The full reasoning can be found below the Sudoku.
Mar 23 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C5 can only be <3>
R2C2 can only be <5>
R3C6 can only be <6>
R4C3 can only be <4>
R5C1 can only be <2>
R3C9 can only be <4>
R3C3 is the only square in row 3 that can be <3>
R3C5 is the only square in row 3 that can be <5>
R5C3 is the only square in row 5 that can be <5>
R7C7 is the only square in row 7 that can be <5>
R7C8 is the only square in row 7 that can be <3>
R5C7 is the only square in row 5 that can be <3>
Squares R5C6 and R6C5 in block 5 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 block.
R5C5 - removing <47> from <46789> leaving <689>
Squares R4C7 and R5C9 in block 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <69>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R5C8 - removing <6> from <146> leaving <14>
Squares R2C7<168>, R2C8<168> and R3C8<18> in block 3 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <168>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R3C7 - removing <18> from <1278> leaving <27>
Squares R6C5 and R6C7 in row 6 and R9C5 and R9C7 in row 9 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in columns 5 and 7 can be removed.
R7C5 - removing <4> from <12478> leaving <1278>
R8C5 - removing <4> from <248> leaving <28>
R8C7 - removing <4> from <4689> leaving <689>
Squares R2C3 and R2C5 in row 2, R4C5 and R4C7 in row 4 and R8C3 and R8C7 in row 8 form a Swordfish pattern on possibility <9>. All other instances of this possibility in columns 3, 5 and 7 can be removed.
R5C5 - removing <9> from <689> leaving <68>
R7C3 - removing <9> from <12689> leaving <1268>
Squares R2C3 (XY), R9C3 (XZ) and R2C5 (YZ) form an XY-Wing pattern on <1>. All squares that are buddies of both the XZ and YZ squares cannot be <1>.
R9C5 - removing <1> from <148> leaving <48>
R9C3 is the only square in row 9 that can be <1>
R6C3 can only be <7>
R6C5 can only be <4>
R1C3 can only be <2>
R5C2 can only be <1>
R6C7 can only be <1>
R9C5 can only be <8>
R5C6 can only be <7>
R5C8 can only be <4>
R9C7 can only be <4>
R5C5 can only be <6>
R8C5 can only be <2>
R7C4 can only be <1>
R1C7 can only be <7>
R3C2 can only be <7>
R3C7 can only be <2>
R5C9 can only be <9>
R4C5 can only be <9>
R7C6 can only be <4>
R5C4 can only be <8>
R7C9 can only be <6>
R4C7 can only be <6>
R3C4 can only be <9>
R7C2 can only be <2>
R7C3 can only be <8>
R8C8 can only be <8>
R8C2 can only be <4>
R7C5 can only be <7>
R8C7 can only be <9>
R3C8 can only be <1>
R3C1 can only be <8>
R2C5 can only be <1>
R2C8 can only be <6>
R2C7 can only be <8>
R7C1 can only be <9>
R2C3 can only be <9>
R8C3 can only be <6>
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