The full reasoning can be found below the Sudoku.
Apr 27 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C1 can only be <4>
R1C7 is the only square in row 1 that can be <5>
R3C2 is the only square in row 3 that can be <5>
R7C5 is the only square in row 7 that can be <5>
R4C6 is the only square in row 4 that can be <5>
R2C8 is the only square in column 8 that can be <3>
R2C2 can only be <4>
R8C2 can only be <2>
R5C3 is the only square in column 3 that can be <2>
R5C8 can only be <7>
R5C7 can only be <4>
R6C5 is the only square in row 6 that can be <4>
R8C3 is the only square in row 8 that can be <4>
R9C9 is the only square in row 9 that can be <4>
Squares R5C4 and R5C5 in row 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <68>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R5C6 - removing <6> from <136> leaving <13>
Squares R6C4 and R6C9 in row 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <29>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R6C6 - removing <2> from <123> leaving <13>
Squares R5C5 and R8C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <68>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C5 - removing <6> from <679> leaving <79>
R3C5 - removing <6> from <2679> leaving <279>
R2C3 is the only square in row 2 that can be <6>
Squares R4C9 and R6C9 in column 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <29>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C9 - removing <29> from <2679> leaving <67>
R3C9 - removing <29> from <26789> leaving <678>
R7C9 - removing <2> from <2678> leaving <678>
Intersection of row 1 with block 2. The value <2> only appears in one or more of squares R1C4, R1C5 and R1C6 of row 1. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
R3C5 - removing <2> from <279> leaving <79>
R4C5 is the only square in column 5 that can be <2>
R4C9 can only be <9>
R6C4 can only be <9>
R4C4 can only be <7>
R6C9 can only be <2>
R1C3 is the only square in row 1 that can be <9>
R1C1 is the only square in row 1 that can be <3>
R6C1 can only be <1>
R6C6 can only be <3>
R3C1 can only be <7>
R5C2 can only be <3>
R5C6 can only be <1>
R3C3 can only be <1>
R3C5 can only be <9>
R9C3 can only be <7>
R2C5 can only be <7>
R7C2 can only be <1>
R7C3 can only be <3>
R2C7 can only be <9>
R8C7 can only be <8>
R8C5 can only be <6>
R3C7 can only be <2>
R3C8 can only be <6>
R7C7 can only be <7>
R9C7 can only be <1>
R3C9 can only be <8>
R7C8 can only be <2>
R8C8 can only be <9>
R1C9 can only be <7>
R7C9 can only be <6>
R7C1 can only be <8>
R5C5 can only be <8>
R9C6 can only be <2>
R9C4 can only be <8>
R1C6 can only be <6>
R1C4 can only be <2>
R5C4 can only be <6>
R9C1 can only be <6>
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