The full reasoning can be found below the Sudoku.
Nov 02 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C6 can only be <7>
R4C2 can only be <3>
R7C3 can only be <3>
R2C4 can only be <1>
R1C7 is the only square in row 1 that can be <1>
R3C1 is the only square in row 3 that can be <3>
R5C5 is the only square in row 5 that can be <1>
R7C9 is the only square in row 7 that can be <4>
R7C7 is the only square in row 7 that can be <5>
R9C1 is the only square in row 9 that can be <1>
R9C3 is the only square in row 9 that can be <8>
R6C6 is the only square in column 6 that can be <8>
R6C2 is the only square in row 6 that can be <5>
R1C1 is the only square in row 1 that can be <5>
R5C6 is the only square in row 5 that can be <5>
R5C1 is the only square in column 1 that can be <4>
R5C3 can only be <2>
R4C4 is the only square in column 4 that can be <4>
Squares R7C5 and R8C6 in block 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <69>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R9C5 - removing <69> from <2679> leaving <27>
Intersection of row 5 with block 6. The value <6> only appears in one or more of squares R5C7, R5C8 and R5C9 of row 5. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain this value.
R4C8 - removing <6> from <679> leaving <79>
Intersection of row 9 with block 9. The values <39> only appears in one or more of squares R9C7, R9C8 and R9C9 of row 9. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain these values.
R8C9 - removing <9> from <679> leaving <67>
Intersection of block 6 with column 8. The value <9> only appears in one or more of squares R4C8, R5C8 and R6C8 of block 6. These squares are the ones that intersect with column 8. Thus, the other (non-intersecting) squares of column 8 cannot contain this value.
R9C8 - removing <9> from <3679> leaving <367>
Squares R1C2 and R9C2 in column 2 and R1C8 and R9C8 in column 8 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in rows 1 and 9 can be removed.
R9C7 - removing <6> from <679> leaving <79>
R1C9 - removing <6> from <2678> leaving <278>
R9C9 - removing <6> from <3679> leaving <379>
R5C7 is the only square in column 7 that can be <6>
Squares R5C4 and R5C9 in row 5 and R8C4 and R8C9 in row 8 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in columns 4 and 9 can be removed.
R1C9 - removing <7> from <278> leaving <28>
R3C9 - removing <7> from <789> leaving <89>
R9C9 - removing <7> from <379> leaving <39>
Squares R9C9 (XY), R5C9 (XZ) and R9C7 (YZ) form an XY-Wing pattern on <7>. All squares that are buddies of both the XZ and YZ squares cannot be <7>.
R8C9 - removing <7> from <67> leaving <6>
R8C6 can only be <9>
R2C9 can only be <2>
R2C1 can only be <6>
R1C9 can only be <8>
R8C1 can only be <2>
R4C6 can only be <6>
R7C5 can only be <6>
R1C5 can only be <4>
R3C9 can only be <9>
R7C1 can only be <9>
R1C2 can only be <2>
R3C7 can only be <7>
R9C9 can only be <3>
R8C4 can only be <7>
R9C2 can only be <6>
R5C4 can only be <3>
R9C5 can only be <2>
R6C5 can only be <9>
R9C8 can only be <7>
R5C9 can only be <7>
R1C3 can only be <7>
R3C5 can only be <8>
R3C3 can only be <4>
R9C7 can only be <9>
R1C8 can only be <6>
R6C4 can only be <2>
R4C8 can only be <9>
R6C8 can only be <3>
R4C5 can only be <7>
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