The full reasoning can be found below the Sudoku.
Sep 01 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R9C4 can only be <1>
R9C5 can only be <4>
R5C5 is the only square in row 5 that can be <1>
R1C5 can only be <3>
R4C4 is the only square in row 4 that can be <3>
R6C3 is the only square in row 6 that can be <7>
R7C3 is the only square in row 7 that can be <4>
R1C7 is the only square in row 1 that can be <4>
R2C2 is the only square in row 2 that can be <4>
R6C9 is the only square in column 9 that can be <8>
R4C6 is the only square in column 6 that can be <8>
R4C7 is the only square in row 4 that can be <5>
Squares R1C6 and R2C6 in column 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <15>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R6C6 - removing <5> from <259> leaving <29>
R6C4 is the only square in row 6 that can be <5>
Squares R3C4 and R3C5 in row 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <79>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R3C7 - removing <7> from <12367> leaving <1236>
Intersection of row 7 with block 8. The value <9> only appears in one or more of squares R7C4, R7C5 and R7C6 of row 7. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain this value.
R8C4 - removing <9> from <79> leaving <7>
R8C8 can only be <6>
R3C4 can only be <9>
R5C8 can only be <2>
R3C5 can only be <7>
R1C8 can only be <5>
R1C6 can only be <1>
R1C3 can only be <2>
R2C6 can only be <5>
R3C2 can only be <5>
R9C2 can only be <8>
R9C7 can only be <3>
R5C2 can only be <9>
R9C3 can only be <5>
R7C8 can only be <7>
R5C7 can only be <6>
R8C2 can only be <2>
R4C3 can only be <6>
R5C3 can only be <8>
R6C7 can only be <9>
R6C6 can only be <2>
R7C7 can only be <1>
R2C8 can only be <3>
R8C1 can only be <1>
R4C1 can only be <2>
R2C3 can only be <1>
R6C5 can only be <6>
R7C6 can only be <9>
R4C5 can only be <9>
R7C5 can only be <2>
R7C1 can only be <3>
R7C9 can only be <5>
R2C7 can only be <7>
R3C7 can only be <2>
R8C7 can only be <8>
R8C3 can only be <9>
R2C9 can only be <6>
R3C3 can only be <3>
R3C9 can only be <1>
R3C1 can only be <6>
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