The full reasoning can be found below the Sudoku.
Mar 27 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C8 can only be <9>
R4C9 can only be <7>
R5C3 is the only square in row 5 that can be <1>
R2C3 is the only square in column 3 that can be <6>
R1C6 is the only square in row 1 that can be <6>
R4C6 can only be <4>
R4C1 can only be <6>
R5C4 is the only square in row 5 that can be <6>
R3C3 is the only square in column 3 that can be <2>
R8C6 is the only square in column 6 that can be <9>
R2C6 is the only square in column 6 that can be <1>
R5C7 is the only square in column 7 that can be <4>
Intersection of row 3 with block 1. The value <4> only appears in one or more of squares R3C1, R3C2 and R3C3 of row 3. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R2C1 - removing <4> from <4589> leaving <589>
R2C2 - removing <4> from <4589> leaving <589>
Intersection of column 3 with block 7. The values <489> only appears in one or more of squares R7C3, R8C3 and R9C3 of column 3. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain these values.
R8C1 - removing <48> from <4578> leaving <57>
R9C2 - removing <89> from <5789> leaving <57>
Squares R9C2 and R9C4 in row 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <57>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R9C5 - removing <57> from <157> leaving <1>
R9C9 - removing <5> from <1589> leaving <189>
R8C9 is the only square in row 8 that can be <1>
R8C8 is the only square in row 8 that can be <2>
R1C8 can only be <5>
R1C7 can only be <9>
R7C8 can only be <3>
R3C7 can only be <8>
R5C8 can only be <8>
R1C1 can only be <7>
R2C7 can only be <3>
R2C9 can only be <2>
R5C2 can only be <9>
R6C9 can only be <5>
R6C4 can only be <2>
R5C9 can only be <3>
R7C9 can only be <9>
R7C3 can only be <4>
R9C9 can only be <8>
R9C3 can only be <9>
R1C5 can only be <2>
R8C1 can only be <5>
R5C1 can only be <2>
R8C3 can only be <8>
R8C7 can only be <7>
R3C1 can only be <4>
R9C2 can only be <7>
R8C5 can only be <4>
R7C7 can only be <5>
R9C4 can only be <5>
R2C4 can only be <4>
R7C4 can only be <7>
R2C5 can only be <5>
R8C4 can only be <3>
R2C2 can only be <8>
R5C5 can only be <7>
R3C6 can only be <7>
R3C2 can only be <5>
R6C1 can only be <8>
R5C6 can only be <5>
R6C2 can only be <4>
R2C1 can only be <9>
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