The full reasoning can be found below the Sudoku.
Mar 09 - Super Hard
Puzzle Copyright © Kevin Stone
Reasoning
R4C7 is the only square in row 4 that can be <4>
R4C2 is the only square in row 4 that can be <7>
R9C3 is the only square in row 9 that can be <6>
R7C1 is the only square in column 1 that can be <7>
R8C3 is the only square in column 3 that can be <8>
R3C3 is the only square in column 3 that can be <4>
R8C2 is the only square in column 2 that can be <4>
R2C7 is the only square in column 7 that can be <8>
R1C8 is the only square in column 8 that can be <7>
R2C8 is the only square in column 8 that can be <4>
R5C8 is the only square in column 8 that can be <6>
R8C9 is the only square in block 9 that can be <5>
Squares R1C7 and R7C7 in column 7 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.
R5C7 - removing <3> from <135> leaving <15>
R6C7 - removing <3> from <135> leaving <15>
Intersection of row 1 with block 2. The values <24> only appears in one or more of squares R1C4, R1C5 and R1C6 of row 1. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain these values.
R2C4 - removing <2> from <235> leaving <35>
R2C5 - removing <2> from <12356> leaving <1356>
R3C4 - removing <2> from <28> leaving <8>
R3C5 - removing <2> from <12678> leaving <1678>
R3C6 - removing <2> from <1278> leaving <178>
Intersection of column 3 with block 4. The values <135> only appears in one or more of squares R4C3, R5C3 and R6C3 of column 3. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain these values.
R5C2 - removing <1> from <129> leaving <29>
R6C1 - removing <1> from <129> leaving <29>
Squares R6C1 and R8C1 in column 1 and R6C8 and R8C8 in column 8 form a Simple X-Wing pattern on possibility <9>. All other instances of this possibility in rows 6 and 8 can be removed.
R6C5 - removing <9> from <2359> leaving <235>
R8C5 - removing <9> from <1239> leaving <123>
Squares R5C7, R6C7, R5C3 and R6C3 form a Type-2 Unique Rectangle on <15>.
R4C3 - removing <3> from <35> leaving <5>
Squares R4C5 and R8C8 form a remote naked pair. <39> can be removed from any square that is common to their groups.
R8C5 - removing <3> from <123> leaving <12>
Squares R8C1 (XY), R8C5 (XZ) and R6C1 (YZ) form an XY-Wing pattern on <2>. All squares that are buddies of both the XZ and YZ squares cannot be <2>.
R6C5 - removing <2> from <235> leaving <35>
R6C1 is the only square in row 6 that can be <2>
R5C2 can only be <9>
R9C2 can only be <1>
R2C2 can only be <2>
R8C1 can only be <9>
R8C8 can only be <3>
R6C8 can only be <9>
R7C7 can only be <6>
R4C9 can only be <3>
R7C9 can only be <9>
R1C7 can only be <3>
R1C6 can only be <2>
R2C9 can only be <6>
R2C1 can only be <1>
R3C9 can only be <2>
R4C5 can only be <9>
R1C4 can only be <4>
R8C6 can only be <1>
R3C1 can only be <6>
R8C5 can only be <2>
R3C6 can only be <7>
R1C5 can only be <6>
R7C4 can only be <3>
R3C5 can only be <1>
R9C6 can only be <5>
R7C6 can only be <8>
R2C4 can only be <5>
R7C5 can only be <4>
R9C4 can only be <9>
R9C5 can only be <7>
R5C6 can only be <3>
R2C5 can only be <3>
R5C4 can only be <2>
R6C5 can only be <5>
R5C3 can only be <1>
R6C7 can only be <1>
R5C5 can only be <8>
R6C3 can only be <3>
R5C7 can only be <5>
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