The full reasoning can be found below the Sudoku.
Mar 31 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C5 can only be <1>
R7C4 can only be <1>
R9C9 can only be <6>
R4C5 can only be <4>
R8C5 can only be <5>
R3C6 can only be <7>
R3C4 can only be <4>
R6C4 can only be <2>
R5C5 can only be <6>
R6C5 can only be <8>
R7C6 can only be <6>
R4C4 can only be <9>
R5C4 can only be <7>
R5C6 is the only square in row 5 that can be <5>
R6C7 is the only square in row 6 that can be <5>
Squares R2C2 and R2C8 in row 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <39>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R2C3 - removing <39> from <3679> leaving <67>
R2C7 - removing <39> from <3679> leaving <67>
Intersection of block 4 with column 3. The value <1> only appears in one or more of squares R4C3, R5C3 and R6C3 of block 4. These squares are the ones that intersect with column 3. Thus, the other (non-intersecting) squares of column 3 cannot contain this value.
R3C3 - removing <1> from <1569> leaving <569>
R8C3 - removing <1> from <1234> leaving <234>
R9C3 - removing <1> from <19> leaving <9>
Squares R2C2 and R2C8 in row 2 and R5C2 and R5C8 in row 5 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in columns 2 and 8 can be removed.
R7C2 - removing <3> from <238> leaving <28>
R7C8 - removing <3> from <23489> leaving <2489>
R8C2 - removing <3> from <123> leaving <12>
R8C8 - removing <3> from <234> leaving <24>
Squares R7C2<28>, R8C2<12> and R9C1<18> in block 7 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <128>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C1 - removing <8> from <358> leaving <35>
R7C3 - removing <2> from <2345> leaving <345>
R8C3 - removing <2> from <234> leaving <34>
R4C3 is the only square in column 3 that can be <2>
R4C7 can only be <3>
R5C2 can only be <3>
R4C6 can only be <1>
R5C8 can only be <2>
R2C2 can only be <9>
R6C3 can only be <1>
R8C8 can only be <4>
R6C6 can only be <3>
R8C3 can only be <3>
R2C8 can only be <3>
R1C9 can only be <5>
R7C1 can only be <5>
R1C3 can only be <7>
R3C9 can only be <2>
R7C9 can only be <3>
R7C3 can only be <4>
R1C7 can only be <8>
R2C3 can only be <6>
R1C1 can only be <3>
R9C7 can only be <1>
R3C8 can only be <9>
R2C7 can only be <7>
R3C3 can only be <5>
R3C7 can only be <6>
R7C8 can only be <8>
R7C2 can only be <2>
R9C1 can only be <8>
R8C7 can only be <2>
R7C7 can only be <9>
R8C2 can only be <1>
R3C2 can only be <8>
R3C1 can only be <1>
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