The full reasoning can be found below the Sudoku.
Jun 12 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R8C3 can only be <3>
R8C8 can only be <6>
R7C8 can only be <2>
R9C8 can only be <3>
R1C1 is the only square in row 1 that can be <4>
R5C8 is the only square in row 5 that can be <4>
R7C3 is the only square in row 7 that can be <4>
R7C4 is the only square in row 7 that can be <5>
R9C6 is the only square in row 9 that can be <4>
R9C4 is the only square in row 9 that can be <2>
R9C5 is the only square in row 9 that can be <6>
R7C1 is the only square in row 7 that can be <6>
R3C5 is the only square in block 2 that can be <3>
R5C5 can only be <8>
R7C5 can only be <9>
R1C5 can only be <7>
R8C4 can only be <8>
R8C9 can only be <9>
R6C1 is the only square in row 6 that can be <8>
R6C7 is the only square in row 6 that can be <3>
R1C4 is the only square in column 4 that can be <9>
Squares R1C2 and R1C8 in row 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <15>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R1C6 - removing <1> from <128> leaving <28>
R1C7 - removing <1> from <128> leaving <28>
Squares R1C8 and R3C8 in block 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <15>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R2C7 - removing <1> from <129> leaving <29>
R3C7 - removing <1> from <1689> leaving <689>
R3C9 - removing <5> from <568> leaving <68>
Squares R4C4 and R5C4 in block 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <13>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R5C6 - removing <1> from <156> leaving <56>
R6C6 - removing <1> from <156> leaving <56>
R6C3 is the only square in row 6 that can be <1>
R9C3 can only be <7>
R9C9 can only be <8>
R7C2 can only be <8>
R9C2 can only be <1>
R3C9 can only be <6>
R7C7 can only be <7>
R6C9 can only be <5>
R6C6 can only be <6>
R1C2 can only be <5>
R1C8 can only be <1>
R3C3 can only be <9>
R3C8 can only be <5>
R3C2 can only be <7>
R3C7 can only be <8>
R2C2 can only be <3>
R3C6 can only be <1>
R1C7 can only be <2>
R5C6 can only be <5>
R1C6 can only be <8>
R2C7 can only be <9>
R4C7 can only be <1>
R2C1 can only be <1>
R5C2 can only be <9>
R2C6 can only be <2>
R4C4 can only be <3>
R5C7 can only be <6>
R5C3 can only be <2>
R4C1 can only be <7>
R5C4 can only be <1>
R5C9 can only be <7>
R4C3 can only be <5>
R5C1 can only be <3>
R4C9 can only be <2>
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