The full reasoning can be found below the Sudoku.
Apr 21 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C7 is the only square in row 2 that can be <5>
R1C2 is the only square in row 1 that can be <5>
R7C2 is the only square in row 7 that can be <7>
R3C7 is the only square in row 3 that can be <7>
R5C7 can only be <4>
R2C1 is the only square in row 2 that can be <7>
R7C8 is the only square in row 7 that can be <8>
R1C9 is the only square in row 1 that can be <8>
R8C4 is the only square in row 8 that can be <5>
R9C9 is the only square in row 9 that can be <9>
R5C3 is the only square in column 3 that can be <8>
R9C8 is the only square in column 8 that can be <2>
R8C9 is the only square in column 9 that can be <4>
R6C9 is the only square in column 9 that can be <7>
R6C1 is the only square in block 4 that can be <2>
Squares R9C1 and R9C2 in row 9 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.
R9C4 - removing <6> from <678> leaving <78>
R9C6 - removing <6> from <678> leaving <78>
Squares R9C1 and R9C2 in block 7 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 block.
R8C1 - removing <6> from <136> leaving <13>
Intersection of row 2 with block 2. The value <6> 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.
R1C4 - removing <6> from <126> leaving <12>
R1C6 - removing <6> from <1236> leaving <123>
R3C5 - removing <6> from <36> leaving <3>
R5C5 can only be <2>
R5C4 can only be <7>
R7C5 can only be <6>
R7C7 can only be <1>
R8C6 can only be <2>
R7C3 can only be <2>
R8C7 can only be <6>
R1C6 can only be <1>
R1C4 can only be <2>
R5C6 can only be <3>
R9C4 can only be <8>
R6C6 can only be <9>
R6C4 can only be <1>
R2C6 can only be <6>
R9C6 can only be <7>
R2C4 can only be <9>
R4C6 can only be <8>
R4C4 can only be <6>
R4C2 is the only square in row 4 that can be <9>
R3C2 can only be <6>
R3C8 can only be <1>
R9C2 can only be <4>
R1C1 can only be <3>
R3C3 can only be <9>
R2C9 can only be <3>
R9C1 can only be <6>
R6C2 can only be <3>
R1C8 can only be <6>
R4C1 can only be <4>
R8C1 can only be <1>
R2C3 can only be <1>
R8C3 can only be <3>
R4C9 can only be <1>
R4C5 can only be <5>
R4C8 can only be <3>
R6C5 can only be <4>
R6C8 can only be <5>
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