The full reasoning can be found below the Sudoku.
Apr 12 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C7 is the only square in row 4 that can be <8>
R3C9 is the only square in row 3 that can be <8>
R2C2 is the only square in row 2 that can be <8>
R2C1 is the only square in row 2 that can be <2>
R5C6 is the only square in row 5 that can be <7>
R6C8 is the only square in row 6 that can be <9>
R1C9 is the only square in row 1 that can be <9>
R6C2 is the only square in row 6 that can be <4>
R5C8 is the only square in row 5 that can be <4>
R7C3 is the only square in row 7 that can be <9>
R9C5 is the only square in row 9 that can be <7>
R9C9 is the only square in row 9 that can be <4>
R5C3 is the only square in column 3 that can be <2>
R7C9 is the only square in column 9 that can be <5>
R9C1 is the only square in column 1 that can be <5>
Squares R2C8 and R2C9 in block 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <36>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R1C8 - removing <3> from <135> leaving <15>
R3C7 - removing <36> from <1356> leaving <15>
Intersection of block 8 with row 7. The values <234> only appears in one or more of squares R7C4, R7C5 and R7C6 of block 8. These squares are the ones that intersect with row 7. Thus, the other (non-intersecting) squares of row 7 cannot contain these values.
R7C1 - removing <3> from <136> leaving <16>
R7C7 - removing <3> from <136> leaving <16>
Intersection of column 7 with block 6. The value <3> only appears in one or more of squares R4C7, R5C7 and R6C7 of column 7. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain this value.
R4C8 - removing <3> from <356> leaving <56>
Squares R2C8, R2C9, R8C8 and R8C9 form a Type-1 Unique Rectangle on <36>.
R8C8 - removing <36> from <1236> leaving <12>
Squares R3C6, R7C6, R3C5 and R7C5 form a Type-4 Unique Rectangle on <23>.
R3C5 - removing <3> from <2345> leaving <245>
R7C5 - removing <3> from <234> leaving <24>
Squares R8C1 (XYZ), R8C9 (XZ) and R7C1 (YZ) form an XYZ-Wing pattern on <6>. All squares that are buddies of all three squares cannot be <6>.
R8C2 - removing <6> from <1236> leaving <123>
Intersection of column 2 with block 4. The values <56> only appears in one or more of squares R4C2, R5C2 and R6C2 of column 2. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain these values.
R4C3 - removing <6> from <136> leaving <13>
R6C3 - removing <6> from <36> leaving <3>
R4C3 can only be <1>
R3C3 can only be <6>
R4C5 is the only square in row 4 that can be <3>
R5C4 can only be <5>
R5C2 can only be <6>
R6C5 can only be <6>
R6C7 can only be <5>
R3C7 can only be <1>
R4C8 can only be <6>
R7C7 can only be <6>
R1C8 can only be <5>
R4C2 can only be <5>
R2C8 can only be <3>
R5C7 can only be <3>
R7C1 can only be <1>
R8C9 can only be <3>
R2C9 can only be <6>
R9C8 can only be <2>
R9C2 can only be <3>
R8C8 can only be <1>
R1C5 can only be <4>
R8C1 can only be <6>
R8C2 can only be <2>
R1C2 can only be <1>
R1C1 can only be <3>
R7C5 can only be <2>
R3C4 can only be <3>
R3C1 can only be <4>
R3C6 can only be <2>
R7C4 can only be <4>
R3C5 can only be <5>
R7C6 can only be <3>
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