The full reasoning can be found below the Sudoku.
Mar 30 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R3C1 is the only square in row 3 that can be <4>
R5C2 is the only square in row 5 that can be <8>
R6C8 is the only square in row 6 that can be <4>
R6C2 is the only square in row 6 that can be <9>
R8C4 is the only square in row 8 that can be <4>
R9C9 is the only square in row 9 that can be <4>
R9C7 is the only square in row 9 that can be <6>
R8C2 is the only square in column 2 that can be <2>
R4C5 is the only square in column 5 that can be <2>
R5C8 is the only square in column 8 that can be <2>
R5C9 is the only square in column 9 that can be <6>
R5C7 is the only square in row 5 that can be <3>
R4C8 can only be <5>
R1C3 is the only square in column 3 that can be <6>
R4C2 is the only square in column 2 that can be <6>
Intersection of row 2 with block 2. The values <69> 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 these values.
R1C5 - removing <9> from <35789> leaving <3578>
R3C6 - removing <9> from <589> leaving <58>
Intersection of row 8 with block 8. The value <9> only appears in one or more of squares R8C4, R8C5 and R8C6 of row 8. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain this value.
R9C5 - removing <9> from <3789> leaving <378>
Intersection of column 2 with block 1. The value <5> only appears in one or more of squares R1C2, R2C2 and R3C2 of column 2. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R1C1 - removing <5> from <159> leaving <19>
R3C3 - removing <5> from <579> leaving <79>
Squares R3C3 and R3C4 in row 3 and R7C3 and R7C4 in row 7 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in columns 3 and 4 can be removed.
R2C4 - removing <7> from <367> leaving <36>
R9C3 - removing <7> from <179> leaving <19>
Squares R5C1, R5C3, R7C1 and R7C3 form a Type-4 Unique Rectangle on <15>.
R7C1 - removing <1> from <135> leaving <35>
R7C3 - removing <1> from <157> leaving <57>
Intersection of row 7 with block 8. The value <1> only appears in one or more of squares R7C4, R7C5 and R7C6 of row 7. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain this value.
R8C6 - removing <1> from <139> leaving <39>
R8C8 is the only square in row 8 that can be <1>
Squares R8C5 and R8C6 in block 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <39>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C4 - removing <3> from <1378> leaving <178>
R7C6 - removing <3> from <138> leaving <18>
R9C5 - removing <3> from <378> leaving <78>
Squares R8C5, R8C6, R2C5 and R2C6 form a Type-4 Unique Rectangle on <39>.
R2C5 - removing <3> from <3579> leaving <579>
R2C6 - removing <3> from <3569> leaving <569>
Squares R7C3 (XY), R5C3 (XZ) and R9C2 (YZ) form an XY-Wing pattern on <1>. All squares that are buddies of both the XZ and YZ squares cannot be <1>.
R9C3 - removing <1> from <19> leaving <9>
R3C3 can only be <7>
R3C4 can only be <8>
R7C3 can only be <5>
R2C2 can only be <5>
R3C6 can only be <5>
R6C4 can only be <6>
R3C7 can only be <2>
R3C9 can only be <9>
R7C7 can only be <8>
R1C9 can only be <3>
R6C6 can only be <8>
R2C4 can only be <3>
R6C5 can only be <5>
R7C6 can only be <1>
R7C1 can only be <3>
R5C3 can only be <1>
R7C4 can only be <7>
R4C6 can only be <3>
R1C7 can only be <5>
R9C8 can only be <3>
R9C1 can only be <1>
R2C8 can only be <7>
R7C9 can only be <2>
R1C2 can only be <1>
R1C5 can only be <7>
R4C4 can only be <1>
R2C5 can only be <9>
R1C8 can only be <8>
R8C6 can only be <9>
R5C1 can only be <5>
R9C5 can only be <8>
R8C5 can only be <3>
R2C6 can only be <6>
R9C2 can only be <7>
R1C1 can only be <9>
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