The full reasoning can be found below the Sudoku.
Apr 08 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C8 is the only square in row 2 that can be <6>
R8C6 is the only square in row 8 that can be <6>
R5C5 is the only square in row 5 that can be <6>
R4C2 is the only square in row 4 that can be <6>
R8C3 is the only square in column 3 that can be <2>
R2C3 is the only square in column 3 that can be <3>
R6C2 is the only square in block 4 that can be <5>
R2C2 is the only square in column 2 that can be <1>
R2C1 is the only square in row 2 that can be <4>
R8C1 can only be <9>
R9C1 can only be <7>
R1C1 can only be <5>
R5C1 can only be <1>
R1C5 can only be <3>
R3C8 is the only square in row 3 that can be <3>
R3C2 is the only square in row 3 that can be <2>
R1C2 can only be <7>
R7C2 is the only square in row 7 that can be <3>
R7C4 is the only square in row 7 that can be <4>
R2C9 is the only square in block 3 that can be <5>
R2C7 is the only square in block 3 that can be <7>
Squares R9C2 and R9C9 in row 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <48>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R9C8 - removing <8> from <589> leaving <59>
Intersection of row 5 with block 5. The value <7> only appears in one or more of squares R5C4, R5C5 and R5C6 of row 5. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain this value.
R4C4 - removing <7> from <25789> leaving <2589>
R4C6 - removing <7> from <5789> leaving <589>
R6C4 - removing <7> from <1789> leaving <189>
R6C6 - removing <7> from <13789> leaving <1389>
Intersection of column 7 with block 6. The value <9> only appears in one or more of squares R4C7, R5C7 and R6C7 of column 7. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain this value.
R4C8 - removing <9> from <2789> leaving <278>
R6C8 - removing <9> from <789> leaving <78>
Squares R8C7<38>, R8C9<348> and R9C9<48> in block 9 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <348>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R8C8 - removing <8> from <158> leaving <15>
Squares R9C2, R9C9, R8C2 and R8C9 form a Type-1 Unique Rectangle on <48>.
R8C9 - removing <48> from <348> leaving <3>
R8C7 can only be <8>
R5C9 can only be <2>
R5C4 can only be <7>
R1C9 can only be <8>
R8C2 can only be <4>
R4C7 can only be <9>
R9C9 can only be <4>
R9C2 can only be <8>
R1C8 can only be <2>
R6C7 can only be <3>
R5C6 can only be <3>
R3C4 can only be <5>
R3C6 can only be <7>
R8C4 can only be <1>
R8C8 can only be <5>
R7C6 can only be <9>
R9C8 can only be <9>
R9C5 can only be <5>
R7C8 can only be <1>
R2C6 can only be <8>
R4C5 can only be <4>
R2C4 can only be <9>
R4C6 can only be <5>
R6C6 can only be <1>
R4C3 can only be <7>
R6C5 can only be <9>
R6C4 can only be <8>
R4C8 can only be <8>
R6C3 can only be <4>
R4C4 can only be <2>
R6C8 can only be <7>
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