2C9 in row 2 and R8C2 and R8C9 in row 8 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in columns 2 and 9 can be removed.
R7C9 - removing <6> from <2689> leaving <289>
Squares R2C1 (XY), R2C8 (XZ) and R1C2 (YZ) form an XY-Wing pattern on <2>. All squares that are buddies of both the XZ and YZ squares cannot be <2>.
R1C9 - removing <2> from <289> leaving <89>
R2C2 - removing <2> from <2469> leaving <469>
R1C2 is the only square in row 1 that can be <2>
Squares R1C7 and R1C9 in block 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <89>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R2C9 - removing <9> from <269> leaving <26>
Squares R8C2 (XY), R8C8 (XZ) and R7C3 (YZ) form an XY-Wing pattern on <2>. All squares that are buddies of both the XZ and YZ squares cannot be <2>.
R7C9 - removing <2> from <289> leaving <89>
R7C3 is the only square in row 7 that can be <2>
R9C3 can only be <4>
R3C3 can only be <6>
R8C2 can only be <6>
R3C7 can only be <4>
R2C8 can only be <2>
R2C9 can only be <6>
R8C8 can only be <4>
R7C7 is the only square in row 7 that can be <6>
R9C5 is the only square in row 9 that can be <2>
R5C5 can only be <9>
R8C4 can only be <8>
R5C6 can only be <8>
R5C1 can only be <4>
R8C6 can only be <9>
R4C4 can only be <5>
R8C9 can only be <2>
R4C2 can only be <8>
R6C4 can only be <4>
R5C4 can only be <2>
R2C1 can only be <9>
R6C2 can only be <5>
R2C2 can only be <4>
R7C1 can only be <8>
R9C2 can only be <9>
R7C9 can only be <9>
R1C9 can only be <8>
R9C7 can only be <8>
R1C7 can only be <9>
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