The full reasoning can be found below the Sudoku.
Mar 27 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C4 is the only square in row 2 that can be <3>
R2C3 is the only square in row 2 that can be <8>
R3C2 is the only square in row 3 that can be <3>
R4C7 is the only square in row 4 that can be <3>
R4C8 is the only square in row 4 that can be <8>
R8C6 is the only square in row 8 that can be <8>
R7C2 is the only square in row 7 that can be <8>
R9C5 is the only square in row 9 that can be <2>
R5C1 is the only square in column 1 that can be <2>
Squares R1C5 and R2C5 in column 5 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 column.
R8C5 - removing <6> from <156> leaving <15>
Squares R1C5 and R2C5 in block 2 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 block.
R2C6 - removing <6> from <2467> leaving <247>
R3C4 - removing <6> from <2467> leaving <247>
R3C6 - removing <6> from <2467> leaving <247>
Squares R8C9 and R9C8 in block 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 block.
R7C8 - removing <6> from <569> leaving <59>
R8C7 - removing <4> from <1459> leaving <159>
Intersection of row 4 with block 5. The value <2> only appears in one or more of squares R4C4, R4C5 and R4C6 of row 4. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain this value.
R6C4 - removing <2> from <2456> leaving <456>
R6C6 - removing <2> from <246> leaving <46>
Intersection of column 2 with block 4. The values <17> only appears in one or more of squares R4C2, R5C2 and R6C2 of column 2. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain these values.
R6C3 - removing <7> from <4579> leaving <459>
Squares R1C2 and R1C8 in row 1 and R9C2 and R9C8 in row 9 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in columns 2 and 8 can be removed.
R3C8 - removing <4> from <24679> leaving <2679>
R4C2 - removing <4> from <14> leaving <1>
R5C2 - removing <4> from <147> leaving <17>
R5C8 - removing <4> from <457> leaving <57>
R6C2 - removing <4> from <479> leaving <79>
R6C8 - removing <4> from <2457> leaving <257>
R5C2 can only be <7>
R5C8 can only be <5>
R5C9 can only be <4>
R6C2 can only be <9>
R5C5 can only be <1>
R7C8 can only be <9>
R8C9 can only be <6>
R6C7 can only be <2>
R6C8 can only be <7>
R2C9 can only be <7>
R9C8 can only be <4>
R9C2 can only be <6>
R1C8 can only be <6>
R1C2 can only be <4>
R1C5 can only be <9>
R3C8 can only be <2>
R8C5 can only be <5>
R8C4 can only be <7>
R8C7 can only be <1>
R7C7 can only be <5>
R7C3 can only be <7>
R2C1 can only be <9>
R2C5 can only be <6>
R2C7 can only be <4>
R8C1 can only be <4>
R3C3 can only be <6>
R2C6 can only be <2>
R3C7 can only be <9>
R7C4 can only be <6>
R7C6 can only be <1>
R8C3 can only be <9>
R3C4 can only be <4>
R4C6 can only be <4>
R3C6 can only be <7>
R6C4 can only be <5>
R4C3 can only be <5>
R6C6 can only be <6>
R6C3 can only be <4>
R4C4 can only be <2>
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