The full reasoning can be found below the Sudoku.
Mar 07 - Very Hard
Puzzle Copyright © Kevin Stone
Reasoning
R4C1 can only be <4>
R4C9 can only be <2>
R5C5 can only be <4>
R9C6 can only be <4>
R9C4 can only be <1>
R1C6 can only be <7>
R1C4 can only be <4>
R7C5 can only be <9>
R8C5 can only be <8>
R2C2 is the only square in row 2 that can be <2>
R2C7 is the only square in row 2 that can be <7>
R5C2 is the only square in row 5 that can be <3>
R5C8 is the only square in row 5 that can be <5>
R7C8 is the only square in row 7 that can be <2>
R7C3 is the only square in row 7 that can be <1>
R8C2 is the only square in row 8 that can be <7>
R9C8 is the only square in row 9 that can be <8>
R1C2 is the only square in row 1 that can be <8>
R3C7 is the only square in row 3 that can be <8>
R2C9 is the only square in block 3 that can be <4>
Squares R3C2 and R3C3 in row 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <49>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R3C8 - removing <9> from <139> leaving <13>
Squares R3C2 and R3C3 in block 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <49>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R1C1 - removing <9> from <169> leaving <16>
Intersection of column 2 with block 7. The value <6> only appears in one or more of squares R7C2, R8C2 and R9C2 of column 2. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R9C1 - removing <6> from <369> leaving <39>
Intersection of column 8 with block 3. The value <6> only appears in one or more of squares R1C8, R2C8 and R3C8 of column 8. 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 <169> leaving <19>
Intersection of column 9 with block 9. The value <3> only appears in one or more of squares R7C9, R8C9 and R9C9 of column 9. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R8C8 - removing <3> from <139> leaving <19>
Squares R3C5, R3C8, R2C5 and R2C8 form a Type-1 Unique Rectangle on <13>.
R2C8 - removing <13> from <136> leaving <6>
R2C3 can only be <5>
R2C1 can only be <1>
R2C5 can only be <3>
R1C1 can only be <6>
R3C5 can only be <1>
R3C8 can only be <3>
R6C1 can only be <9>
R6C9 can only be <6>
R9C1 can only be <3>
R5C3 can only be <6>
R5C7 can only be <9>
R9C9 can only be <9>
R8C1 can only be <5>
R9C2 can only be <6>
R1C9 can only be <1>
R8C7 can only be <4>
R8C8 can only be <1>
R1C8 can only be <9>
R8C9 can only be <3>
R8C3 can only be <9>
R7C7 can only be <6>
R7C2 can only be <4>
R3C2 can only be <9>
R3C3 can only be <4>
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