The full reasoning can be found below the Sudoku.
Mar 25 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C4 is the only square in row 1 that can be <9>
R4C4 can only be <3>
R6C6 can only be <4>
R5C5 can only be <9>
R4C7 is the only square in row 4 that can be <7>
R4C9 is the only square in row 4 that can be <8>
R6C1 is the only square in row 6 that can be <3>
R8C3 is the only square in row 8 that can be <7>
R9C6 is the only square in row 9 that can be <7>
R9C4 is the only square in row 9 that can be <1>
R4C1 is the only square in column 1 that can be <9>
R7C7 is the only square in column 7 that can be <6>
R7C6 can only be <3>
R8C4 is the only square in row 8 that can be <6>
R5C8 is the only square in column 8 that can be <6>
R6C9 is the only square in column 9 that can be <2>
R3C7 is the only square in column 7 that can be <2>
R2C7 is the only square in column 7 that can be <8>
Squares R2C1 and R5C1 in column 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <45>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C1 - removing <5> from <258> leaving <28>
R8C1 - removing <4> from <248> leaving <28>
Intersection of row 9 with block 9. The value <5> 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 this value.
R7C8 - removing <5> from <589> leaving <89>
Squares R7C3<24>, R7C4<45> and R7C5<245> in row 7 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <245>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R7C2 - removing <24> from <2489> leaving <89>
R4C2 is the only square in column 2 that can be <2>
R4C3 can only be <6>
Squares R3C3<145>, R3C4<45>, R3C5<345> and R3C8<135> in row 3 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <1345>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R3C2 - removing <14> from <1468> leaving <68>
R3C6 - removing <1> from <168> leaving <68>
Squares R3C3 and R3C8 in row 3 and R6C3 and R6C8 in row 6 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in columns 3 and 8 can be removed.
R1C3 - removing <1> from <125> leaving <25>
R1C8 - removing <1> from <15> leaving <5>
R1C3 can only be <2>
R1C1 can only be <8>
R7C3 can only be <4>
R7C4 can only be <5>
R9C2 can only be <9>
R7C5 can only be <2>
R3C4 can only be <4>
R8C5 can only be <4>
R8C9 can only be <3>
R8C8 can only be <8>
R2C9 can only be <1>
R9C7 can only be <5>
R7C2 can only be <8>
R9C9 can only be <4>
R6C7 can only be <9>
R1C6 can only be <1>
R8C1 can only be <2>
R3C2 can only be <6>
R2C6 can only be <6>
R3C6 can only be <8>
R2C2 can only be <4>
R5C9 can only be <5>
R3C8 can only be <3>
R3C5 can only be <5>
R5C1 can only be <4>
R6C8 can only be <1>
R6C3 can only be <5>
R7C8 can only be <9>
R2C1 can only be <5>
R5C2 can only be <1>
R3C3 can only be <1>
R2C5 can only be <3>
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