The full reasoning can be found below the Sudoku.
Dec 26 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C4 can only be <6>
R2C5 is the only square in row 2 that can be <2>
R3C9 is the only square in row 3 that can be <3>
R3C1 is the only square in row 3 that can be <9>
R6C3 is the only square in row 6 that can be <3>
R4C7 is the only square in row 4 that can be <3>
R4C2 is the only square in row 4 that can be <9>
R5C5 is the only square in row 5 that can be <3>
R9C1 is the only square in row 9 that can be <3>
R9C2 is the only square in row 9 that can be <6>
R6C9 is the only square in row 6 that can be <6>
R6C8 is the only square in row 6 that can be <2>
R5C4 is the only square in row 5 that can be <2>
R7C6 is the only square in row 7 that can be <6>
R8C5 is the only square in column 5 that can be <9>
R2C6 is the only square in column 6 that can be <7>
R3C6 is the only square in column 6 that can be <4>
R8C4 is the only square in column 4 that can be <4>
R2C7 is the only square in column 7 that can be <6>
R5C8 is the only square in column 8 that can be <7>
Intersection of row 2 with block 1. The value <8> only appears in one or more of squares R2C1, R2C2 and R2C3 of row 2. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R1C1 - removing <8> from <14568> leaving <1456>
R1C2 - removing <8> from <1478> leaving <147>
R1C3 - removing <8> from <15678> leaving <1567>
R3C3 - removing <8> from <158> leaving <15>
Intersection of row 9 with block 9. The values <14> only appears in one or more of squares R9C7, R9C8 and R9C9 of row 9. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain these values.
R8C7 - removing <1> from <18> leaving <8>
R8C9 - removing <1> from <127> leaving <27>
R7C7 can only be <9>
R5C9 is the only square in row 5 that can be <9>
R9C5 is the only square in row 9 that can be <8>
R1C5 can only be <5>
R7C4 can only be <5>
R3C4 can only be <8>
R1C8 is the only square in row 1 that can be <8>
Intersection of block 3 with column 9. The value <4> only appears in one or more of squares R1C9, R2C9 and R3C9 of block 3. These squares are the ones that intersect with column 9. Thus, the other (non-intersecting) squares of column 9 cannot contain this value.
R9C9 - removing <4> from <145> leaving <15>
Squares R4C1<14>, R5C2<148> and R6C2<18> in block 4 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <148>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R5C1 - removing <148> from <14568> leaving <56>
R5C3 - removing <18> from <1568> leaving <56>
R2C3 is the only square in column 3 that can be <8>
R7C1 is the only square in column 1 that can be <8>
R7C2 can only be <7>
R7C9 can only be <2>
R8C3 can only be <1>
R8C9 can only be <7>
R8C1 can only be <2>
R3C3 can only be <5>
R3C8 can only be <1>
R5C3 can only be <6>
R2C1 can only be <4>
R4C8 can only be <4>
R1C9 can only be <4>
R4C1 can only be <1>
R9C8 can only be <5>
R5C7 can only be <1>
R5C1 can only be <5>
R1C3 can only be <7>
R5C6 can only be <8>
R9C7 can only be <4>
R9C9 can only be <1>
R1C2 can only be <1>
R2C9 can only be <5>
R1C1 can only be <6>
R6C2 can only be <8>
R5C2 can only be <4>
R6C6 can only be <1>
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