Jun 27 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R8C5 can only be <9>
R9C5 can only be <1>
R5C4 is the only square in row 5 that can be <2>
R5C5 is the only square in row 5 that can be <5>
R6C4 is the only square in column 4 that can be <1>
Squares R2C5 and R6C5 in column 5 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 column.
R4C5 - removing <6> from <678> leaving <78>
Squares R2C5 and R3C4 in block 2 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.
R3C6 - removing <3> from <378> leaving <78>
Intersection of column 9 with block 9. The value <9> only appears in one or more of squares R7C9, R8C9 and R9C9 of column 9. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R7C7 - removing <9> from <56789> leaving <5678>
R9C7 - removing <9> from <2679> leaving <267>
Squares R1C1 and R5C1 in column 1 and R1C9 and R5C9 in column 9 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in rows 1 and 5 can be removed.
R1C3 - removing <4> from <1457> leaving <157>
R5C6 - removing <4> from <478> leaving <78>
R1C7 - removing <4> from <1458> leaving <158>
Squares R3C6 and R5C6 in column 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <78>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R4C6 - removing <78> from <4789> leaving <49>
Squares R1C5 and R1C7 in row 1, R4C3 and R4C5 in row 4 and R8C3 and R8C7 in row 8 form a Swordfish pattern on possibility <8>. All other instances of this possibility in columns 3, 5 and 7 can be removed.
R3C7 - removing <8> from <12568> leaving <1256>
R7C3 - removing <8> from <1678> leaving <167>
R7C7 - removing <8> from <5678> leaving <567>
Squares R2C3 (XY), R2C5 (XZ) and R6C3 (YZ) form an XY-Wing pattern on <6>. All squares that are buddies of both the XZ and YZ squares cannot be <6>.
R6C5 - removing <6> from <36> leaving <3>
R2C5 can only be <6>
R2C7 can only be <4>
R3C4 can only be <3>
R2C3 can only be <3>
R1C9 can only be <5>
R7C4 can only be <4>
R7C6 can only be <3>
R4C4 can only be <6>
R1C1 is the only square in row 1 that can be <4>
R3C3 is the only square in row 3 that can be <5>
R5C9 is the only square in row 5 that can be <4>
R7C7 is the only square in row 7 that can be <5>
Squares R3C8 (XY), R5C8 (XZ) and R3C6 (YZ) form an XY-Wing pattern on <7>. All squares that are buddies of both the XZ and YZ squares cannot be <7>.
R5C6 - removing <7> from <78> leaving <8>
R5C2 can only be <1>
R3C6 can only be <7>
R4C5 can only be <7>
R1C5 can only be <8>
R4C7 can only be <9>
R4C6 can only be <4>
R6C7 can only be <6>
R5C1 can only be <6>
R3C2 can only be <9>
R6C3 can only be <4>
R5C8 can only be <7>
R1C7 can only be <1>
R1C3 can only be <7>
R3C7 can only be <2>
R3C1 can only be <1>
R7C2 can only be <8>
R3C9 can only be <6>
R8C7 can only be <8>
R9C7 can only be <7>
R3C8 can only be <8>
R7C9 can only be <9>
R4C3 can only be <8>
R6C6 can only be <9>
R7C8 can only be <6>
R8C3 can only be <2>
R9C9 can only be <2>
R9C1 can only be <9>
R9C3 can only be <6>
R7C3 can only be <1>
R7C1 can only be <7>
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