The full reasoning can be found below the Sudoku.
Aug 07 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C4 can only be <3>
R1C3 is the only square in row 1 that can be <3>
R3C7 is the only square in row 3 that can be <3>
R9C5 is the only square in row 9 that can be <3>
R7C2 is the only square in row 7 that can be <3>
R4C1 is the only square in block 4 that can be <1>
R4C4 can only be <7>
R1C4 can only be <1>
R1C6 can only be <5>
R1C5 can only be <7>
Squares R6C7 and R6C9 in row 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <27>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R6C3 - removing <2> from <28> leaving <8>
R6C5 - removing <2> from <1268> leaving <168>
R5C6 is the only square in column 6 that can be <8>
R7C6 is the only square in column 6 that can be <9>
Squares R5C2 and R8C2 in column 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <25>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C2 - removing <2> from <128> leaving <18>
Squares R2C2 and R3C2 in block 1 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 block.
R3C1 - removing <8> from <689> leaving <69>
Squares R6C7 and R6C9 in block 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <27>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R4C7 - removing <2> from <259> leaving <59>
R6C7 is the only square in column 7 that can be <2>
R6C9 can only be <7>
R7C7 is the only square in column 7 that can be <7>
R7C1 is the only square in row 7 that can be <8>
R9C7 is the only square in row 9 that can be <8>
R9C9 is the only square in row 9 that can be <5>
R8C7 can only be <9>
R8C8 can only be <6>
R4C7 can only be <5>
R7C8 can only be <1>
R4C3 can only be <2>
R5C8 can only be <9>
R5C5 can only be <2>
R7C9 can only be <4>
R2C8 can only be <7>
R3C8 can only be <5>
R4C5 can only be <9>
R2C3 can only be <6>
R5C2 can only be <5>
R8C2 can only be <2>
R8C1 can only be <4>
R2C5 can only be <8>
R3C3 can only be <7>
R7C3 can only be <5>
R3C1 can only be <9>
R2C2 can only be <1>
R3C9 can only be <1>
R1C1 can only be <2>
R3C2 can only be <8>
R2C9 can only be <2>
R7C5 can only be <6>
R3C5 can only be <4>
R6C5 can only be <1>
R9C4 can only be <4>
R9C6 can only be <1>
R8C5 can only be <5>
R9C1 can only be <6>
R3C4 can only be <6>
R6C6 can only be <6>
R1C9 can only be <9>
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