The full reasoning can be found below the Sudoku.
Mar 23 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R6C8 can only be <6>
R9C7 can only be <9>
R6C2 can only be <2>
R7C8 can only be <7>
R9C9 can only be <5>
R9C1 can only be <3>
R6C6 can only be <7>
R6C4 can only be <8>
R8C6 can only be <5>
R6C5 can only be <4>
R8C4 can only be <7>
R8C3 can only be <6>
R9C5 can only be <1>
R9C3 can only be <7>
R7C5 can only be <8>
R8C7 can only be <8>
R1C3 can only be <1>
R1C7 is the only square in row 1 that can be <3>
R1C1 is the only square in row 1 that can be <4>
R3C3 is the only square in row 3 that can be <8>
R4C5 is the only square in row 4 that can be <3>
R5C6 is the only square in row 5 that can be <2>
R5C3 is the only square in row 5 that can be <3>
R7C2 is the only square in row 7 that can be <1>
Squares R5C1 and R5C5 in row 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <56>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R5C4 - removing <5> from <159> leaving <19>
Intersection of row 3 with block 3. The values <19> only appears in one or more of squares R3C7, R3C8 and R3C9 of row 3. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain these values.
R2C7 - removing <1> from <126> leaving <26>
Intersection of block 1 with row 3. The value <6> only appears in one or more of squares R3C1, R3C2 and R3C3 of block 1. These squares are the ones that intersect with row 3. Thus, the other (non-intersecting) squares of row 3 cannot contain this value.
R3C5 - removing <6> from <567> leaving <57>
R3C7 - removing <6> from <126> leaving <12>
R3C9 - removing <6> from <679> leaving <79>
Squares R3C2 and R5C5 form a remote naked pair. <56> can be removed from any square that is common to their groups.
R3C5 - removing <5> from <57> leaving <7>
R3C9 can only be <9>
R1C5 can only be <6>
R3C8 can only be <1>
R5C9 can only be <4>
R5C7 can only be <1>
R7C9 can only be <6>
R7C7 can only be <4>
R1C9 can only be <7>
R5C5 can only be <5>
R2C6 can only be <1>
R2C4 can only be <5>
R4C6 can only be <6>
R3C7 can only be <2>
R4C8 can only be <9>
R4C2 can only be <5>
R5C1 can only be <6>
R4C4 can only be <1>
R5C4 can only be <9>
R2C3 can only be <2>
R2C7 can only be <6>
R3C2 can only be <6>
R3C1 can only be <5>
R7C3 can only be <5>
R7C1 can only be <2>
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