The full reasoning can be found below the Sudoku.
Apr 05 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C8 is the only square in row 1 that can be <8>
R1C2 is the only square in row 1 that can be <3>
R5C5 is the only square in row 5 that can be <1>
R2C2 is the only square in column 2 that can be <4>
R2C8 can only be <5>
R5C8 can only be <3>
R3C8 can only be <4>
R8C8 can only be <6>
R9C8 can only be <7>
R5C9 is the only square in row 5 that can be <5>
R4C5 is the only square in row 4 that can be <5>
R9C7 is the only square in row 9 that can be <5>
R8C3 is the only square in row 8 that can be <5>
R1C1 is the only square in row 1 that can be <5>
R7C2 is the only square in column 2 that can be <7>
R9C4 is the only square in column 4 that can be <8>
R9C9 can only be <1>
R8C9 can only be <3>
R8C7 can only be <2>
R3C9 can only be <9>
R2C7 can only be <1>
R8C2 can only be <9>
R3C7 can only be <3>
R8C4 can only be <1>
R5C2 can only be <6>
R5C1 can only be <9>
R9C2 can only be <2>
R1C6 is the only square in column 6 that can be <1>
R1C4 is the only square in row 1 that can be <4>
Squares R7C1 and R7C3 in row 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <16>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R7C5 - removing <6> from <236> leaving <23>
R7C6 - removing <6> from <236> leaving <23>
Intersection of column 4 with block 5. The value <9> only appears in one or more of squares R4C4, R5C4 and R6C4 of column 4. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain this value.
R4C6 - removing <9> from <469> leaving <46>
R6C5 - removing <9> from <379> leaving <37>
R6C6 - removing <9> from <349> leaving <34>
Squares R7C1, R7C3, R3C1 and R3C3 form a Type-4 Unique Rectangle on <16>.
R3C1 - removing <6> from <1267> leaving <127>
R3C3 - removing <6> from <1267> leaving <127>
Intersection of row 3 with block 2. The value <6> only appears in one or more of squares R3C4, R3C5 and R3C6 of row 3. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
R2C6 - removing <6> from <269> leaving <29>
Squares R7C7, R7C9, R4C7 and R4C9 form a Type-1 Unique Rectangle on <48>.
R4C7 - removing <48> from <489> leaving <9>
R6C4 is the only square in row 6 that can be <9>
Squares R1C5 (XY), R3C4 (XZ) and R9C5 (YZ) form an XY-Wing pattern on <6>. All squares that are buddies of both the XZ and YZ squares cannot be <6>.
R3C5 - removing <6> from <267> leaving <27>
R3C4 is the only square in row 3 that can be <6>
R4C4 can only be <7>
R4C3 can only be <8>
R6C5 can only be <3>
R6C6 can only be <4>
R7C5 can only be <2>
R6C7 can only be <8>
R4C6 can only be <6>
R7C7 can only be <4>
R4C9 can only be <4>
R7C6 can only be <3>
R3C5 can only be <7>
R7C9 can only be <8>
R1C5 can only be <9>
R9C6 can only be <9>
R9C5 can only be <6>
R2C6 can only be <2>
R1C3 can only be <7>
R2C1 can only be <6>
R6C3 can only be <2>
R2C3 can only be <9>
R7C1 can only be <1>
R6C1 can only be <7>
R3C3 can only be <1>
R7C3 can only be <6>
R3C1 can only be <2>
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