The full reasoning can be found below the Sudoku.
Apr 12 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C5 is the only square in row 1 that can be <8>
R3C2 is the only square in row 3 that can be <5>
R3C8 is the only square in row 3 that can be <7>
R4C6 is the only square in row 4 that can be <7>
R5C5 is the only square in row 5 that can be <5>
R6C6 is the only square in row 6 that can be <8>
R6C3 is the only square in row 6 that can be <9>
R5C6 is the only square in row 5 that can be <9>
R8C3 is the only square in row 8 that can be <5>
R9C3 is the only square in row 9 that can be <7>
R9C9 is the only square in row 9 that can be <8>
R5C8 is the only square in row 5 that can be <8>
Intersection of row 6 with block 5. The value <2> 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 <2> from <2346> leaving <346>
Intersection of column 3 with block 1. The value <2> only appears in one or more of squares R1C3, R2C3 and R3C3 of column 3. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R1C1 - removing <2> from <1239> leaving <139>
R2C2 - removing <2> from <1249> leaving <149>
R3C1 - removing <2> from <1234> leaving <134>
Intersection of row 3 with block 2. The value <2> only appears in one or more of squares R3C4, R3C5 and R3C6 of row 3. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
R2C5 - removing <2> from <123> leaving <13>
Squares R1C1 and R1C7 in row 1 and R9C1 and R9C7 in row 9 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in columns 1 and 7 can be removed.
R2C7 - removing <1> from <12349> leaving <2349>
R3C1 - removing <1> from <134> leaving <34>
R7C1 - removing <1> from <1249> leaving <249>
R3C4 is the only square in row 3 that can be <1>
R2C5 can only be <3>
R3C6 can only be <2>
R7C6 can only be <3>
R4C5 is the only square in row 4 that can be <1>
R9C5 is the only square in column 5 that can be <6>
R7C9 is the only square in row 7 that can be <6>
R5C4 is the only square in row 5 that can be <6>
R4C7 is the only square in row 4 that can be <6>
R8C8 is the only square in column 8 that can be <3>
R1C9 is the only square in column 9 that can be <9>
R2C2 is the only square in row 2 that can be <9>
R2C8 is the only square in row 2 that can be <1>
R7C8 can only be <4>
R7C4 can only be <2>
R8C7 can only be <9>
R9C7 can only be <1>
R9C1 can only be <4>
R7C1 can only be <9>
R7C2 can only be <1>
R8C5 can only be <4>
R8C2 can only be <2>
R6C5 can only be <2>
R3C1 can only be <3>
R3C9 can only be <4>
R1C1 can only be <1>
R5C1 can only be <2>
R1C3 can only be <2>
R5C9 can only be <3>
R2C7 can only be <2>
R5C2 can only be <4>
R4C3 can only be <3>
R6C7 can only be <4>
R6C4 can only be <3>
R1C7 can only be <3>
R2C3 can only be <4>
R4C4 can only be <4>
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