Feb 23 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R8C4 can only be <7>
R8C6 can only be <4>
R8C9 can only be <2>
R5C6 is the only square in row 5 that can be <6>
R9C2 is the only square in column 2 that can be <4>
R9C3 is the only square in row 9 that can be <9>
R5C4 is the only square in row 5 that can be <9>
R4C2 is the only square in row 4 that can be <9>
R9C5 is the only square in row 9 that can be <5>
R7C5 can only be <1>
R8C8 is the only square in column 8 that can be <8>
Squares R6C2 and R6C4 in row 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <18>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R6C5 - removing <8> from <478> leaving <47>
R6C8 - removing <1> from <145> leaving <45>
Squares R1C2 and R8C2 in column 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <36>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C2 - removing <3> from <138> leaving <18>
Intersection of row 4 with block 5. The value <3> only appears in one or more of squares R4C4, R4C5 and R4C6 of row 4. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain this value.
R5C5 - removing <3> from <2348> leaving <248>
Intersection of column 9 with block 3. The value <5> only appears in one or more of squares R1C9, R2C9 and R3C9 of column 9. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R2C8 - removing <5> from <125> leaving <12>
Squares R2C2 and R6C2 in column 2 and R2C4 and R6C4 in column 4 form a Simple X-Wing pattern on possibility <8>. All other instances of this possibility in rows 2 and 6 can be removed.
R2C1 - removing <8> from <1358> leaving <135>
Squares R3C5 (XY), R4C5 (XZ) and R2C4 (YZ) form an XY-Wing pattern on <3>. All squares that are buddies of both the XZ and YZ squares cannot be <3>.
R4C4 - removing <3> from <13> leaving <1>
R1C5 - removing <3> from <237> leaving <27>
R6C4 can only be <8>
R6C2 can only be <1>
R2C4 can only be <3>
R2C2 can only be <8>
R3C5 is the only square in row 3 that can be <8>
R4C5 is the only square in row 4 that can be <3>
Squares R2C6 and R2C8 in row 2 and R4C6 and R4C8 in row 4 form a Simple X-Wing pattern on possibility <2>. All other instances of this possibility in columns 6 and 8 can be removed.
R1C8 - removing <2> from <246> leaving <46>
Squares R2C1 (XY), R2C8 (XZ) and R3C3 (YZ) form an XY-Wing pattern on <2>. All squares that are buddies of both the XZ and YZ squares cannot be <2>.
R3C7 - removing <2> from <126> leaving <16>
R3C3 is the only square in row 3 that can be <2>
R1C3 can only be <3>
R1C2 can only be <6>
R5C3 can only be <8>
R5C1 can only be <3>
R7C3 can only be <5>
R7C1 can only be <8>
R1C8 can only be <4>
R8C2 can only be <3>
R6C8 can only be <5>
R8C1 can only be <6>
R6C6 can only be <7>
R4C8 can only be <2>
R4C6 can only be <5>
R2C8 can only be <1>
R6C5 can only be <4>
R2C6 can only be <2>
R1C5 can only be <7>
R2C1 can only be <5>
R9C8 can only be <6>
R3C7 can only be <6>
R3C9 can only be <5>
R9C7 can only be <1>
R3C1 can only be <1>
R2C9 can only be <7>
R5C5 can only be <2>
R5C7 can only be <4>
R1C7 can only be <2>
R7C9 can only be <4>
R5C9 can only be <1>
R7C7 can only be <7>
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