The full reasoning can be found below the Sudoku.
Apr 30 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R3C6 can only be <2>
R4C7 can only be <5>
R5C6 can only be <9>
R6C5 can only be <5>
R7C4 can only be <7>
R1C5 can only be <3>
R4C3 can only be <1>
R4C5 can only be <6>
R6C7 can only be <3>
R7C6 can only be <4>
R5C4 can only be <1>
R6C3 can only be <8>
R3C4 can only be <5>
R9C5 can only be <9>
R7C5 can only be <2>
R3C5 can only be <7>
R9C3 can only be <4>
R2C3 is the only square in row 2 that can be <7>
R3C7 is the only square in row 3 that can be <6>
R7C3 is the only square in row 7 that can be <6>
R7C1 is the only square in row 7 that can be <5>
R5C1 can only be <3>
R5C3 can only be <5>
R1C3 is the only square in column 3 that can be <2>
R1C9 can only be <9>
R5C9 is the only square in column 9 that can be <2>
R5C7 can only be <7>
R9C9 is the only square in row 9 that can be <7>
Squares R8C2 and R8C3 in row 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <39>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R8C7 - removing <9> from <249> leaving <24>
R8C8 - removing <3> from <234> leaving <24>
R7C7 is the only square in column 7 that can be <9>
Squares R8C2 and R8C3 in block 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <39>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C2 - removing <3> from <138> leaving <18>
Squares R2C7<12>, R2C8<23> and R3C9<13> in block 3 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <123>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R3C8 - removing <3> from <348> leaving <48>
Squares R1C1 and R1C7 in row 1 and R9C1 and R9C7 in row 9 form a Simple X-Wing pattern on possibility <8>. All other instances of this possibility in columns 1 and 7 can be removed.
R3C1 - removing <8> from <148> leaving <14>
Squares R8C2, R8C3, R3C2 and R3C3 form a Type-1 Unique Rectangle on <39>.
R3C2 - removing <39> from <1389> leaving <18>
R3C3 is the only square in row 3 that can be <9>
R8C3 can only be <3>
R8C2 can only be <9>
R3C9 is the only square in row 3 that can be <3>
R7C9 can only be <1>
R2C8 can only be <2>
R7C2 can only be <8>
R9C7 can only be <8>
R9C1 can only be <1>
R1C7 can only be <4>
R7C8 can only be <3>
R1C1 can only be <8>
R8C7 can only be <2>
R3C8 can only be <8>
R2C7 can only be <1>
R8C8 can only be <4>
R3C2 can only be <1>
R3C1 can only be <4>
R2C2 can only be <3>
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