The full reasoning can be found below the Sudoku.
Apr 06 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R8C7 can only be <5>
R8C8 can only be <9>
R9C7 can only be <7>
R8C2 can only be <3>
R7C7 can only be <2>
R7C9 can only be <1>
R6C9 can only be <2>
R8C6 can only be <4>
R7C2 can only be <9>
R8C5 can only be <6>
R1C9 can only be <9>
R4C9 can only be <4>
R9C2 can only be <1>
R9C3 can only be <5>
R9C1 can only be <4>
R1C5 is the only square in row 1 that can be <4>
R1C4 is the only square in row 1 that can be <7>
R3C1 is the only square in row 3 that can be <7>
R4C8 is the only square in row 4 that can be <1>
R6C3 is the only square in row 6 that can be <1>
R7C5 is the only square in row 7 that can be <7>
R2C2 is the only square in column 2 that can be <8>
R2C5 is the only square in column 5 that can be <3>
Intersection of row 1 with block 3. The value <8> only appears in one or more of squares R1C7, R1C8 and R1C9 of row 1. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R3C8 - removing <8> from <2568> leaving <256>
Intersection of block 2 with row 3. The values <28> only appears in one or more of squares R3C4, R3C5 and R3C6 of block 2. These squares are the ones that intersect with row 3. Thus, the other (non-intersecting) squares of row 3 cannot contain these values.
R3C3 - removing <2> from <269> leaving <69>
R3C8 - removing <2> from <256> leaving <56>
Squares R6C1<59>, R6C5<589> and R6C6<589> in row 6 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <589>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R6C8 - removing <8> from <678> leaving <67>
R1C8 is the only square in column 8 that can be <8>
R1C7 can only be <6>
R1C3 can only be <2>
R4C7 can only be <8>
R3C8 can only be <5>
R2C8 can only be <2>
R2C3 can only be <9>
R2C4 can only be <5>
R3C3 can only be <6>
R7C4 can only be <3>
R7C6 can only be <5>
R5C4 can only be <6>
R5C8 can only be <7>
R4C4 can only be <9>
R5C2 can only be <2>
R6C8 can only be <6>
R6C2 can only be <7>
R4C1 can only be <5>
R3C4 can only be <8>
R6C6 can only be <8>
R5C6 can only be <3>
R4C2 can only be <6>
R6C5 can only be <5>
R9C6 can only be <9>
R9C5 can only be <8>
R3C6 can only be <2>
R3C5 can only be <9>
R4C5 can only be <2>
R6C1 can only be <9>
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