The full reasoning can be found below the Sudoku.
Mar 03 - Hard
Puzzle Copyright © Kevin Stone
Reasoning
R2C1 is the only square in column 1 that can be <6>
Intersection of row 2 with block 2. The value <9> only appears in one or more of squares R2C4, R2C5 and R2C6 of row 2. 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 <9> from <379> leaving <37>
Squares R3C5 and R5C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <37>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R4C5 - removing <3> from <136> leaving <16>
R6C5 - removing <7> from <1679> leaving <169>
Intersection of row 3 with block 3. The value <4> only appears in one or more of squares R3C7, R3C8 and R3C9 of row 3. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R2C7 - removing <4> from <14> leaving <1>
R2C9 - removing <4> from <247> leaving <27>
R1C7 can only be <5>
R5C7 can only be <4>
R1C3 is the only square in row 1 that can be <1>
R9C3 is the only square in column 3 that can be <4>
R9C2 is the only square in row 9 that can be <7>
R1C2 can only be <2>
R1C8 can only be <3>
R2C3 can only be <7>
R1C6 can only be <6>
R3C8 can only be <4>
R2C9 can only be <2>
R3C9 can only be <7>
R3C5 can only be <3>
R1C4 can only be <7>
R5C5 can only be <7>
R5C4 can only be <3>
R4C9 is the only square in row 4 that can be <3>
R6C1 is the only square in row 6 that can be <7>
R7C9 is the only square in row 7 that can be <4>
R7C2 is the only square in row 7 that can be <8>
R8C6 is the only square in row 8 that can be <3>
R4C1 is the only square in column 1 that can be <1>
R4C5 can only be <6>
R4C8 can only be <5>
R4C2 can only be <4>
R6C8 can only be <6>
R6C9 can only be <8>
R9C8 can only be <1>
R8C9 can only be <6>
R7C8 can only be <2>
R4C4 can only be <8>
R6C2 can only be <5>
R4C6 can only be <2>
R8C4 can only be <9>
R5C6 can only be <5>
R5C3 can only be <2>
R3C2 can only be <9>
R7C1 can only be <9>
R8C7 can only be <8>
R2C4 can only be <4>
R9C4 can only be <6>
R7C5 can only be <1>
R9C6 can only be <8>
R9C7 can only be <9>
R2C6 can only be <9>
R6C4 can only be <1>
R6C6 can only be <4>
R3C1 can only be <5>
R8C3 can only be <5>
R6C5 can only be <9>
R8C1 can only be <2>
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