The full reasoning can be found below the Sudoku.
Sep 02 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R3C2 can only be <9>
R3C3 can only be <6>
R3C4 can only be <4>
R5C5 is the only square in row 5 that can be <3>
R6C7 is the only square in row 6 that can be <7>
R3C7 can only be <8>
R3C9 can only be <7>
R8C6 is the only square in row 8 that can be <4>
R9C3 is the only square in column 3 that can be <3>
R9C1 is the only square in row 9 that can be <9>
R9C8 is the only square in row 9 that can be <7>
R8C1 is the only square in row 8 that can be <7>
R8C4 is the only square in row 8 that can be <6>
R9C9 is the only square in row 9 that can be <6>
R2C7 is the only square in row 2 that can be <6>
R1C5 is the only square in row 1 that can be <6>
R7C1 is the only square in row 7 that can be <6>
R7C8 is the only square in row 7 that can be <8>
R4C9 is the only square in row 4 that can be <8>
R8C2 is the only square in row 8 that can be <8>
R6C1 is the only square in row 6 that can be <8>
R9C5 is the only square in column 5 that can be <2>
R1C7 is the only square in column 7 that can be <9>
Squares R6C2 and R9C2 in column 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <15>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C2 - removing <5> from <235> leaving <23>
R2C2 - removing <5> from <235> leaving <23>
R2C8 is the only square in row 2 that can be <5>
R1C1 is the only square in row 1 that can be <5>
R5C1 can only be <2>
Squares R4C5 and R6C5 in block 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <14>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R4C4 - removing <1> from <159> leaving <59>
R6C6 - removing <1> from <159> leaving <59>
Intersection of column 9 with block 3. The value <2> only appears in one or more of squares R1C9, R2C9 and R3C9 of column 9. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R1C8 - removing <2> from <124> leaving <14>
Squares R6C2 and R7C6 form a remote naked pair. <15> can be removed from any square that is common to their groups.
R6C6 - removing <5> from <59> leaving <9>
R4C4 can only be <5>
R9C4 can only be <1>
R9C2 can only be <5>
R2C4 can only be <9>
R7C6 can only be <5>
R6C2 can only be <1>
R6C5 can only be <4>
R6C3 can only be <5>
R4C5 can only be <1>
R4C7 can only be <2>
R4C8 can only be <4>
R7C7 can only be <1>
R4C3 can only be <9>
R1C8 can only be <1>
R5C9 can only be <1>
R5C7 can only be <5>
R2C9 can only be <2>
R5C3 can only be <4>
R7C3 can only be <2>
R8C8 can only be <2>
R8C3 can only be <1>
R1C6 can only be <3>
R2C2 can only be <3>
R1C9 can only be <4>
R1C2 can only be <2>
R2C6 can only be <1>
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