The full reasoning can be found below the Sudoku.
Mar 28 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C7 is the only square in row 5 that can be <3>
R6C5 is the only square in row 6 that can be <3>
R9C2 is the only square in row 9 that can be <3>
R1C3 is the only square in row 1 that can be <3>
R1C8 is the only square in row 1 that can be <9>
R2C9 is the only square in row 2 that can be <3>
R2C3 is the only square in row 2 that can be <9>
R4C4 is the only square in column 4 that can be <9>
R2C4 is the only square in block 2 that can be <1>
Intersection of row 1 with block 2. The value <5> 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.
R3C5 - removing <5> from <4567> leaving <467>
Intersection of row 9 with block 9. The values <56> only appears in one or more of squares R9C7, R9C8 and R9C9 of row 9. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain these values.
R8C7 - removing <6> from <24679> leaving <2479>
R8C9 - removing <6> from <146> leaving <14>
Squares R7C9 and R8C9 in column 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <14>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R4C9 - removing <1> from <156> leaving <56>
R9C9 - removing <14> from <1456> leaving <56>
R4C2 is the only square in row 4 that can be <1>
R6C1 can only be <4>
R6C3 can only be <5>
R6C4 can only be <2>
R6C6 can only be <6>
R5C3 can only be <8>
R6C8 can only be <1>
R5C2 can only be <7>
R5C4 can only be <4>
R5C6 can only be <5>
R9C4 can only be <8>
R5C8 can only be <2>
R1C4 can only be <7>
R1C1 can only be <8>
R1C6 can only be <4>
R2C1 can only be <7>
R1C2 can only be <6>
R9C6 can only be <1>
R3C5 can only be <6>
R2C8 can only be <6>
R2C5 can only be <8>
R2C7 can only be <4>
R9C8 can only be <5>
R1C5 can only be <5>
R8C6 can only be <7>
R9C9 can only be <6>
R3C8 can only be <7>
R4C9 can only be <5>
R4C5 can only be <7>
R9C7 can only be <2>
R3C7 can only be <5>
R7C8 can only be <8>
R4C6 can only be <8>
R4C7 can only be <6>
R9C5 can only be <4>
R8C7 can only be <9>
R7C7 can only be <7>
R8C5 can only be <2>
R8C1 can only be <1>
R7C5 can only be <9>
R8C9 can only be <4>
R3C1 can only be <2>
R7C3 can only be <4>
R8C2 can only be <8>
R8C3 can only be <6>
R7C9 can only be <1>
R3C2 can only be <4>
R3C3 can only be <1>
R7C2 can only be <2>
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