The full reasoning can be found below the Sudoku.
Sep 04 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R6C9 can only be <6>
R1C5 is the only square in row 1 that can be <7>
R2C2 is the only square in row 2 that can be <1>
R2C7 is the only square in row 2 that can be <5>
R3C6 is the only square in row 3 that can be <5>
R4C2 is the only square in row 4 that can be <6>
R1C7 is the only square in row 1 that can be <6>
R3C3 is the only square in row 3 that can be <6>
R5C4 is the only square in row 5 that can be <1>
R6C8 is the only square in row 6 that can be <2>
R5C1 is the only square in row 5 that can be <2>
R7C9 is the only square in row 7 that can be <1>
R7C3 is the only square in row 7 that can be <7>
R8C7 is the only square in row 8 that can be <2>
R7C4 is the only square in row 7 that can be <2>
R8C3 is the only square in row 8 that can be <5>
R5C2 is the only square in row 5 that can be <5>
R9C3 is the only square in column 3 that can be <3>
Squares R4C1 and R8C1 in column 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <49>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C1 - removing <49> from <4789> leaving <78>
R3C1 - removing <49> from <4789> leaving <78>
Squares R2C1 and R3C1 in block 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <78>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R2C3 - removing <8> from <489> leaving <49>
Intersection of row 1 with block 2. The value <8> 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.
R2C5 - removing <8> from <89> leaving <9>
R3C4 - removing <8> from <3489> leaving <349>
R2C3 can only be <4>
R2C9 can only be <7>
R1C2 can only be <3>
R2C1 can only be <8>
R3C2 can only be <9>
R3C1 can only be <7>
R7C2 can only be <4>
R8C1 can only be <9>
R4C1 can only be <4>
R3C4 is the only square in row 3 that can be <3>
R4C4 can only be <9>
R4C7 can only be <3>
R6C6 can only be <8>
R5C9 can only be <4>
R5C7 can only be <9>
R8C9 can only be <3>
R6C3 can only be <9>
R1C6 can only be <4>
R8C5 can only be <6>
R1C4 can only be <8>
R5C3 can only be <8>
R5C8 can only be <7>
R7C7 can only be <8>
R7C8 can only be <9>
R3C7 can only be <4>
R7C6 can only be <3>
R8C8 can only be <4>
R5C5 can only be <3>
R9C5 can only be <8>
R9C6 can only be <9>
R3C8 can only be <8>
R9C8 can only be <6>
R9C4 can only be <4>
R5C6 can only be <6>
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