The full reasoning can be found below the Sudoku.
Jun 09 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R6C7 can only be <5>
R8C1 can only be <5>
R1C4 is the only square in row 1 that can be <2>
R6C5 is the only square in row 6 that can be <4>
R6C8 is the only square in row 6 that can be <8>
R9C1 is the only square in column 1 that can be <9>
R4C5 is the only square in column 5 that can be <2>
R4C3 can only be <1>
R4C2 is the only square in row 4 that can be <9>
R5C2 is the only square in block 4 that can be <6>
R5C3 is the only square in row 5 that can be <5>
R5C8 is the only square in row 5 that can be <3>
R5C7 is the only square in row 5 that can be <1>
Squares R1C1 and R2C1 in block 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <36>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R1C2 - removing <3> from <13458> leaving <1458>
R1C3 - removing <3> from <38> leaving <8>
R2C2 - removing <3> from <135> leaving <15>
R3C2 - removing <3> from <134> leaving <14>
Intersection of row 3 with block 2. The value <3> only appears in one or more of squares R3C4, R3C5 and R3C6 of row 3. 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 <3> from <356> leaving <56>
Squares R8C8<167>, R8C9<167> and R9C9<67> in block 9 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <167>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C8 - removing <7> from <2457> leaving <245>
R9C7 - removing <67> from <467> leaving <4>
R9C8 - removing <67> from <24567> leaving <245>
R1C7 can only be <6>
R1C1 can only be <3>
R4C7 can only be <7>
R4C8 can only be <6>
R1C9 can only be <1>
R2C1 can only be <6>
R2C8 can only be <7>
R2C5 can only be <5>
R2C2 can only be <1>
R7C5 can only be <3>
R1C6 can only be <9>
R2C9 can only be <3>
R8C8 can only be <1>
R7C4 can only be <7>
R1C8 can only be <4>
R3C6 can only be <1>
R5C6 can only be <7>
R3C5 can only be <6>
R1C2 can only be <5>
R3C8 can only be <9>
R3C2 can only be <4>
R3C4 can only be <3>
R8C5 can only be <8>
R5C4 can only be <8>
R9C6 can only be <5>
R7C2 can only be <2>
R8C2 can only be <7>
R5C5 can only be <9>
R9C4 can only be <6>
R9C9 can only be <7>
R9C8 can only be <2>
R7C6 can only be <4>
R9C3 can only be <3>
R7C8 can only be <5>
R8C9 can only be <6>
R6C2 can only be <3>
R9C2 can only be <8>
R6C3 can only be <2>
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