The full reasoning can be found below the Sudoku.
Sep 06 - Hard
Puzzle Copyright © Kevin Stone
Reasoning
R5C7 is the only square in row 5 that can be <4>
R1C3 is the only square in row 1 that can be <4>
R3C9 is the only square in row 3 that can be <4>
R7C6 is the only square in column 6 that can be <9>
R9C6 is the only square in column 6 that can be <5>
R9C2 can only be <7>
R2C9 is the only square in column 9 that can be <1>
R7C5 is the only square in column 5 that can be <1>
R9C3 is the only square in row 9 that can be <1>
R7C3 is the only square in column 3 that can be <2>
Squares R2C5 and R2C8 in row 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <23>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R2C1 - removing <3> from <356> leaving <56>
R2C2 - removing <3> from <356> leaving <56>
R1C2 is the only square in column 2 that can be <3>
Squares R1C7 and R1C8 in row 1 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.
R1C4 - removing <8> from <178> leaving <17>
Squares R2C1 and R7C1 in column 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <56>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R3C1 - removing <6> from <679> leaving <79>
R4C1 - removing <56> from <356789> leaving <3789>
R6C1 - removing <56> from <3568> leaving <38>
R8C1 - removing <56> from <569> leaving <9>
R3C1 can only be <7>
R5C2 is the only square in column 2 that can be <9>
R4C7 is the only square in row 4 that can be <9>
R1C7 can only be <8>
R1C8 can only be <9>
R3C3 is the only square in row 3 that can be <9>
R9C8 is the only square in row 9 that can be <8>
R5C8 can only be <6>
R5C3 can only be <7>
R8C8 can only be <2>
R8C5 can only be <7>
R2C8 can only be <3>
R9C7 can only be <3>
R9C4 can only be <2>
R3C7 can only be <2>
R2C5 can only be <2>
R6C7 can only be <5>
R5C5 can only be <8>
R3C5 can only be <3>
R6C3 can only be <6>
R7C7 can only be <6>
R4C9 can only be <8>
R7C1 can only be <5>
R8C9 can only be <5>
R7C4 can only be <3>
R8C2 can only be <6>
R7C9 can only be <7>
R3C6 can only be <6>
R3C4 can only be <8>
R4C1 can only be <3>
R6C9 can only be <2>
R4C3 can only be <5>
R2C1 can only be <6>
R6C4 can only be <1>
R2C2 can only be <5>
R4C6 can only be <7>
R6C1 can only be <8>
R4C4 can only be <6>
R1C6 can only be <1>
R6C6 can only be <3>
R1C4 can only be <7>
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