The full reasoning can be found below the Sudoku.
Jun 10 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C4 can only be <2>
R4C6 can only be <4>
R5C3 can only be <6>
R6C4 can only be <7>
R6C6 can only be <6>
R7C5 can only be <5>
R4C5 can only be <9>
R5C1 can only be <7>
R5C6 can only be <5>
R6C5 can only be <3>
R5C4 can only be <8>
R9C5 can only be <7>
R5C5 can only be <1>
R1C1 is the only square in row 1 that can be <6>
R2C2 is the only square in row 2 that can be <7>
R3C7 is the only square in row 3 that can be <7>
R8C9 is the only square in row 8 that can be <6>
R8C2 is the only square in row 8 that can be <3>
R1C3 is the only square in row 1 that can be <3>
R1C9 is the only square in row 1 that can be <5>
R9C9 is the only square in row 9 that can be <3>
Squares R2C1 and R8C1 in column 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <29>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R3C1 - removing <2> from <125> leaving <15>
R7C1 - removing <2> from <128> leaving <18>
R9C1 - removing <9> from <1589> leaving <158>
Squares R2C9 and R5C9 in column 9 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 column.
R7C9 - removing <4> from <148> leaving <18>
Squares R7C1 and R7C9 in row 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <18>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R7C7 - removing <8> from <248> leaving <24>
Squares R3C1 and R3C9 in row 3 and R7C1 and R7C9 in row 7 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in columns 1 and 9 can be removed.
R9C1 - removing <1> from <158> leaving <58>
Squares R2C1 and R2C8 in row 2 and R8C1 and R8C8 in row 8 form a Simple X-Wing pattern on possibility <2>. All other instances of this possibility in columns 1 and 8 can be removed.
R1C8 - removing <2> from <129> leaving <19>
Squares R1C2 and R1C8 in row 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <19>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R1C7 - removing <9> from <289> leaving <28>
Squares R7C7 (XY), R8C8 (XZ) and R5C7 (YZ) form an XY-Wing pattern on <9>. All squares that are buddies of both the XZ and YZ squares cannot be <9>.
R9C7 - removing <9> from <489> leaving <48>
R5C7 is the only square in column 7 that can be <9>
R5C9 can only be <4>
R2C9 can only be <9>
R2C1 can only be <2>
R1C8 can only be <1>
R1C2 can only be <9>
R3C9 can only be <8>
R2C8 can only be <4>
R8C1 can only be <9>
R3C3 can only be <5>
R9C8 can only be <9>
R3C1 can only be <1>
R9C3 can only be <4>
R3C5 can only be <2>
R7C9 can only be <1>
R1C7 can only be <2>
R7C1 can only be <8>
R8C8 can only be <2>
R9C2 can only be <1>
R7C7 can only be <4>
R9C7 can only be <8>
R7C3 can only be <2>
R9C1 can only be <5>
R1C5 can only be <8>
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