The full reasoning can be found below the Sudoku.
Mar 28 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C3 can only be <8>
R4C7 can only be <9>
R6C3 can only be <1>
R4C4 can only be <3>
R5C2 can only be <6>
R4C6 can only be <5>
R1C8 is the only square in row 1 that can be <8>
R5C5 is the only square in row 5 that can be <1>
R5C4 is the only square in row 5 that can be <9>
R7C4 can only be <7>
R7C6 can only be <3>
R6C4 can only be <4>
R3C4 can only be <6>
R9C2 is the only square in row 9 that can be <8>
R3C6 is the only square in column 6 that can be <4>
Squares R8C1 and R8C9 in row 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <26>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R8C8 - removing <2> from <239> leaving <39>
Squares R7C7 and R8C9 in block 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <26>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C8 - removing <2> from <249> leaving <49>
Squares R7C2 and R7C8 in row 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <49>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R7C5 - removing <9> from <59> leaving <5>
R9C5 can only be <9>
Squares R1C1 and R8C1 in column 1 and R1C9 and R8C9 in column 9 form a Simple X-Wing pattern on possibility <2>. All other instances of this possibility in rows 1 and 8 can be removed.
R1C3 - removing <2> from <236> leaving <36>
R1C7 - removing <2> from <12367> leaving <1367>
Squares R2C2 and R2C8 in row 2 and R8C2 and R8C8 in row 8 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in columns 2 and 8 can be removed.
R1C2 - removing <3> from <1347> leaving <147>
R3C2 - removing <3> from <137> leaving <17>
R3C8 - removing <3> from <2357> leaving <257>
R9C8 - removing <3> from <347> leaving <47>
Squares R2C1 and R2C9 in row 2 and R8C1 and R8C9 in row 8 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in columns 1 and 9 can be removed.
R1C1 - removing <6> from <246> leaving <24>
R1C9 - removing <6> from <1267> leaving <127>
Squares R1C3 (XY), R9C3 (XZ) and R2C1 (YZ) form an XY-Wing pattern on <5>. All squares that are buddies of both the XZ and YZ squares cannot be <5>.
R9C1 - removing <5> from <45> leaving <4>
R3C3 - removing <5> from <235> leaving <23>
R9C8 can only be <7>
R1C1 can only be <2>
R7C2 can only be <9>
R9C9 can only be <1>
R5C8 can only be <2>
R9C7 can only be <3>
R1C9 can only be <7>
R8C1 can only be <6>
R3C3 can only be <3>
R1C5 can only be <3>
R2C9 can only be <6>
R2C1 can only be <5>
R8C9 can only be <2>
R3C5 can only be <7>
R1C3 can only be <6>
R9C3 can only be <5>
R2C2 can only be <7>
R3C2 can only be <1>
R5C6 can only be <7>
R3C8 can only be <5>
R6C7 can only be <7>
R6C6 can only be <2>
R7C8 can only be <4>
R8C2 can only be <3>
R7C3 can only be <2>
R8C8 can only be <9>
R7C7 can only be <6>
R1C7 can only be <1>
R1C2 can only be <4>
R3C7 can only be <2>
R2C8 can only be <3>
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