The full reasoning can be found below the Sudoku.
Apr 12 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R3C3 can only be <3>
R4C6 can only be <9>
R1C4 is the only square in row 1 that can be <9>
R6C9 is the only square in row 6 that can be <9>
R8C5 is the only square in row 8 that can be <9>
R9C2 is the only square in row 9 that can be <1>
R9C3 is the only square in row 9 that can be <9>
Intersection of row 7 with block 9. The value <3> only appears in one or more of squares R7C7, R7C8 and R7C9 of row 7. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R8C8 - removing <3> from <2356> leaving <256>
R8C9 - removing <3> from <3456> leaving <456>
Intersection of row 9 with block 8. The value <4> only appears in one or more of squares R9C4, R9C5 and R9C6 of row 9. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain this value.
R7C5 - removing <4> from <47> leaving <7>
R8C4 - removing <4> from <3457> leaving <357>
R8C6 - removing <4> from <234> leaving <23>
R4C4 is the only square in column 4 that can be <7>
R4C2 is the only square in row 4 that can be <8>
R6C4 is the only square in row 6 that can be <8>
Intersection of column 9 with block 3. The value <1> 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 <1> from <1367> leaving <367>
R2C8 - removing <1> from <13678> leaving <3678>
R1C6 is the only square in row 1 that can be <1>
R6C6 can only be <4>
R3C5 can only be <8>
R2C5 can only be <4>
R6C1 can only be <5>
R6C2 can only be <3>
R9C6 can only be <2>
R5C5 can only be <1>
R8C6 can only be <3>
R2C4 can only be <3>
R4C1 can only be <2>
R6C8 can only be <1>
R8C4 can only be <5>
R2C6 can only be <6>
R2C9 can only be <1>
R2C1 can only be <7>
R9C4 can only be <4>
R2C2 can only be <2>
R2C8 can only be <8>
R1C3 can only be <4>
R9C8 can only be <5>
R9C7 can only be <8>
R4C8 can only be <6>
R1C2 can only be <6>
R5C3 can only be <7>
R7C3 can only be <2>
R4C9 can only be <5>
R8C8 can only be <2>
R3C9 can only be <6>
R5C2 can only be <4>
R5C8 can only be <3>
R1C7 can only be <3>
R3C1 can only be <1>
R1C8 can only be <7>
R5C7 can only be <2>
R7C7 can only be <6>
R3C7 can only be <5>
R8C9 can only be <4>
R8C2 can only be <7>
R7C1 can only be <4>
R8C1 can only be <6>
R7C9 can only be <3>
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