The full reasoning can be found below the Sudoku.
Apr 01 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C7 can only be <7>
R9C7 can only be <6>
R1C3 can only be <5>
R5C7 can only be <3>
R1C6 is the only square in row 1 that can be <3>
R2C1 is the only square in row 2 that can be <9>
R6C1 is the only square in row 6 that can be <3>
Squares R5C3 and R6C2 in block 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <79>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R4C2 - removing <9> from <29> leaving <2>
R5C1 - removing <7> from <25678> leaving <2568>
R5C2 - removing <79> from <2789> leaving <28>
R4C5 can only be <5>
R5C2 can only be <8>
R4C1 can only be <6>
R6C5 can only be <4>
R5C5 can only be <2>
R5C1 can only be <5>
R5C9 is the only square in row 5 that can be <6>
R5C8 is the only square in row 5 that can be <4>
R5C3 is the only square in row 5 that can be <7>
R9C3 can only be <9>
R6C2 can only be <9>
R6C8 can only be <5>
R6C9 can only be <7>
Intersection of row 2 with block 2. The value <7> only appears in one or more of squares R2C4, R2C5 and R2C6 of row 2. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
R3C4 - removing <7> from <124567> leaving <12456>
R3C5 - removing <7> from <678> leaving <68>
Squares R3C1<178>, R3C2<17> and R3C8<18> in row 3 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <178>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R3C4 - removing <1> from <12456> leaving <2456>
R3C5 - removing <8> from <68> leaving <6>
R3C6 - removing <18> from <12458> leaving <245>
R3C9 - removing <18> from <1248> leaving <24>
R8C5 can only be <3>
R8C9 can only be <9>
R4C9 can only be <1>
R7C8 can only be <8>
R4C8 can only be <9>
R7C5 can only be <7>
R3C8 can only be <1>
R9C9 can only be <5>
R7C9 can only be <3>
R3C2 can only be <7>
R7C2 can only be <1>
R2C5 can only be <8>
R9C4 can only be <4>
R9C1 can only be <7>
R9C6 can only be <8>
R8C6 can only be <2>
R2C9 can only be <4>
R2C6 can only be <1>
R3C9 can only be <2>
R3C1 can only be <8>
R3C4 can only be <5>
R1C9 can only be <8>
R7C1 can only be <2>
R8C1 can only be <4>
R8C4 can only be <6>
R1C1 can only be <1>
R2C4 can only be <7>
R5C6 can only be <9>
R1C4 can only be <2>
R3C6 can only be <4>
R7C4 can only be <9>
R5C4 can only be <1>
R7C6 can only be <5>
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