The full reasoning can be found below the Sudoku.
Dec 28 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R7C9 is the only square in row 7 that can be <4>
R7C1 is the only square in row 7 that can be <8>
R8C4 is the only square in row 8 that can be <4>
R8C5 is the only square in row 8 that can be <9>
R8C2 is the only square in row 8 that can be <6>
R5C1 is the only square in column 1 that can be <7>
R1C4 is the only square in column 4 that can be <7>
R4C4 is the only square in column 4 that can be <9>
R4C6 is the only square in row 4 that can be <6>
R6C4 can only be <1>
R3C4 can only be <6>
R1C7 is the only square in row 1 that can be <6>
R5C2 is the only square in row 5 that can be <1>
R6C9 is the only square in row 6 that can be <6>
R9C5 is the only square in row 9 that can be <6>
R9C7 is the only square in block 9 that can be <2>
Squares R8C7 and R8C8 in row 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <58>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R8C3 - removing <5> from <135> leaving <13>
Squares R8C1 and R8C3 in block 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <13>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C3 - removing <1> from <1257> leaving <257>
Intersection of column 9 with block 3. The value <2> only appears in one or more of squares R1C9, R2C9 and R3C9 of column 9. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R2C8 - removing <2> from <23789> leaving <3789>
R3C8 - removing <2> from <2358> leaving <358>
Squares R8C7, R8C8, R3C7 and R3C8 form a Type-2 Unique Rectangle on <58>.
R3C1 - removing <3> from <123> leaving <12>
R2C7 - removing <3> from <378> leaving <78>
R2C8 - removing <3> from <3789> leaving <789>
R3C5 - removing <3> from <1238> leaving <128>
Squares R9C3, R9C6, R7C3 and R7C6 form a Type-4 Unique Rectangle on <57>.
R7C3 - removing <5> from <257> leaving <27>
R7C6 - removing <5> from <157> leaving <17>
Squares R1C3 (XY), R3C1 (XZ) and R8C3 (YZ) form an XY-Wing pattern on <1>. All squares that are buddies of both the XZ and YZ squares cannot be <1>.
R8C1 - removing <1> from <13> leaving <3>
R2C3 - removing <1> from <1234> leaving <234>
R8C3 can only be <1>
R4C1 can only be <2>
R3C1 can only be <1>
R6C8 is the only square in row 6 that can be <2>
R6C7 is the only square in row 6 that can be <7>
R2C7 can only be <8>
R8C7 can only be <5>
R8C8 can only be <8>
R3C7 can only be <3>
R3C8 can only be <5>
R3C9 can only be <2>
R4C8 can only be <3>
R3C5 can only be <8>
R2C9 can only be <9>
R5C8 can only be <9>
R5C9 can only be <5>
R2C8 can only be <7>
R5C5 can only be <3>
R1C5 can only be <2>
R6C6 can only be <5>
R6C2 can only be <3>
R9C6 can only be <7>
R9C3 can only be <5>
R7C6 can only be <1>
R1C3 can only be <3>
R2C5 can only be <1>
R2C6 can only be <3>
R7C5 can only be <5>
R7C2 can only be <2>
R4C3 can only be <4>
R4C2 can only be <5>
R2C3 can only be <2>
R7C3 can only be <7>
R2C2 can only be <4>
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