The full reasoning can be found below the Sudoku.
Mar 09 - Hard
Puzzle Copyright © Kevin Stone
Reasoning
R1C9 can only be <1>
R9C1 can only be <8>
R9C3 can only be <6>
R1C1 can only be <2>
R1C3 can only be <3>
R1C7 can only be <8>
R1C5 can only be <6>
R3C2 is the only square in row 3 that can be <6>
R9C9 is the only square in row 9 that can be <5>
R5C3 is the only square in column 3 that can be <5>
Intersection of row 4 with block 5. The value <7> only appears in one or more of squares R4C4, R4C5 and R4C6 of row 4. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain this value.
R5C5 - removing <7> from <1234789> leaving <123489>
R5C6 - removing <7> from <6789> leaving <689>
Intersection of block 6 with row 5. The values <79> only appears in one or more of squares R5C7, R5C8 and R5C9 of block 6. These squares are the ones that intersect with row 5. Thus, the other (non-intersecting) squares of row 5 cannot contain these values.
R5C1 - removing <9> from <49> leaving <4>
R5C2 - removing <9> from <2489> leaving <248>
R5C5 - removing <9> from <123489> leaving <12348>
R5C6 - removing <9> from <689> leaving <68>
Squares R5C6 and R6C4 in block 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 block.
R5C4 - removing <68> from <12368> leaving <123>
R5C5 - removing <8> from <1238> leaving <123>
R6C5 - removing <8> from <4589> leaving <459>
R6C6 - removing <68> from <5689> leaving <59>
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 <249> leaving <29>
R2C8 - removing <4> from <245> leaving <25>
R8C7 is the only square in column 7 that can be <4>
R8C3 can only be <9>
R7C9 can only be <7>
R5C9 can only be <9>
R9C7 can only be <2>
R2C3 can only be <4>
R7C1 can only be <1>
R9C5 can only be <7>
R2C7 can only be <9>
R2C2 can only be <1>
R5C7 can only be <7>
R3C9 can only be <4>
R3C8 can only be <5>
R7C2 can only be <4>
R7C8 can only be <8>
R3C1 can only be <9>
R8C2 can only be <7>
R7C5 can only be <9>
R8C8 can only be <1>
R3C5 can only be <1>
R2C8 can only be <2>
R4C6 is the only square in row 4 that can be <7>
R4C2 is the only square in row 4 that can be <9>
R6C2 can only be <8>
R6C4 can only be <6>
R5C2 can only be <2>
R6C8 can only be <4>
R5C6 can only be <8>
R6C5 can only be <5>
R4C8 can only be <3>
R4C4 can only be <2>
R5C8 can only be <6>
R5C5 can only be <3>
R5C4 can only be <1>
R2C6 can only be <5>
R8C6 can only be <6>
R6C6 can only be <9>
R2C5 can only be <8>
R2C4 can only be <3>
R8C5 can only be <2>
R4C5 can only be <4>
R8C4 can only be <8>
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