The full reasoning can be found below the Sudoku.
Dec 29 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R3C2 can only be <3>
R3C4 can only be <7>
R7C2 can only be <1>
R2C2 can only be <8>
R8C2 can only be <5>
R2C9 is the only square in row 2 that can be <6>
R3C6 is the only square in row 3 that can be <6>
R4C3 is the only square in row 4 that can be <6>
R5C7 is the only square in row 5 that can be <7>
R1C3 is the only square in row 1 that can be <7>
R2C8 is the only square in row 2 that can be <7>
R6C1 is the only square in row 6 that can be <8>
R7C1 is the only square in row 7 that can be <7>
R8C5 is the only square in row 8 that can be <7>
R8C7 is the only square in row 8 that can be <8>
R9C7 is the only square in row 9 that can be <5>
R6C9 is the only square in row 6 that can be <5>
R5C1 is the only square in row 5 that can be <5>
R8C8 is the only square in column 8 that can be <1>
Intersection of row 1 with block 2. The value <1> only appears in one or more of squares R1C4, R1C5 and R1C6 of row 1. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
R2C5 - removing <1> from <1239> leaving <239>
Intersection of column 4 with block 8. The value <4> only appears in one or more of squares R7C4, R8C4 and R9C4 of column 4. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain this value.
R9C5 - removing <4> from <149> leaving <19>
Intersection of column 7 with block 3. The value <9> only appears in one or more of squares R1C7, R2C7 and R3C7 of column 7. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R3C9 - removing <9> from <249> leaving <24>
R3C1 is the only square in row 3 that can be <9>
R8C1 can only be <3>
Squares R2C1 and R2C3 in row 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <12>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R2C5 - removing <2> from <239> leaving <39>
R2C7 - removing <2> from <239> leaving <39>
R1C5 is the only square in column 5 that can be <2>
R4C7 is the only square in column 7 that can be <2>
R4C1 can only be <1>
R2C1 can only be <2>
R6C3 can only be <3>
R6C7 can only be <4>
R5C3 can only be <2>
R6C5 can only be <1>
R4C9 can only be <3>
R2C3 can only be <1>
R4C5 can only be <4>
R5C9 can only be <1>
R9C5 can only be <9>
R9C3 can only be <4>
R2C5 can only be <3>
R7C6 can only be <3>
R2C7 can only be <9>
R1C4 can only be <1>
R1C7 can only be <3>
R7C4 can only be <4>
R5C6 can only be <8>
R8C3 can only be <9>
R1C6 can only be <9>
R9C4 can only be <8>
R5C4 can only be <3>
R9C6 can only be <1>
R7C8 can only be <2>
R7C9 can only be <9>
R3C8 can only be <4>
R8C9 can only be <4>
R3C9 can only be <2>
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