The full reasoning can be found below the Sudoku.
Dec 01 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C5 is the only square in row 2 that can be <8>
R1C7 is the only square in row 1 that can be <8>
R5C3 is the only square in row 5 that can be <5>
R5C7 is the only square in row 5 that can be <6>
R6C3 is the only square in row 6 that can be <8>
R9C7 is the only square in row 9 that can be <5>
R9C9 is the only square in row 9 that can be <9>
R7C4 is the only square in row 7 that can be <9>
R9C3 is the only square in row 9 that can be <3>
R1C3 is the only square in column 3 that can be <6>
R7C5 is the only square in column 5 that can be <6>
R9C5 is the only square in column 5 that can be <7>
R9C1 can only be <1>
R5C9 is the only square in column 9 that can be <4>
Intersection of column 2 with block 4. The values <17> only appears in one or more of squares R4C2, R5C2 and R6C2 of column 2. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain these values.
R4C3 - removing <7> from <247> leaving <24>
Intersection of column 5 with block 2. The value <2> only appears in one or more of squares R1C5, R2C5 and R3C5 of column 5. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
R2C6 - removing <2> from <236> leaving <36>
R3C6 - removing <2> from <12345> leaving <1345>
Squares R2C4 and R2C6 in row 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <36>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R2C8 - removing <3> from <239> leaving <29>
Squares R2C4 and R2C6 in block 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <36>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R3C4 - removing <3> from <1345> leaving <145>
R3C6 - removing <3> from <1345> leaving <145>
Squares R4C3<24>, R4C4<14> and R4C6<124> in row 4 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <124>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R4C2 - removing <124> from <12479> leaving <79>
R4C7 - removing <12> from <1239> leaving <39>
R4C8 - removing <12> from <12379> leaving <379>
Intersection of row 4 with block 5. The value <1> only appears in one or more of squares R4C4, R4C5 and R4C6 of row 4. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain this value.
R6C4 - removing <1> from <146> leaving <46>
R6C6 - removing <1> from <1246> leaving <246>
Squares R2C2 and R2C8 in row 2 and R8C2 and R8C8 in row 8 form a Simple X-Wing pattern on possibility <2>. All other instances of this possibility in columns 2 and 8 can be removed.
R5C2 - removing <2> from <129> leaving <19>
R5C8 - removing <2> from <129> leaving <19>
R6C2 - removing <2> from <1247> leaving <147>
R6C8 - removing <2> from <127> leaving <17>
R5C1 is the only square in row 5 that can be <2>
R1C1 can only be <4>
R4C3 can only be <4>
R7C1 can only be <7>
R4C4 can only be <1>
R4C6 can only be <2>
R7C3 can only be <2>
R3C1 can only be <9>
R3C3 can only be <7>
R8C2 can only be <4>
R8C5 can only be <1>
R1C5 can only be <2>
R1C9 can only be <1>
R3C5 can only be <4>
R7C9 can only be <3>
R2C2 can only be <2>
R3C4 can only be <5>
R7C6 can only be <4>
R7C7 can only be <1>
R3C9 can only be <2>
R8C8 can only be <2>
R2C8 can only be <9>
R5C8 can only be <1>
R3C6 can only be <1>
R8C4 can only be <3>
R3C7 can only be <3>
R5C2 can only be <9>
R6C8 can only be <7>
R6C7 can only be <2>
R6C2 can only be <1>
R4C8 can only be <3>
R6C6 can only be <6>
R8C6 can only be <5>
R2C4 can only be <6>
R2C6 can only be <3>
R6C4 can only be <4>
R4C7 can only be <9>
R4C2 can only be <7>
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