The full reasoning can be found below the Sudoku.
Mar 26 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C7 can only be <9>
R7C9 can only be <9>
R2C9 can only be <8>
R1C7 can only be <5>
R3C7 can only be <4>
R1C8 can only be <6>
R4C7 can only be <7>
R6C9 can only be <3>
R8C9 can only be <5>
R5C7 can only be <2>
R8C7 can only be <3>
R2C1 is the only square in row 2 that can be <6>
R3C4 is the only square in row 3 that can be <1>
R3C5 is the only square in row 3 that can be <6>
R5C1 is the only square in row 5 that can be <5>
R7C4 is the only square in row 7 that can be <6>
R9C4 is the only square in row 9 that can be <5>
R9C6 is the only square in row 9 that can be <3>
R2C6 can only be <7>
R2C3 can only be <3>
R1C4 is the only square in row 1 that can be <3>
R5C2 is the only square in row 5 that can be <3>
R5C9 is the only square in row 5 that can be <1>
R4C9 can only be <4>
R4C2 is the only square in row 4 that can be <1>
R5C5 is the only square in row 5 that can be <4>
R9C3 is the only square in row 9 that can be <4>
R7C6 is the only square in row 7 that can be <4>
R1C6 is the only square in column 6 that can be <2>
Squares R6C4 and R6C8 in row 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <89>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R6C1 - removing <89> from <2789> leaving <27>
R6C3 - removing <89> from <2789> leaving <27>
Intersection of row 8 with block 7. The value <2> only appears in one or more of squares R8C1, R8C2 and R8C3 of row 8. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R7C3 - removing <2> from <278> leaving <78>
Intersection of column 2 with block 1. The value <8> only appears in one or more of squares R1C2, R2C2 and R3C2 of column 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 <8> from <789> leaving <79>
Squares R1C2 and R1C5 in row 1 and R9C2 and R9C5 in row 9 form a Simple X-Wing pattern on possibility <9>. All other instances of this possibility in columns 2 and 5 can be removed.
R3C2 - removing <9> from <789> leaving <78>
Squares R3C1 and R3C6 in row 3 and R4C1 and R4C6 in row 4 form a Simple X-Wing pattern on possibility <9>. All other instances of this possibility in columns 1 and 6 can be removed.
R8C1 - removing <9> from <289> leaving <28>
Squares R4C1 and R8C4 form a remote naked pair. <89> can be removed from any square that is common to their groups.
R8C1 - removing <8> from <28> leaving <2>
R6C1 can only be <7>
R6C3 can only be <2>
R3C1 can only be <9>
R3C6 can only be <8>
R4C1 can only be <8>
R1C2 can only be <8>
R3C2 can only be <7>
R4C6 can only be <9>
R1C5 can only be <9>
R5C3 can only be <9>
R6C4 can only be <8>
R5C8 can only be <8>
R8C3 can only be <8>
R6C8 can only be <9>
R8C4 can only be <9>
R7C3 can only be <7>
R9C5 can only be <2>
R9C8 can only be <7>
R7C5 can only be <8>
R9C2 can only be <9>
R7C8 can only be <2>
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