The full reasoning can be found below the Sudoku.
Mar 31 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C2 is the only square in row 1 that can be <5>
R3C7 is the only square in row 3 that can be <4>
R4C8 is the only square in row 4 that can be <4>
R4C1 is the only square in row 4 that can be <2>
R7C4 is the only square in row 7 that can be <4>
R8C2 is the only square in row 8 that can be <4>
R3C5 is the only square in column 5 that can be <9>
R7C7 is the only square in column 7 that can be <6>
R5C8 is the only square in column 8 that can be <1>
R5C9 is the only square in row 5 that can be <2>
R3C6 is the only square in row 3 that can be <2>
R2C8 is the only square in row 2 that can be <2>
R3C4 is the only square in row 3 that can be <1>
R7C5 is the only square in row 7 that can be <2>
R6C2 is the only square in column 2 that can be <1>
R4C5 is the only square in row 4 that can be <1>
R5C2 is the only square in column 2 that can be <9>
R8C5 is the only square in column 5 that can be <5>
R7C9 is the only square in block 9 that can be <5>
R9C1 is the only square in column 1 that can be <5>
Squares R9C3 and R9C8 in row 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <89>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R9C4 - removing <8> from <368> leaving <36>
R9C6 - removing <8> from <368> leaving <36>
Squares R7C6 and R8C6 in column 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <18>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C6 - removing <8> from <378> leaving <37>
R6C6 - removing <8> from <678> leaving <67>
Squares R2C2 and R3C2 in block 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <67>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R3C1 - removing <7> from <378> leaving <38>
R3C3 - removing <67> from <3678> leaving <38>
R3C2 is the only square in row 3 that can be <6>
R2C2 can only be <7>
R3C9 is the only square in row 3 that can be <7>
Intersection of column 4 with block 2. The value <8> only appears in one or more of squares R1C4, R2C4 and R3C4 of column 4. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
R2C5 - removing <8> from <368> leaving <36>
Squares R9C3, R9C8, R7C3 and R7C8 form a Type-4 Unique Rectangle on <89>.
R7C3 - removing <8> from <1789> leaving <179>
R7C8 - removing <8> from <789> leaving <79>
Squares R1C9, R6C9, R1C7 and R6C7 form a Type-4 Unique Rectangle on <89>.
R1C7 - removing <8> from <389> leaving <39>
R6C7 - removing <8> from <5789> leaving <579>
Squares R1C6 (XY), R2C5 (XZ) and R6C6 (YZ) form an XY-Wing pattern on <6>. All squares that are buddies of both the XZ and YZ squares cannot be <6>.
R6C5 - removing <6> from <68> leaving <8>
R5C5 - removing <6> from <368> leaving <38>
R6C9 can only be <9>
R5C5 can only be <3>
R1C9 can only be <8>
R2C7 can only be <3>
R2C5 can only be <6>
R1C7 can only be <9>
R5C1 can only be <7>
R4C4 can only be <7>
R2C4 can only be <8>
R4C7 can only be <5>
R1C4 can only be <3>
R6C6 can only be <6>
R4C3 can only be <3>
R6C7 can only be <7>
R5C3 can only be <6>
R5C7 can only be <8>
R7C1 can only be <8>
R6C3 can only be <5>
R9C6 can only be <3>
R7C6 can only be <1>
R3C1 can only be <3>
R9C3 can only be <9>
R8C6 can only be <8>
R8C8 can only be <7>
R8C3 can only be <1>
R7C8 can only be <9>
R9C8 can only be <8>
R7C3 can only be <7>
R9C4 can only be <6>
R1C6 can only be <7>
R3C3 can only be <8>
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