The full reasoning can be found below the Sudoku.
Dec 23 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C5 can only be <6>
R5C4 can only be <1>
R6C5 can only be <4>
R8C4 can only be <5>
R8C6 can only be <4>
R1C5 can only be <5>
R3C5 can only be <7>
R6C8 can only be <5>
R9C5 can only be <3>
R5C6 can only be <7>
R6C2 can only be <9>
R2C4 can only be <6>
R7C5 can only be <2>
R5C5 can only be <8>
R2C6 can only be <1>
R1C8 is the only square in row 1 that can be <6>
R3C1 is the only square in row 3 that can be <6>
R3C9 is the only square in row 3 that can be <9>
R8C9 is the only square in row 8 that can be <6>
R2C8 is the only square in column 8 that can be <8>
Squares R2C3 and R5C3 in column 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <25>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C3 - removing <2> from <128> leaving <18>
Squares R3C2 and R3C8 in row 3 and R7C2 and R7C8 in row 7 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in columns 2 and 8 can be removed.
R1C2 - removing <1> from <128> leaving <28>
R9C2 - removing <1> from <147> leaving <47>
R9C8 - removing <1> from <147> leaving <47>
Squares R9C2 and R9C8 in row 9 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 row.
R9C7 - removing <4> from <149> leaving <19>
Squares R2C3 and R5C3 in column 3 and R2C9 and R5C9 in column 9 form a Simple X-Wing pattern on possibility <2>. All other instances of this possibility in rows 2 and 5 can be removed.
R2C2 - removing <2> from <2457> leaving <457>
R2C7 - removing <2> from <234> leaving <34>
R5C7 - removing <2> from <234> leaving <34>
Squares R2C7 and R5C7 in column 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <34>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R8C7 - removing <3> from <239> leaving <29>
Squares R3C2 and R3C8 in row 3 and R9C2 and R9C8 in row 9 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in columns 2 and 8 can be removed.
R2C2 - removing <4> from <457> leaving <57>
R7C2 - removing <4> from <1345> leaving <135>
R7C8 - removing <4> from <134> leaving <13>
Squares R7C8 (XY), R3C8 (XZ) and R7C9 (YZ) form an XY-Wing pattern on <4>. All squares that are buddies of both the XZ and YZ squares cannot be <4>.
R2C9 - removing <4> from <234> leaving <23>
R9C8 - removing <4> from <47> leaving <7>
R9C2 can only be <4>
R3C2 can only be <1>
R3C8 can only be <4>
R1C3 can only be <8>
R2C7 can only be <3>
R1C2 can only be <2>
R8C3 can only be <9>
R2C9 can only be <2>
R5C7 can only be <4>
R2C3 can only be <5>
R1C7 can only be <1>
R5C9 can only be <3>
R5C1 can only be <5>
R7C9 can only be <4>
R4C8 can only be <2>
R8C7 can only be <2>
R9C3 can only be <1>
R8C8 can only be <3>
R8C1 can only be <7>
R7C8 can only be <1>
R9C7 can only be <9>
R4C2 can only be <3>
R2C2 can only be <7>
R5C3 can only be <2>
R7C2 can only be <5>
R7C1 can only be <3>
R8C2 can only be <8>
R2C1 can only be <4>
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