The full reasoning can be found below the Sudoku.
Apr 10 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C2 can only be <5>
R1C6 is the only square in row 1 that can be <3>
R1C5 is the only square in row 1 that can be <5>
R3C1 is the only square in row 3 that can be <7>
R7C1 can only be <6>
R4C7 is the only square in row 4 that can be <3>
R8C7 is the only square in row 8 that can be <5>
R9C1 is the only square in row 9 that can be <3>
R9C6 is the only square in row 9 that can be <5>
R5C6 is the only square in column 6 that can be <1>
Squares R5C4 and R5C5 in row 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <28>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R5C2 - removing <2> from <267> leaving <67>
R5C8 - removing <8> from <468> leaving <46>
R5C9 - removing <28> from <24578> leaving <457>
Squares R7C9 and R9C7 in block 9 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.
R9C9 - removing <78> from <1789> leaving <19>
Intersection of row 7 with block 8. The value <2> only appears in one or more of squares R7C4, R7C5 and R7C6 of row 7. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain this value.
R8C5 - removing <2> from <29> leaving <9>
R8C8 can only be <1>
R9C9 can only be <9>
R3C4 is the only square in row 3 that can be <9>
R9C3 is the only square in row 9 that can be <1>
R1C1 is the only square in row 1 that can be <1>
R6C1 can only be <5>
R5C1 can only be <4>
R5C8 can only be <6>
R4C1 can only be <9>
R5C2 can only be <7>
R6C8 can only be <8>
R4C8 can only be <4>
R2C8 can only be <9>
R5C9 can only be <5>
R8C2 can only be <2>
R6C3 can only be <2>
R6C7 can only be <7>
R4C3 can only be <8>
R8C3 can only be <7>
R4C2 can only be <1>
R6C9 can only be <1>
R9C7 can only be <8>
R6C2 can only be <6>
R4C9 can only be <2>
R9C5 can only be <6>
R2C7 can only be <6>
R7C9 can only be <7>
R2C5 can only be <8>
R1C7 can only be <2>
R2C3 can only be <4>
R1C9 can only be <4>
R3C9 can only be <8>
R9C4 can only be <7>
R1C4 can only be <6>
R1C3 can only be <9>
R5C5 can only be <2>
R3C6 can only be <2>
R7C6 can only be <8>
R5C4 can only be <8>
R7C4 can only be <2>
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