The full reasoning can be found below the Sudoku.
Mar 04 - Hard
Puzzle Copyright © Kevin Stone
Reasoning
R3C8 is the only square in row 3 that can be <6>
R5C5 is the only square in row 5 that can be <9>
R6C1 is the only square in row 6 that can be <1>
R7C5 is the only square in row 7 that can be <3>
R7C3 is the only square in row 7 that can be <6>
R3C3 is the only square in column 3 that can be <1>
R8C7 is the only square in column 7 that can be <2>
R9C6 is the only square in row 9 that can be <2>
R2C7 is the only square in column 7 that can be <3>
Intersection of row 5 with block 6. The value <8> only appears in one or more of squares R5C7, R5C8 and R5C9 of row 5. 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 <8> from <248> leaving <24>
R4C9 - removing <8> from <3468> leaving <346>
Intersection of column 5 with block 2. The value <4> only appears in one or more of squares R1C5, R2C5 and R3C5 of column 5. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
R1C6 - removing <4> from <34568> leaving <3568>
R2C6 - removing <4> from <458> leaving <58>
Squares R2C4 and R2C6 in row 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <58>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R2C1 - removing <58> from <45789> leaving <479>
R2C3 - removing <5> from <457> leaving <47>
R2C9 - removing <58> from <4589> leaving <49>
R8C3 is the only square in column 3 that can be <5>
R8C6 can only be <6>
R8C4 can only be <7>
R1C4 is the only square in row 1 that can be <6>
R1C5 is the only square in row 1 that can be <1>
R9C5 can only be <5>
R9C4 can only be <1>
R3C5 can only be <4>
R1C6 is the only square in row 1 that can be <3>
R7C7 is the only square in row 7 that can be <5>
R3C7 can only be <8>
R3C2 can only be <5>
R5C7 can only be <4>
R5C3 can only be <7>
R4C8 can only be <2>
R4C2 can only be <4>
R6C8 can only be <7>
R5C1 can only be <6>
R2C3 can only be <4>
R6C9 can only be <3>
R7C8 can only be <8>
R6C4 can only be <5>
R4C9 can only be <6>
R7C2 can only be <7>
R2C9 can only be <9>
R2C1 can only be <7>
R8C9 can only be <4>
R1C8 can only be <4>
R6C2 can only be <2>
R4C1 can only be <5>
R5C9 can only be <8>
R6C6 can only be <4>
R2C4 can only be <8>
R4C6 can only be <8>
R8C1 can only be <9>
R1C9 can only be <5>
R9C9 can only be <7>
R9C8 can only be <9>
R9C2 can only be <8>
R2C6 can only be <5>
R4C4 can only be <3>
R1C1 can only be <8>
R9C1 can only be <4>
R1C2 can only be <9>
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