The full reasoning can be found below the Sudoku.
Apr 26 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C1 is the only square in row 1 that can be <3>
R1C3 is the only square in row 1 that can be <2>
R1C7 is the only square in row 1 that can be <9>
R2C2 is the only square in row 2 that can be <7>
R3C4 is the only square in row 3 that can be <4>
R4C9 is the only square in row 4 that can be <3>
R9C4 is the only square in row 9 that can be <3>
R1C8 is the only square in column 8 that can be <1>
R3C8 is the only square in column 8 that can be <8>
R1C4 is the only square in row 1 that can be <8>
R6C8 is the only square in column 8 that can be <7>
R6C7 is the only square in block 6 that can be <5>
R6C4 can only be <6>
Squares R3C1 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.
R5C1 - removing <6> from <126> leaving <12>
Squares R2C5 and R8C5 in column 5 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.
R4C5 - removing <15> from <1245> leaving <24>
R5C5 - removing <1> from <1248> leaving <248>
Squares R8C4 and R8C5 in block 8 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 block.
R7C6 - removing <5> from <457> leaving <47>
R9C6 - removing <1> from <147> leaving <47>
Squares R7C6 and R9C6 in column 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <47>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R4C6 - removing <4> from <1459> leaving <159>
R6C6 - removing <4> from <49> leaving <9>
R6C1 can only be <2>
R6C2 can only be <8>
R5C1 can only be <1>
R6C5 can only be <4>
R7C2 can only be <6>
R4C5 can only be <2>
R7C1 can only be <5>
R4C2 can only be <9>
R9C2 can only be <2>
R4C8 can only be <6>
R5C5 can only be <8>
R8C8 can only be <2>
R5C9 can only be <4>
R9C1 can only be <9>
R4C3 can only be <4>
R5C3 can only be <6>
R5C7 can only be <2>
R7C3 can only be <8>
R3C1 can only be <6>
R7C9 can only be <7>
R9C3 can only be <1>
R7C6 can only be <4>
R9C9 can only be <8>
R8C7 can only be <6>
R9C7 can only be <4>
R9C6 can only be <7>
R3C7 can only be <7>
R3C9 can only be <5>
R2C3 can only be <5>
R1C9 can only be <6>
R1C6 can only be <5>
R2C5 can only be <1>
R2C6 can only be <6>
R8C5 can only be <5>
R8C4 can only be <1>
R4C6 can only be <1>
R4C4 can only be <5>
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