The full reasoning can be found below the Sudoku.
Mar 29 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R6C7 can only be <6>
R6C9 can only be <4>
R6C3 can only be <1>
R6C1 can only be <5>
R6C5 can only be <2>
R4C1 can only be <6>
R4C3 can only be <4>
R5C2 can only be <8>
R3C8 is the only square in row 3 that can be <5>
R4C5 is the only square in row 4 that can be <5>
R5C8 is the only square in row 5 that can be <3>
R8C5 is the only square in row 8 that can be <4>
R9C1 is the only square in row 9 that can be <8>
R9C9 is the only square in row 9 that can be <3>
R3C4 is the only square in column 4 that can be <3>
R3C3 can only be <8>
R2C7 is the only square in row 2 that can be <8>
R7C6 is the only square in column 6 that can be <7>
R7C2 is the only square in row 7 that can be <5>
R8C9 is the only square in row 8 that can be <5>
R9C6 is the only square in row 9 that can be <5>
Squares R7C4 and R9C4 in column 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <29>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C4 - removing <29> from <2469> leaving <46>
R5C4 - removing <9> from <469> leaving <46>
Intersection of row 7 with block 9. The value <1> only appears in one or more of squares R7C7, R7C8 and R7C9 of row 7. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R8C7 - removing <1> from <1279> leaving <279>
R8C8 - removing <1> from <179> leaving <79>
Intersection of column 9 with block 3. The value <2> only appears in one or more of squares R1C9, R2C9 and R3C9 of column 9. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R3C7 - removing <2> from <12> leaving <1>
R7C8 is the only square in row 7 that can be <1>
R7C3 is the only square in row 7 that can be <6>
R2C3 can only be <3>
R9C2 can only be <2>
R9C4 can only be <9>
R3C2 can only be <4>
R8C2 can only be <1>
R9C8 can only be <6>
R7C4 can only be <2>
R2C1 can only be <2>
R8C3 can only be <9>
R3C6 can only be <2>
R7C7 can only be <9>
R4C7 can only be <7>
R8C8 can only be <7>
R8C1 can only be <3>
R8C7 can only be <2>
R1C1 can only be <1>
R4C9 can only be <9>
R2C9 can only be <7>
R2C2 can only be <6>
R1C9 can only be <2>
R2C5 can only be <9>
R1C2 can only be <7>
R2C8 can only be <4>
R5C5 can only be <6>
R1C6 can only be <4>
R1C8 can only be <9>
R5C4 can only be <4>
R1C4 can only be <6>
R5C6 can only be <9>
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