The full reasoning can be found below the Sudoku.
Mar 07 - Super Hard
Puzzle Copyright © Kevin Stone
Reasoning
R3C8 is the only square in row 3 that can be <9>
R7C7 is the only square in row 7 that can be <4>
R6C1 is the only square in column 1 that can be <1>
R2C1 is the only square in column 1 that can be <4>
R2C3 is the only square in row 2 that can be <7>
R5C5 is the only square in column 5 that can be <3>
R5C6 is the only square in row 5 that can be <4>
R3C5 is the only square in row 3 that can be <4>
R6C9 is the only square in row 6 that can be <4>
R6C6 is the only square in column 6 that can be <8>
R1C7 is the only square in column 7 that can be <8>
R2C7 is the only square in column 7 that can be <6>
Intersection of row 2 with block 3. The value <3> only appears in one or more of squares R2C7, R2C8 and R2C9 of row 2. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R1C9 - removing <3> from <1235> leaving <125>
R2C9 is the only square in column 9 that can be <3>
Squares R2C8 and R6C8 in column 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <25>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R5C8 - removing <2> from <127> leaving <17>
R7C8 - removing <5> from <357> leaving <37>
R9C8 - removing <25> from <12357> leaving <137>
Intersection of row 8 with block 9. The value <1> only appears in one or more of squares R8C7, R8C8 and R8C9 of row 8. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R9C7 - removing <1> from <125> leaving <25>
R9C8 - removing <1> from <137> leaving <37>
R5C8 is the only square in column 8 that can be <1>
R5C2 is the only square in row 5 that can be <7>
R4C9 is the only square in row 4 that can be <7>
R5C3 is the only square in row 5 that can be <8>
R3C2 is the only square in row 3 that can be <8>
R8C1 is the only square in row 8 that can be <7>
R8C5 is the only square in row 8 that can be <8>
R7C1 is the only square in row 7 that can be <8>
R8C3 is the only square in row 8 that can be <9>
R9C5 is the only square in column 5 that can be <9>
R8C7 is the only square in column 7 that can be <1>
Intersection of column 5 with block 2. The value <2> only appears in one or more of squares R1C5, R2C5 and R3C5 of column 5. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
R1C4 - removing <2> from <12567> leaving <1567>
Squares R5C4, R5C7, R4C4 and R4C7 form a Type-3 Unique Rectangle on <29>. Upon close inspection, it is clear that:
(R4C4 or R4C7)<56> and R4C6<56> form a naked pair on <56> in row 4. No other squares in the row can contain these possibilities
R4C2 - removing <6> from <236> leaving <23>
R7C2 is the only square in column 2 that can be <6>
R7C5 can only be <5>
R7C4 can only be <7>
R2C5 can only be <2>
R2C8 can only be <5>
R1C5 can only be <6>
R6C8 can only be <2>
R6C3 can only be <6>
R5C7 can only be <9>
R7C8 can only be <3>
R9C8 can only be <7>
R5C4 can only be <2>
R4C7 can only be <5>
R6C4 can only be <5>
R1C4 can only be <1>
R4C6 can only be <6>
R1C9 can only be <2>
R9C4 can only be <6>
R3C6 can only be <5>
R3C9 can only be <1>
R8C9 can only be <5>
R3C3 can only be <2>
R1C6 can only be <7>
R9C6 can only be <1>
R9C7 can only be <2>
R4C4 can only be <9>
R8C2 can only be <2>
R9C1 can only be <3>
R4C2 can only be <3>
R9C3 can only be <5>
R4C1 can only be <2>
R1C3 can only be <3>
R1C2 can only be <5>
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