The full reasoning can be found below the Sudoku.
May 18 - Hard
Puzzle Copyright © Kevin Stone
Reasoning
R7C2 can only be <3>
R7C4 can only be <2>
R7C1 can only be <7>
R7C9 can only be <5>
R3C6 is the only square in row 3 that can be <5>
R3C1 is the only square in row 3 that can be <2>
R1C5 is the only square in row 1 that can be <2>
R4C6 is the only square in row 4 that can be <2>
R4C2 is the only square in row 4 that can be <5>
R6C7 is the only square in row 6 that can be <5>
R8C8 is the only square in row 8 that can be <2>
R1C1 is the only square in column 1 that can be <1>
R6C1 is the only square in column 1 that can be <3>
R4C3 can only be <7>
R4C5 is the only square in row 4 that can be <3>
R1C7 is the only square in column 7 that can be <9>
Squares R6C5 and R6C8 in row 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <14>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R6C4 - removing <14> from <14679> leaving <679>
R6C6 - removing <14> from <1479> leaving <79>
Squares R3C8 and R3C9 in block 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <46>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R1C9 - removing <4> from <3478> leaving <378>
R2C8 - removing <46> from <4678> leaving <78>
R2C9 - removing <46> from <34678> leaving <378>
Squares R8C7 and R9C7 in block 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <38>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R9C8 - removing <8> from <678> leaving <67>
R9C9 - removing <38> from <3678> leaving <67>
Squares R9C8 and R9C9 in row 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <67>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R9C1 - removing <6> from <689> leaving <89>
R9C3 - removing <6> from <46> leaving <4>
R9C5 can only be <1>
R1C3 can only be <3>
R6C5 can only be <4>
R2C3 can only be <6>
R6C8 can only be <1>
R5C6 can only be <9>
R4C8 can only be <8>
R4C9 can only be <9>
R2C8 can only be <7>
R4C4 can only be <1>
R5C9 can only be <4>
R5C1 can only be <6>
R6C6 can only be <7>
R9C6 can only be <3>
R3C9 can only be <6>
R6C4 can only be <6>
R9C7 can only be <8>
R8C6 can only be <4>
R9C1 can only be <9>
R8C7 can only be <3>
R9C8 can only be <6>
R1C9 can only be <8>
R3C8 can only be <4>
R9C9 can only be <7>
R2C4 can only be <4>
R5C4 can only be <8>
R6C2 can only be <9>
R8C4 can only be <9>
R2C6 can only be <1>
R8C1 can only be <8>
R1C2 can only be <4>
R2C9 can only be <3>
R2C2 can only be <8>
R1C4 can only be <7>
R8C2 can only be <6>
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