The full reasoning can be found below the Sudoku.
Apr 09 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R3C3 can only be <7>
R4C4 can only be <3>
R3C5 can only be <5>
R1C7 is the only square in row 1 that can be <5>
R1C5 is the only square in row 1 that can be <9>
R1C9 is the only square in row 1 that can be <7>
R3C1 is the only square in row 3 that can be <1>
R4C6 is the only square in row 4 that can be <5>
R6C8 is the only square in row 6 that can be <6>
R1C1 is the only square in row 1 that can be <6>
R7C1 is the only square in row 7 that can be <7>
R8C1 is the only square in row 8 that can be <5>
R5C3 is the only square in row 5 that can be <5>
R4C5 is the only square in column 5 that can be <1>
R6C5 is the only square in column 5 that can be <2>
R2C5 is the only square in column 5 that can be <7>
Squares R2C4 and R2C6 in row 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <46>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R2C9 - removing <6> from <236> leaving <23>
Intersection of row 6 with block 5. The value <9> only appears in one or more of squares R6C4, R6C5 and R6C6 of row 6. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain this value.
R5C4 - removing <9> from <479> leaving <47>
R5C6 - removing <9> from <489> leaving <48>
Intersection of row 9 with block 9. The values <126> only appears in one or more of squares R9C7, R9C8 and R9C9 of row 9. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain these values.
R8C9 - removing <6> from <3689> leaving <389>
Intersection of column 5 with block 8. The values <348> only appears in one or more of squares R7C5, R8C5 and R9C5 of column 5. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain these values.
R8C6 - removing <8> from <689> leaving <69>
Squares R8C4 and R8C6 in row 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <69>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R8C9 - removing <9> from <389> leaving <38>
Intersection of block 7 with row 9. The value <8> only appears in one or more of squares R9C1, R9C2 and R9C3 of block 7. These squares are the ones that intersect with row 9. Thus, the other (non-intersecting) squares of row 9 cannot contain this value.
R9C5 - removing <8> from <348> leaving <34>
R9C7 - removing <8> from <2689> leaving <269>
R9C8 - removing <8> from <1238> leaving <123>
R9C9 - removing <8> from <123689> leaving <12369>
Intersection of column 8 with block 6. The value <8> only appears in one or more of squares R4C8, R5C8 and R6C8 of column 8. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain this value.
R5C7 - removing <8> from <289> leaving <29>
R5C9 - removing <8> from <1289> leaving <129>
Squares R7C7<89>, R7C9<389> and R8C9<38> in block 9 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <389>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R9C7 - removing <9> from <269> leaving <26>
R9C8 - removing <3> from <123> leaving <12>
R9C9 - removing <39> from <12369> leaving <126>
R9C3 is the only square in row 9 that can be <9>
R1C8 is the only square in column 8 that can be <3>
R1C3 can only be <4>
R2C9 can only be <2>
R2C1 can only be <3>
R1C2 can only be <2>
R7C3 can only be <3>
R9C1 can only be <8>
R9C2 can only be <4>
R5C1 can only be <2>
R9C5 can only be <3>
R8C5 can only be <8>
R4C2 can only be <8>
R4C8 can only be <2>
R6C2 can only be <7>
R9C8 can only be <1>
R5C7 can only be <9>
R5C9 can only be <1>
R7C7 can only be <8>
R5C8 can only be <8>
R9C9 can only be <6>
R6C4 can only be <9>
R5C2 can only be <3>
R6C6 can only be <8>
R8C4 can only be <6>
R5C6 can only be <4>
R7C5 can only be <4>
R7C9 can only be <9>
R3C7 can only be <6>
R8C9 can only be <3>
R8C6 can only be <9>
R2C4 can only be <4>
R9C7 can only be <2>
R3C9 can only be <8>
R2C6 can only be <6>
R5C4 can only be <7>
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