Sep 26 - Super Hard

Puzzle Copyright © Kevin Stone

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## Reasoning

R6C1 can only be <3>

R6C5 can only be <1>

R4C1 can only be <6>

R4C5 can only be <3>

R2C2 is the only square in row 2 that can be <1>

R2C4 is the only square in row 2 that can be <2>

R5C8 is the only square in row 5 that can be <6>

R5C7 is the only square in row 5 that can be <3>

R2C8 is the only square in row 2 that can be <3>

R6C2 is the only square in row 6 that can be <5>

R7C2 is the only square in row 7 that can be <3>

R8C4 is the only square in row 8 that can be <3>

R8C3 is the only square in column 3 that can be <8>

R9C8 is the only square in row 9 that can be <8>

R6C8 can only be <9>

R6C9 can only be <8>

R4C9 can only be <1>

R4C8 can only be <2>

R4C2 can only be <8>

R3C7 is the only square in row 3 that can be <8>

R2C6 is the only square in row 2 that can be <8>

R8C8 is the only square in row 8 that can be <1>

R9C4 is the only square in row 9 that can be <9>

Squares R5C6 and R9C6 in column 6 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 column.

R1C6 - removing <47> from <4567> leaving <56>

R8C6 - removing <47> from <4567> leaving <56>

Squares R8C1 and R9C2 in block 7 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.

R8C2 - removing <47> from <2467> leaving <26>

Intersection of row 3 with block 1. The value <9> only appears in one or more of squares R3C1, R3C2 and R3C3 of row 3. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.

R2C3 - removing <9> from <569> leaving <56>

Squares R2C1 and R8C1 in column 1 and R2C9 and R8C9 in column 9 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in rows 2 and 8 can be removed.

R2C5 - removing <4> from <4567> leaving <567>

R8C5 - removing <4> from <4567> leaving <567>

Squares R2C3 and R2C5 in row 2 and R7C3 and R7C5 in row 7 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in columns 3 and 5 can be removed.

R8C5 - removing <6> from <567> leaving <57>

Squares R2C1 and R2C5 in row 2 and R8C1 and R8C5 in row 8 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in columns 1 and 5 can be removed.

R3C5 - removing <7> from <457> leaving <45>

Squares R3C5 (XY), R1C4 (XZ) and R8C5 (YZ) form an XY-Wing pattern on <7>. All squares that are buddies of both the XZ and YZ squares cannot be <7>.

R2C5 - removing <7> from <567> leaving <56>

R2C1 is the only square in row 2 that can be <7>

R8C1 can only be <4>

R8C9 can only be <9>

R9C2 can only be <7>

R2C9 can only be <4>

R9C6 can only be <4>

R5C6 can only be <7>

R5C4 can only be <4>

R1C4 can only be <7>

R1C8 can only be <5>

R1C6 can only be <6>

R3C8 can only be <7>

R7C8 can only be <4>

R2C7 can only be <9>

R1C2 can only be <4>

R8C6 can only be <5>

R2C5 can only be <5>

R2C3 can only be <6>

R3C5 can only be <4>

R7C5 can only be <6>

R8C5 can only be <7>

R3C2 can only be <9>

R7C3 can only be <2>

R8C7 can only be <2>

R8C2 can only be <6>

R7C7 can only be <5>

R3C3 can only be <5>

R5C2 can only be <2>

R5C3 can only be <9>

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