The full reasoning can be found below the Sudoku.
Mar 27 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C5 can only be <1>
R4C5 is the only square in row 4 that can be <5>
R4C6 is the only square in row 4 that can be <3>
R5C4 is the only square in row 5 that can be <1>
R6C5 is the only square in row 6 that can be <8>
R6C6 is the only square in row 6 that can be <4>
R7C5 is the only square in row 7 that can be <4>
R9C3 is the only square in row 9 that can be <8>
R3C5 is the only square in column 5 that can be <3>
R7C8 is the only square in column 8 that can be <3>
R3C8 is the only square in column 8 that can be <1>
R2C1 is the only square in row 2 that can be <1>
R2C3 is the only square in row 2 that can be <3>
R8C7 is the only square in row 8 that can be <1>
R7C2 is the only square in row 7 that can be <1>
R8C1 is the only square in row 8 that can be <3>
Squares R2C4 and R2C6 in row 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <27>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R2C7 - removing <27> from <2579> leaving <59>
R2C9 - removing <2> from <259> leaving <59>
Squares R3C1 and R3C3 in row 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <47>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R3C2 - removing <7> from <67> leaving <6>
R3C7 - removing <7> from <2678> leaving <268>
Squares R3C1 and R3C3 in block 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <47>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R1C2 - removing <7> from <579> leaving <59>
R1C3 - removing <7> from <579> leaving <59>
Squares R1C2 and R1C3 in row 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <59>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R1C7 - removing <59> from <5679> leaving <67>
R1C8 - removing <9> from <679> leaving <67>
Intersection of row 7 with block 9. The value <6> only appears in one or more of squares R7C7, R7C8 and R7C9 of row 7. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R8C9 - removing <6> from <2569> leaving <259>
Squares R3C1, R3C3, R5C1 and R5C3 form a Type-3 Unique Rectangle on <47>. Upon close inspection, it is clear that:
(R5C1 or R5C3)<29> and R4C2<29> form a naked pair on <29> in block 4. No other squares in the block can contain these possibilities
R6C2 - removing <29> from <279> leaving <7>
(R5C1 or R5C3)<29> and R5C5<29> form a naked pair on <29> in row 5. No other squares in the row can contain these possibilities
R5C6 - removing <2> from <267> leaving <67>
R5C7 - removing <29> from <2689> leaving <68>
R5C9 - removing <29> from <2689> leaving <68>
(R5C1 or R5C3)<29>, R5C9<2689>, R5C7<2689> and R5C5<29> form a naked quad on <2689> in row 5. No other squares in the row can contain these possibilities
R5C6 - removing <6> from <67> leaving <7>
R2C6 can only be <2>
R2C4 can only be <7>
R8C6 can only be <6>
R4C4 is the only square in column 4 that can be <6>
R1C8 is the only square in column 8 that can be <6>
R1C7 can only be <7>
R9C8 is the only square in row 9 that can be <7>
Squares R4C2 and R9C5 form a remote naked pair. <29> can be removed from any square that is common to their groups.
R9C2 - removing <29> from <259> leaving <5>
R1C2 can only be <9>
R1C3 can only be <5>
R4C2 can only be <2>
R4C8 can only be <9>
R6C8 can only be <2>
R6C4 can only be <9>
R8C4 can only be <2>
R5C5 can only be <2>
R8C3 can only be <9>
R9C5 can only be <9>
R9C7 can only be <2>
R3C7 can only be <8>
R3C9 can only be <2>
R5C7 can only be <6>
R5C9 can only be <8>
R7C7 can only be <9>
R7C1 can only be <7>
R7C9 can only be <6>
R2C7 can only be <5>
R8C9 can only be <5>
R5C3 can only be <4>
R2C9 can only be <9>
R5C1 can only be <9>
R3C3 can only be <7>
R7C3 can only be <2>
R3C1 can only be <4>
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