The full reasoning can be found below the Sudoku.
Apr 20 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C8 is the only square in row 1 that can be <1>
R3C5 is the only square in row 3 that can be <5>
R3C7 is the only square in row 3 that can be <9>
R2C6 is the only square in row 2 that can be <9>
R6C6 is the only square in row 6 that can be <1>
R6C7 is the only square in row 6 that can be <8>
R4C1 is the only square in row 4 that can be <8>
R9C5 is the only square in row 9 that can be <9>
Intersection of row 3 with block 1. The value <6> 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 <6> from <267> leaving <27>
R2C2 - removing <6> from <234678> leaving <23478>
Intersection of block 4 with column 3. The value <2> only appears in one or more of squares R4C3, R5C3 and R6C3 of block 4. These squares are the ones that intersect with column 3. Thus, the other (non-intersecting) squares of column 3 cannot contain this value.
R1C3 - removing <2> from <2347> leaving <347>
R8C3 - removing <2> from <279> leaving <79>
Squares R4C7<237>, R5C7<37> and R6C9<27> in block 6 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <237>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R5C8 - removing <37> from <3457> leaving <45>
R5C9 - removing <7> from <457> leaving <45>
Intersection of column 8 with block 3. The value <3> only appears in one or more of squares R1C8, R2C8 and R3C8 of column 8. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R2C7 - removing <3> from <2367> leaving <267>
Squares R1C3 and R7C3 in column 3 and R1C6 and R7C6 in column 6 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in rows 1 and 7 can be removed.
R1C2 - removing <4> from <23478> leaving <2378>
R7C2 - removing <4> from <467> leaving <67>
R1C5 - removing <4> from <3478> leaving <378>
R7C5 - removing <4> from <48> leaving <8>
R1C9 - removing <4> from <247> leaving <27>
R1C2 is the only square in row 1 that can be <8>
R1C9 is the only square in row 1 that can be <2>
R6C9 can only be <7>
R6C5 can only be <3>
R5C7 can only be <3>
R4C7 can only be <2>
R6C3 can only be <2>
R1C5 can only be <7>
R4C5 can only be <4>
R4C4 can only be <7>
R9C7 can only be <6>
R2C7 can only be <7>
R2C1 can only be <2>
R4C3 can only be <3>
R1C3 can only be <4>
R1C6 can only be <3>
R2C2 can only be <3>
R8C6 can only be <5>
R3C4 can only be <4>
R2C8 can only be <4>
R2C4 can only be <8>
R2C9 can only be <6>
R3C8 can only be <3>
R5C8 can only be <5>
R9C4 can only be <1>
R5C9 can only be <4>
R7C8 can only be <7>
R9C8 can only be <2>
R7C2 can only be <6>
R8C9 can only be <9>
R7C6 can only be <4>
R8C3 can only be <7>
R7C9 can only be <5>
R9C1 can only be <5>
R8C4 can only be <3>
R9C2 can only be <4>
R8C8 can only be <8>
R7C3 can only be <9>
R3C2 can only be <7>
R8C1 can only be <1>
R5C3 can only be <6>
R3C1 can only be <6>
R5C2 can only be <1>
R8C2 can only be <2>
R5C1 can only be <7>
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