The full reasoning can be found below the Sudoku.
Apr 20 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C7 can only be <7>
R2C7 can only be <8>
R2C2 is the only square in row 2 that can be <2>
R2C4 is the only square in row 2 that can be <7>
R3C2 is the only square in row 3 that can be <7>
R5C5 is the only square in row 5 that can be <2>
R6C4 can only be <6>
R4C4 can only be <9>
R1C4 can only be <4>
R7C4 can only be <2>
R4C2 is the only square in row 4 that can be <6>
R6C9 is the only square in row 6 that can be <2>
R6C1 is the only square in row 6 that can be <3>
R1C9 is the only square in row 1 that can be <3>
R3C3 is the only square in row 3 that can be <3>
R7C8 is the only square in row 7 that can be <3>
R8C6 is the only square in row 8 that can be <3>
R9C5 is the only square in column 5 that can be <7>
Squares R9C3 and R9C6 in row 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <69>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R9C1 - removing <9> from <189> leaving <18>
R9C9 - removing <9> from <189> leaving <18>
Squares R4C6 and R6C6 in column 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <57>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R3C6 - removing <5> from <569> leaving <69>
Intersection of column 8 with block 6. The values <78> only appears in one or more of squares R4C8, R5C8 and R6C8 of column 8. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain these values.
R4C9 - removing <8> from <48> leaving <4>
R3C1 is the only square in column 1 that can be <4>
R2C3 can only be <9>
R2C8 can only be <4>
R9C3 can only be <6>
R1C1 can only be <5>
R9C6 can only be <9>
R3C6 can only be <6>
R7C5 can only be <6>
R1C5 can only be <9>
R4C1 can only be <8>
R3C5 can only be <5>
R9C1 can only be <1>
R6C2 can only be <5>
R6C6 can only be <7>
R5C3 can only be <4>
R6C8 can only be <8>
R4C6 can only be <5>
R9C9 can only be <8>
R7C1 can only be <9>
R4C8 can only be <7>
R5C2 can only be <9>
R8C3 can only be <5>
R7C2 can only be <8>
R7C9 can only be <1>
R8C2 can only be <4>
R7C7 can only be <5>
R3C9 can only be <9>
R8C7 can only be <6>
R8C8 can only be <9>
R3C8 can only be <1>
R5C8 can only be <5>
R5C7 can only be <1>
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