The full reasoning can be found below the Sudoku.
Mar 04 - Super Hard
Puzzle Copyright © Kevin Stone
Reasoning
R1C4 is the only square in row 1 that can be <2>
R7C7 is the only square in row 7 that can be <6>
R7C8 is the only square in row 7 that can be <1>
R8C6 is the only square in row 8 that can be <1>
R8C4 is the only square in row 8 that can be <6>
R2C6 is the only square in row 2 that can be <6>
R8C3 is the only square in row 8 that can be <5>
R7C5 is the only square in row 7 that can be <5>
R9C1 is the only square in row 9 that can be <6>
R9C9 is the only square in row 9 that can be <4>
R8C2 is the only square in row 8 that can be <4>
R3C3 is the only square in column 3 that can be <2>
R3C7 is the only square in column 7 that can be <1>
R1C1 is the only square in row 1 that can be <1>
R3C5 is the only square in block 2 that can be <4>
Squares R4C1 and R4C6 in row 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <48>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R4C2 - removing <8> from <128> leaving <12>
R4C8 - removing <4> from <234> leaving <23>
Squares R1C9 and R5C9 in column 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <39>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R4C9 - removing <3> from <135> leaving <15>
R6C9 - removing <9> from <159> leaving <15>
Intersection of row 1 with block 2. The value <7> 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 this value.
R2C4 - removing <7> from <379> leaving <39>
Intersection of column 1 with block 4. The values <489> only appears in one or more of squares R4C1, R5C1 and R6C1 of column 1. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain these values.
R5C3 - removing <89> from <789> leaving <7>
R6C2 - removing <9> from <1279> leaving <127>
Squares R1C5 and R5C5 in column 5 and R1C9 and R5C9 in column 9 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in rows 1 and 5 can be removed.
R5C7 - removing <3> from <349> leaving <49>
Squares R3C2, R3C8, R2C2 and R2C8 form a Type-4 Unique Rectangle on <79>.
R2C2 - removing <9> from <789> leaving <78>
R2C8 - removing <9> from <3479> leaving <347>
Squares R2C4 (XY), R1C5 (XZ) and R9C4 (YZ) form an XY-Wing pattern on <7>. All squares that are buddies of both the XZ and YZ squares cannot be <7>.
R9C5 - removing <7> from <78> leaving <8>
R5C5 can only be <3>
R5C9 can only be <9>
R1C5 can only be <7>
R4C4 can only be <5>
R5C7 can only be <4>
R1C9 can only be <3>
R1C6 can only be <9>
R9C6 can only be <7>
R2C4 can only be <3>
R4C9 can only be <1>
R6C4 can only be <7>
R4C2 can only be <2>
R6C9 can only be <5>
R5C1 can only be <8>
R2C7 can only be <9>
R6C8 can only be <2>
R6C6 can only be <4>
R9C4 can only be <9>
R6C1 can only be <9>
R4C6 can only be <8>
R6C2 can only be <1>
R4C8 can only be <3>
R2C3 can only be <8>
R8C7 can only be <3>
R3C8 can only be <7>
R3C2 can only be <9>
R2C8 can only be <4>
R4C1 can only be <4>
R8C8 can only be <9>
R2C2 can only be <7>
R7C3 can only be <9>
R7C2 can only be <8>
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