The full reasoning can be found below the Sudoku.
Apr 18 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R6C6 can only be <5>
R3C7 is the only square in row 3 that can be <4>
R4C5 is the only square in row 4 that can be <4>
R4C9 is the only square in row 4 that can be <5>
R4C6 is the only square in row 4 that can be <2>
R2C6 can only be <7>
R2C4 can only be <3>
R3C5 can only be <2>
R2C5 can only be <5>
R5C6 is the only square in row 5 that can be <1>
R8C6 can only be <8>
R5C3 is the only square in row 5 that can be <4>
R5C2 is the only square in row 5 that can be <5>
R1C3 is the only square in row 1 that can be <5>
R6C1 is the only square in row 6 that can be <7>
R6C4 is the only square in row 6 that can be <9>
R4C4 can only be <8>
R4C1 can only be <9>
R5C4 can only be <6>
R8C4 can only be <7>
R6C5 can only be <3>
R6C9 can only be <6>
R5C1 can only be <8>
R3C1 can only be <3>
R5C7 is the only square in row 5 that can be <9>
R8C3 is the only square in row 8 that can be <9>
R9C7 is the only square in row 9 that can be <5>
R9C3 is the only square in column 3 that can be <3>
Squares R7C1<126>, R8C2<26> and R9C1<16> in block 7 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <126>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C3 - removing <1> from <178> leaving <78>
R9C2 - removing <6> from <678> leaving <78>
R2C3 is the only square in column 3 that can be <1>
Squares R7C1<126>, R7C5<16> and R7C7<126> in row 7 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <126>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R7C9 - removing <12> from <1278> leaving <78>
Squares R3C9 and R7C9 in column 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <78>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C9 - removing <7> from <1237> leaving <123>
R9C9 - removing <78> from <178> leaving <1>
R9C1 can only be <6>
R1C1 can only be <2>
R8C2 can only be <2>
R1C9 can only be <3>
R7C1 can only be <1>
R5C9 can only be <2>
R5C8 can only be <3>
R7C5 can only be <6>
R7C7 can only be <2>
R8C5 can only be <1>
R2C7 can only be <6>
R2C2 can only be <8>
R1C7 can only be <1>
R8C7 can only be <3>
R1C8 can only be <7>
R8C8 can only be <6>
R1C2 can only be <6>
R9C8 can only be <8>
R3C9 can only be <8>
R2C8 can only be <2>
R9C2 can only be <7>
R3C3 can only be <7>
R7C3 can only be <8>
R7C9 can only be <7>
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