The full reasoning can be found below the Sudoku.
Mar 29 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R7C9 can only be <8>
R3C7 is the only square in row 3 that can be <1>
R8C5 is the only square in row 8 that can be <8>
R8C3 is the only square in row 8 that can be <2>
Squares R1C5<59>, R6C5<359> and R9C5<39> in column 5 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <359>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C5 - removing <9> from <269> leaving <26>
R5C5 - removing <3> from <1236> leaving <126>
Squares R4C5<126>, R4C6<26> and R5C5<126> in block 5 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.
R4C4 - removing <2> from <248> leaving <48>
R5C4 - removing <2> from <248> leaving <48>
R5C6 - removing <26> from <2367> leaving <37>
Squares R4C4 and R5C4 in column 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <48>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R6C4 - removing <8> from <589> leaving <59>
Squares R1C3 and R1C7 in row 1 and R6C3 and R6C7 in row 6 form a Simple X-Wing pattern on possibility <8>. All other instances of this possibility in columns 3 and 7 can be removed.
R3C3 - removing <8> from <34568> leaving <3456>
R4C3 - removing <8> from <168> leaving <16>
R4C7 - removing <8> from <248> leaving <24>
R4C4 is the only square in row 4 that can be <8>
R5C4 can only be <4>
R5C9 can only be <2>
R3C9 can only be <4>
R4C7 can only be <4>
R8C7 can only be <6>
R8C2 can only be <5>
R8C8 can only be <4>
R2C3 is the only square in row 2 that can be <4>
R7C8 is the only square in row 7 that can be <5>
R2C7 is the only square in column 7 that can be <2>
R2C5 can only be <6>
R2C2 can only be <9>
R5C5 can only be <1>
R5C1 can only be <6>
R4C5 can only be <2>
R2C8 can only be <3>
R5C8 can only be <8>
R4C6 can only be <6>
R4C3 can only be <1>
R3C1 can only be <3>
R5C2 can only be <7>
R3C8 can only be <9>
R6C7 can only be <3>
R7C1 can only be <1>
R3C6 can only be <2>
R1C7 can only be <8>
R5C6 can only be <3>
R7C2 can only be <6>
R6C3 can only be <8>
R1C3 can only be <5>
R3C2 can only be <8>
R1C5 can only be <9>
R3C3 can only be <6>
R6C5 can only be <5>
R9C5 can only be <3>
R3C4 can only be <5>
R7C6 can only be <9>
R6C4 can only be <9>
R7C4 can only be <2>
R7C7 can only be <7>
R6C6 can only be <7>
R7C3 can only be <3>
R9C7 can only be <9>
R9C3 can only be <7>
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