The full reasoning can be found below the Sudoku.
Mar 31 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C7 can only be <6>
R6C7 can only be <5>
R8C7 can only be <9>
R4C7 can only be <3>
R2C7 can only be <2>
R1C4 is the only square in row 1 that can be <8>
R4C9 is the only square in row 4 that can be <8>
R7C8 is the only square in row 7 that can be <2>
R2C1 is the only square in column 1 that can be <1>
R1C5 is the only square in column 5 that can be <2>
R1C6 can only be <1>
R7C2 is the only square in block 7 that can be <9>
Intersection of row 2 with block 1. The value <4> only appears in one or more of squares R2C1, R2C2 and R2C3 of row 2. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R3C1 - removing <4> from <345> leaving <35>
R3C2 - removing <4> from <458> leaving <58>
Intersection of row 9 with block 8. The values <149> only appears in one or more of squares R9C4, R9C5 and R9C6 of row 9. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain these values.
R7C4 - removing <4> from <467> leaving <67>
R7C6 - removing <4> from <347> leaving <37>
R8C5 - removing <1> from <13567> leaving <3567>
Squares R4C4 and R7C4 in column 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <67>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R3C4 - removing <7> from <479> leaving <49>
R6C4 - removing <67> from <1679> leaving <19>
R6C3 is the only square in row 6 that can be <6>
R4C3 can only be <5>
R4C4 is the only square in row 4 that can be <6>
R7C4 can only be <7>
R7C6 can only be <3>
R5C3 is the only square in column 3 that can be <9>
R5C2 is the only square in row 5 that can be <4>
R2C2 can only be <8>
R2C8 can only be <7>
R3C2 can only be <5>
R2C9 can only be <9>
R5C8 can only be <1>
R2C5 can only be <3>
R3C9 can only be <6>
R3C1 can only be <3>
R8C2 can only be <7>
R3C8 can only be <8>
R7C9 can only be <4>
R5C5 can only be <7>
R8C8 can only be <6>
R6C9 can only be <7>
R6C1 can only be <2>
R7C1 can only be <5>
R8C9 can only be <1>
R8C5 can only be <5>
R2C3 can only be <4>
R3C5 can only be <9>
R4C6 can only be <2>
R6C6 can only be <9>
R4C1 can only be <7>
R6C4 can only be <1>
R9C6 can only be <4>
R7C5 can only be <6>
R8C1 can only be <4>
R8C3 can only be <3>
R3C6 can only be <7>
R3C4 can only be <4>
R9C5 can only be <1>
R9C4 can only be <9>
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