The full reasoning can be found below the Sudoku.
May 02 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C4 can only be <8>
R8C7 can only be <6>
R5C4 can only be <6>
R3C4 can only be <7>
R9C4 can only be <4>
R2C9 is the only square in row 2 that can be <6>
R2C8 is the only square in row 2 that can be <7>
R8C8 can only be <3>
R3C5 is the only square in row 3 that can be <6>
R5C1 is the only square in row 5 that can be <4>
R3C2 is the only square in row 3 that can be <4>
R5C3 is the only square in row 5 that can be <7>
R6C9 is the only square in row 6 that can be <3>
R8C9 is the only square in row 8 that can be <4>
R8C2 is the only square in row 8 that can be <7>
R9C5 is the only square in row 9 that can be <7>
R7C9 is the only square in row 7 that can be <7>
Squares R1C5 and R1C6 in row 1 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 row.
R1C7 - removing <9> from <1259> leaving <125>
R1C9 - removing <9> from <259> leaving <25>
Squares R6C1 and R8C1 in column 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 column.
R2C1 - removing <18> from <1389> leaving <39>
R3C1 - removing <8> from <2589> leaving <259>
R4C1 - removing <18> from <128> leaving <2>
R7C1 - removing <8> from <23568> leaving <2356>
Squares R2C2 and R4C2 in column 2 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 column.
R1C2 - removing <1> from <125> leaving <25>
R7C2 - removing <8> from <258> leaving <25>
R1C7 is the only square in row 1 that can be <1>
R2C7 can only be <9>
R2C1 can only be <3>
R3C1 is the only square in row 3 that can be <9>
R7C8 is the only square in row 7 that can be <9>
R6C8 can only be <8>
R6C1 can only be <1>
R4C9 can only be <5>
R1C9 can only be <2>
R5C7 can only be <2>
R5C9 can only be <9>
R7C7 can only be <5>
R5C6 can only be <8>
R6C5 can only be <9>
R8C1 can only be <8>
R4C2 can only be <8>
R1C5 can only be <3>
R7C1 can only be <6>
R7C2 can only be <2>
R9C8 can only be <2>
R8C3 can only be <1>
R2C3 can only be <8>
R9C3 can only be <3>
R3C8 can only be <5>
R1C6 can only be <9>
R7C5 can only be <8>
R1C2 can only be <5>
R3C9 can only be <8>
R2C2 can only be <1>
R3C3 can only be <2>
R4C5 can only be <1>
R5C5 can only be <5>
R7C6 can only be <3>
R9C1 can only be <5>
R9C6 can only be <6>
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