The full reasoning can be found below the Sudoku.
May 11 - Super Hard
Puzzle Copyright © Kevin Stone
Reasoning
R2C9 is the only square in row 2 that can be <3>
R5C8 is the only square in row 5 that can be <8>
R5C2 is the only square in row 5 that can be <5>
R9C5 is the only square in column 5 that can be <6>
R7C8 is the only square in row 7 that can be <6>
R6C4 is the only square in column 4 that can be <6>
R6C7 is the only square in row 6 that can be <3>
R4C6 is the only square in row 4 that can be <3>
R6C9 is the only square in row 6 that can be <4>
R8C6 is the only square in row 8 that can be <4>
R3C4 is the only square in row 3 that can be <4>
R3C6 is the only square in row 3 that can be <7>
R7C7 is the only square in row 7 that can be <4>
R1C6 is the only square in column 6 that can be <1>
R5C6 is the only square in column 6 that can be <9>
R1C4 is the only square in column 4 that can be <9>
R9C8 is the only square in column 8 that can be <1>
R4C9 is the only square in column 9 that can be <9>
R9C7 is the only square in block 9 that can be <7>
Squares R6C2 and R6C8 in row 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <27>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R6C1 - removing <27> from <2789> leaving <89>
R6C3 - removing <2> from <289> leaving <89>
Squares R7C6 and R7C9 in row 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <28>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R7C2 - removing <2> from <1237> leaving <137>
R7C3 - removing <2> from <123> leaving <13>
R7C4 - removing <2> from <237> leaving <37>
Squares R7C6 and R9C6 in block 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <28>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R8C5 - removing <2> from <257> leaving <57>
R9C4 - removing <2> from <235> leaving <35>
Intersection of row 2 with block 2. The value <5> 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.
R1C5 - removing <5> from <258> leaving <28>
Squares R4C3<12>, R7C3<13> and R9C3<23> in column 3 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <123>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C3 - removing <23> from <2358> leaving <58>
R3C3 - removing <12> from <12589> leaving <589>
R1C2 is the only square in row 1 that can be <3>
R1C1 is the only square in row 1 that can be <6>
R4C2 is the only square in row 4 that can be <6>
Squares R6C1, R6C3, R3C1 and R3C3 form a Type-3 Unique Rectangle on <89>. Upon close inspection, it is clear that:
(R3C1 or R3C3)<125>, R3C8<25> and R3C2<12> form a naked triplet on <125> in row 3. No other squares in the row can contain these possibilities
R3C7 - removing <25> from <258> leaving <8>
Squares R7C6, R7C9, R9C6 and R9C9 form a Type-1 Unique Rectangle on <28>.
R9C9 - removing <28> from <258> leaving <5>
R9C4 can only be <3>
R8C9 can only be <2>
R8C1 can only be <7>
R7C9 can only be <8>
R9C3 can only be <2>
R7C4 can only be <7>
R7C2 can only be <1>
R5C4 can only be <2>
R8C5 can only be <5>
R7C6 can only be <2>
R9C6 can only be <8>
R4C3 can only be <1>
R4C1 can only be <2>
R7C3 can only be <3>
R5C5 can only be <7>
R2C4 can only be <5>
R3C2 can only be <2>
R3C8 can only be <5>
R6C2 can only be <7>
R2C1 can only be <8>
R3C3 can only be <9>
R1C7 can only be <2>
R4C7 can only be <5>
R4C8 can only be <7>
R6C8 can only be <2>
R1C5 can only be <8>
R2C5 can only be <2>
R6C1 can only be <9>
R1C3 can only be <5>
R3C1 can only be <1>
R6C3 can only be <8>
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