The full reasoning can be found below the Sudoku.
Apr 05 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R3C8 is the only square in row 3 that can be <8>
R6C2 is the only square in row 6 that can be <8>
R4C9 is the only square in row 4 that can be <8>
R6C1 is the only square in row 6 that can be <1>
R6C3 is the only square in row 6 that can be <6>
R6C8 is the only square in row 6 that can be <5>
R5C9 can only be <3>
R1C9 can only be <7>
R6C7 can only be <2>
R6C5 can only be <3>
R2C9 can only be <9>
R8C9 can only be <1>
R7C9 can only be <5>
R4C5 can only be <2>
R5C5 can only be <4>
R1C5 can only be <6>
R9C5 can only be <9>
R3C4 is the only square in row 3 that can be <9>
R5C1 is the only square in row 5 that can be <2>
R8C2 is the only square in row 8 that can be <2>
R1C8 is the only square in row 1 that can be <2>
R3C3 is the only square in row 3 that can be <2>
R7C6 is the only square in row 7 that can be <2>
R8C4 is the only square in row 8 that can be <8>
R5C4 can only be <5>
R5C6 can only be <8>
R4C3 is the only square in column 3 that can be <5>
R4C2 can only be <3>
R1C4 is the only square in row 1 that can be <3>
R9C6 is the only square in column 6 that can be <7>
Squares R2C3 and R2C8 in row 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <34>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R2C1 - removing <3> from <367> leaving <67>
R2C2 - removing <4> from <1467> leaving <167>
R2C6 - removing <4> from <14> leaving <1>
R3C2 is the only square in row 3 that can be <1>
Squares R2C1 and R8C1 in column 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <67>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R9C1 - removing <6> from <356> leaving <35>
Intersection of row 8 with block 9. The value <4> only appears in one or more of squares R8C7, R8C8 and R8C9 of row 8. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R7C7 - removing <4> from <3479> leaving <379>
R7C8 - removing <4> from <34679> leaving <3679>
R9C8 - removing <4> from <346> leaving <36>
Squares R3C7 and R7C3 form a remote naked pair. <34> can be removed from any square that is common to their groups.
R7C7 - removing <3> from <379> leaving <79>
R3C7 is the only square in column 7 that can be <3>
R3C1 can only be <5>
R2C8 can only be <4>
R2C3 can only be <3>
R3C6 can only be <4>
R9C1 can only be <3>
R1C2 can only be <4>
R1C6 can only be <5>
R9C8 can only be <6>
R7C3 can only be <4>
R9C4 can only be <4>
R8C8 can only be <7>
R9C2 can only be <5>
R7C4 can only be <6>
R7C2 can only be <7>
R8C1 can only be <6>
R8C7 can only be <4>
R4C8 can only be <9>
R7C7 can only be <9>
R4C7 can only be <7>
R7C8 can only be <3>
R2C2 can only be <6>
R2C1 can only be <7>
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