The full reasoning can be found below the Sudoku.
Apr 07 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R3C1 is the only square in row 3 that can be <1>
R3C9 is the only square in row 3 that can be <7>
R5C3 is the only square in row 5 that can be <1>
R5C9 is the only square in row 5 that can be <3>
R7C1 is the only square in row 7 that can be <7>
R7C2 is the only square in row 7 that can be <5>
R4C1 is the only square in row 4 that can be <5>
R8C4 is the only square in row 8 that can be <7>
R9C1 is the only square in row 9 that can be <3>
R1C6 is the only square in row 1 that can be <3>
R1C4 is the only square in row 1 that can be <1>
R1C7 is the only square in row 1 that can be <5>
R2C2 is the only square in row 2 that can be <3>
R8C8 is the only square in row 8 that can be <3>
R8C7 is the only square in row 8 that can be <4>
R2C8 is the only square in row 2 that can be <4>
R1C1 is the only square in row 1 that can be <4>
R9C5 is the only square in row 9 that can be <4>
Squares R5C1 and R6C1 in block 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <26>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R4C2 - removing <26> from <2469> leaving <49>
R6C2 - removing <26> from <2469> leaving <49>
Squares R4C2 and R6C2 in column 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <49>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R8C2 - removing <9> from <269> leaving <26>
Intersection of row 8 with block 7. The value <2> only appears in one or more of squares R8C1, R8C2 and R8C3 of row 8. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R9C3 - removing <2> from <269> leaving <69>
Squares R4C2, R6C2, R4C9 and R6C9 form a Type-3 Unique Rectangle on <49>. Upon close inspection, it is clear that:
(R4C9 or R6C9)<26>, R6C8<126> and R4C8<126> form a naked triplet on <126> in block 6. No other squares in the block can contain these possibilities
R5C7 - removing <26> from <269> leaving <9>
R7C5 is the only square in column 5 that can be <9>
R8C6 can only be <6>
R8C2 can only be <2>
R8C3 can only be <9>
R3C2 can only be <6>
R9C3 can only be <6>
R9C7 can only be <2>
R2C7 can only be <6>
R1C5 is the only square in row 1 that can be <6>
R5C5 can only be <2>
R5C1 can only be <6>
R3C5 can only be <8>
R4C4 can only be <6>
R3C8 can only be <2>
R2C6 can only be <5>
R1C9 can only be <8>
R4C8 can only be <1>
R6C4 can only be <8>
R4C6 can only be <9>
R6C8 can only be <6>
R6C1 can only be <2>
R9C4 can only be <5>
R6C9 can only be <4>
R7C8 can only be <8>
R6C2 can only be <9>
R4C9 can only be <2>
R7C9 can only be <6>
R9C9 can only be <9>
R9C6 can only be <8>
R2C4 can only be <2>
R1C3 can only be <2>
R2C3 can only be <8>
R4C2 can only be <4>
R6C6 can only be <1>
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