Jan 20 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R8C4 can only be <1>
R9C9 can only be <2>
R8C6 can only be <3>
R7C5 can only be <6>
R2C9 can only be <7>
R9C5 can only be <8>
R2C7 is the only square in row 2 that can be <3>
R5C5 is the only square in row 5 that can be <3>
R6C4 is the only square in row 6 that can be <8>
R8C7 is the only square in row 8 that can be <7>
R6C6 is the only square in column 6 that can be <5>
R6C2 is the only square in row 6 that can be <4>
R3C3 is the only square in row 3 that can be <4>
R4C6 is the only square in row 4 that can be <4>
R5C9 is the only square in row 5 that can be <4>
R1C8 is the only square in column 8 that can be <8>
Squares R7C7 and R8C9 in block 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <59>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C8 - removing <9> from <139> leaving <13>
Intersection of row 1 with block 1. The value <6> only appears in one or more of squares R1C1, R1C2 and R1C3 of row 1. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R2C1 - removing <6> from <1268> leaving <128>
Intersection of block 3 with row 3. The value <2> only appears in one or more of squares R3C7, R3C8 and R3C9 of block 3. These squares are the ones that intersect with row 3. Thus, the other (non-intersecting) squares of row 3 cannot contain this value.
R3C2 - removing <2> from <129> leaving <19>
R3C5 - removing <2> from <125> leaving <15>
Squares R3C2 and R3C5 in row 3 and R4C2 and R4C5 in row 4 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in columns 2 and 5 can be removed.
R7C2 - removing <1> from <139> leaving <39>
R9C2 - removing <1> from <136> leaving <36>
Squares R1C1 and R8C1 in column 1 and R1C9 and R8C9 in column 9 form a Simple X-Wing pattern on possibility <9>. All other instances of this possibility in rows 1 and 8 can be removed.
R1C2 - removing <9> from <269> leaving <26>
Squares R6C5, R6C8, R4C5 and R4C8 form a Type-4 Unique Rectangle on <27>.
R4C5 - removing <2> from <127> leaving <17>
R4C8 - removing <2> from <279> leaving <79>
Squares R4C4 (XY), R6C5 (XZ) and R4C8 (YZ) form an XY-Wing pattern on <7>. All squares that are buddies of both the XZ and YZ squares cannot be <7>.
R4C5 - removing <7> from <17> leaving <1>
R6C8 - removing <7> from <27> leaving <2>
R4C2 can only be <2>
R3C5 can only be <5>
R5C6 can only be <6>
R2C6 can only be <1>
R6C5 can only be <7>
R3C8 can only be <9>
R5C7 can only be <9>
R1C5 can only be <2>
R3C2 can only be <1>
R3C7 can only be <2>
R4C8 can only be <7>
R1C9 can only be <5>
R4C4 can only be <9>
R1C2 can only be <6>
R5C4 can only be <2>
R2C4 can only be <6>
R7C7 can only be <5>
R7C3 can only be <1>
R8C9 can only be <9>
R8C1 can only be <2>
R9C2 can only be <3>
R1C1 can only be <9>
R7C8 can only be <3>
R5C3 can only be <8>
R9C1 can only be <6>
R7C2 can only be <9>
R9C8 can only be <1>
R8C3 can only be <5>
R2C1 can only be <8>
R2C3 can only be <2>
R5C1 can only be <1>
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