The full reasoning can be found below the Sudoku.
May 04 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C1 is the only square in row 1 that can be <8>
R2C1 is the only square in row 2 that can be <2>
R8C2 is the only square in row 8 that can be <8>
Intersection of row 1 with block 3. The value <3> 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.
R2C8 - removing <3> from <1356> leaving <156>
R2C9 - removing <3> from <1346> leaving <146>
Intersection of row 8 with block 9. The values <36> only appears in one or more of squares R8C7, R8C8 and R8C9 of row 8. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain these values.
R7C7 - removing <3> from <357> leaving <57>
R7C8 - removing <3> from <1357> leaving <157>
Squares R7C7 and R9C7 in column 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <57>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C7 - removing <5> from <356> leaving <36>
R3C7 - removing <57> from <4567> leaving <46>
R5C7 - removing <7> from <3467> leaving <346>
R1C3 is the only square in row 1 that can be <5>
R3C8 is the only square in row 3 that can be <7>
R2C8 is the only square in block 3 that can be <5>
R7C8 can only be <1>
R2C9 is the only square in column 9 that can be <1>
R3C7 is the only square in block 3 that can be <4>
R3C5 can only be <9>
R8C5 can only be <7>
R2C2 is the only square in row 2 that can be <9>
R2C4 is the only square in row 2 that can be <6>
Squares R7C7 and R9C7 in block 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <57>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R9C9 - removing <7> from <79> leaving <9>
R9C3 can only be <1>
R3C3 can only be <6>
R8C1 can only be <5>
R3C2 can only be <1>
R5C3 can only be <3>
R5C7 can only be <6>
R7C3 can only be <9>
R1C7 can only be <3>
R9C1 can only be <7>
R9C7 can only be <5>
R6C1 can only be <4>
R7C2 can only be <3>
R7C7 can only be <7>
R1C9 can only be <6>
R8C9 can only be <3>
R5C2 can only be <7>
R4C2 can only be <6>
R6C2 can only be <5>
R4C1 can only be <1>
R8C8 can only be <6>
R6C9 can only be <7>
R4C9 can only be <4>
R4C4 can only be <2>
R4C8 can only be <3>
R5C5 can only be <4>
R4C6 can only be <7>
R6C8 can only be <8>
R2C5 can only be <3>
R7C5 can only be <2>
R6C4 can only be <9>
R5C8 can only be <2>
R2C6 can only be <4>
R7C6 can only be <5>
R6C6 can only be <3>
R8C4 can only be <1>
R7C4 can only be <4>
R3C6 can only be <8>
R8C6 can only be <9>
R5C4 can only be <8>
R3C4 can only be <5>
R5C6 can only be <1>
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