The full reasoning can be found below the Sudoku.
Dec 23 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C5 is the only square in row 5 that can be <7>
R4C5 is the only square in column 5 that can be <4>
R4C2 can only be <1>
Squares R5C9 and R9C9 in column 9 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 column.
R2C9 - removing <12> from <1279> leaving <79>
R8C9 - removing <2> from <278> leaving <78>
Intersection of column 5 with block 8. The value <2> only appears in one or more of squares R7C5, R8C5 and R9C5 of column 5. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain this value.
R8C4 - removing <2> from <2569> leaving <569>
Intersection of block 6 with column 8. The value <8> only appears in one or more of squares R4C8, R5C8 and R6C8 of block 6. These squares are the ones that intersect with column 8. Thus, the other (non-intersecting) squares of column 8 cannot contain this value.
R1C8 - removing <8> from <578> leaving <57>
R3C8 - removing <8> from <1458> leaving <145>
R7C8 - removing <8> from <1248> leaving <124>
R8C8 - removing <8> from <234678> leaving <23467>
Squares R7C7<1248>, R7C8<124>, R8C7<248> and R9C9<12> in block 9 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <1248>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R8C8 - removing <24> from <23467> leaving <367>
R8C9 - removing <8> from <78> leaving <7>
R9C8 - removing <12> from <1236> leaving <36>
R2C9 can only be <9>
R1C9 can only be <8>
R1C5 is the only square in row 1 that can be <9>
R7C5 can only be <2>
R3C3 is the only square in row 3 that can be <8>
R7C7 is the only square in row 7 that can be <8>
R7C2 is the only square in row 7 that can be <9>
R8C1 is the only square in row 8 that can be <8>
R6C5 is the only square in column 5 that can be <3>
R6C2 can only be <6>
R3C5 is the only square in row 3 that can be <6>
R9C5 can only be <5>
R2C4 can only be <5>
R2C6 can only be <3>
R6C4 can only be <1>
R2C3 is the only square in row 2 that can be <6>
R8C2 is the only square in row 8 that can be <5>
R3C2 can only be <4>
R2C2 can only be <7>
R2C1 can only be <1>
R9C1 can only be <3>
R1C2 can only be <3>
R9C2 can only be <2>
R9C8 can only be <6>
R1C1 can only be <5>
R5C1 can only be <4>
R8C3 can only be <4>
R9C9 can only be <1>
R8C8 can only be <3>
R5C9 can only be <2>
R7C8 can only be <4>
R1C8 can only be <7>
R5C3 can only be <3>
R5C4 can only be <6>
R4C8 can only be <8>
R7C3 can only be <1>
R2C8 can only be <2>
R8C7 can only be <2>
R2C7 can only be <4>
R4C6 can only be <9>
R6C8 can only be <5>
R5C6 can only be <5>
R8C4 can only be <9>
R5C7 can only be <1>
R6C6 can only be <8>
R3C7 can only be <5>
R3C8 can only be <1>
R8C6 can only be <6>
R4C4 can only be <2>
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