The full reasoning can be found below the Sudoku.
Dec 24 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C7 is the only square in row 1 that can be <5>
R1C5 is the only square in row 1 that can be <7>
R5C9 is the only square in row 5 that can be <4>
R3C1 is the only square in row 3 that can be <4>
R1C8 is the only square in row 1 that can be <4>
R4C6 is the only square in row 4 that can be <4>
R6C4 is the only square in row 6 that can be <7>
R2C2 is the only square in column 2 that can be <8>
R8C6 is the only square in column 6 that can be <9>
R4C4 is the only square in column 4 that can be <9>
Squares R2C4 and R2C6 in row 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <23>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R2C1 - removing <23> from <1239> leaving <19>
R2C8 - removing <3> from <1369> leaving <169>
R2C9 - removing <3> from <1369> leaving <169>
Squares R4C8 and R8C8 in column 8 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 column.
R2C8 - removing <1> from <169> leaving <69>
R6C8 - removing <13> from <138> leaving <8>
R9C8 - removing <13> from <13689> leaving <689>
R5C7 can only be <3>
R5C3 can only be <9>
R7C7 can only be <2>
R4C8 can only be <1>
R8C8 can only be <3>
R5C1 can only be <5>
R8C4 can only be <2>
R5C5 can only be <8>
R4C2 can only be <3>
R2C4 can only be <3>
R9C5 can only be <3>
R4C5 can only be <5>
R6C5 can only be <2>
R2C6 can only be <2>
R6C6 can only be <3>
R6C2 can only be <1>
R8C2 can only be <5>
Squares R9C2 and R9C8 in row 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <69>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R9C1 - removing <9> from <1279> leaving <127>
R9C3 - removing <6> from <126> leaving <12>
R9C9 - removing <69> from <16789> leaving <178>
Intersection of row 2 with block 3. The value <6> only appears in one or more of squares R2C7, R2C8 and R2C9 of row 2. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R1C9 - removing <6> from <369> leaving <39>
Squares R2C1 and R2C9 in row 2 and R8C1 and R8C9 in row 8 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in columns 1 and 9 can be removed.
R3C9 - removing <1> from <138> leaving <38>
R9C1 - removing <1> from <127> leaving <27>
R9C9 - removing <1> from <178> leaving <78>
Squares R1C2 and R2C8 form a remote naked pair. <69> can be removed from any square that is common to their groups.
R2C1 - removing <9> from <19> leaving <1>
R1C9 - removing <9> from <39> leaving <3>
R3C9 can only be <8>
R8C1 can only be <7>
R3C3 can only be <3>
R7C3 can only be <6>
R3C7 can only be <1>
R9C9 can only be <7>
R7C9 can only be <9>
R1C3 can only be <2>
R9C2 can only be <9>
R7C1 can only be <3>
R2C9 can only be <6>
R9C8 can only be <6>
R8C9 can only be <1>
R9C1 can only be <2>
R9C7 can only be <8>
R9C3 can only be <1>
R1C1 can only be <9>
R1C2 can only be <6>
R2C8 can only be <9>
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