Aug 01 - Super Hard

## Reasoning

R1C6 is the only square in row 1 that can be <2>

R3C2 is the only square in row 3 that can be <8>

R3C6 is the only square in row 3 that can be <3>

R9C3 is the only square in row 9 that can be <2>

R4C9 is the only square in row 4 that can be <2>

R6C2 is the only square in row 6 that can be <2>

R1C3 is the only square in column 3 that can be <6>

R7C5 is the only square in column 5 that can be <7>

R6C9 is the only square in column 9 that can be <3>

R4C4 is the only square in column 4 that can be <3>

R3C9 is the only square in column 9 that can be <6>

R1C7 is the only square in block 3 that can be <7>

Squares R7C1 and R7C3 in row 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <39>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.

R7C4 - removing <9> from <569> leaving <56>

R7C8 - removing <3> from <356> leaving <56>

R8C8 is the only square in column 8 that can be <3>

R8C1 is the only square in row 8 that can be <7>

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

R9C8 is the only square in row 9 that can be <7>

R9C1 is the only square in row 9 that can be <8>

R6C1 can only be <5>

Squares R6C4 and R6C6 in row 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <67>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.

R6C7 - removing <6> from <468> leaving <48>

Squares R1C4 and R3C5 in block 2 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 block.

R2C4 - removing <59> from <4579> leaving <47>

R2C6 - removing <59> from <4579> leaving <47>

Squares R6C4 and R6C6 in block 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <67>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.

R4C6 - removing <6> from <569> leaving <59>

Intersection of column 8 with block 6. The value <1> only appears in one or more of squares R4C8, R5C8 and R6C8 of column 8. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain this value.

R4C7 - removing <1> from <1568> leaving <568>

R5C7 - removing <1> from <145> leaving <45>

R9C7 is the only square in column 7 that can be <1>

Squares R3C7 and R4C6 form a remote naked pair. <59> can be removed from any square that is common to their groups.

R4C7 - removing <5> from <568> leaving <68>

Squares R3C5 and R5C5 in column 5 and R3C7 and R5C7 in column 7 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in rows 3 and 5 can be removed.

R5C8 - removing <5> from <15> leaving <1>

Squares R7C4 (XY), R1C4 (XZ) and R8C6 (YZ) form an XY-Wing pattern on <9>. All squares that are buddies of both the XZ and YZ squares cannot be <9>.

R9C4 - removing <9> from <459> leaving <45>

R1C4 is the only square in column 4 that can be <9>

R3C5 can only be <5>

R3C7 can only be <9>

R5C5 can only be <9>

R8C7 can only be <6>

R5C2 can only be <3>

R4C6 can only be <5>

R8C6 can only be <9>

R4C7 can only be <8>

R7C8 can only be <5>

R4C8 can only be <6>

R6C7 can only be <4>

R5C3 can only be <4>

R1C2 can only be <5>

R5C7 can only be <5>

R6C3 can only be <8>

R7C4 can only be <6>

R9C9 can only be <9>

R9C6 can only be <4>

R9C4 can only be <5>

R2C6 can only be <7>

R1C9 can only be <1>

R2C2 can only be <9>

R1C1 can only be <3>

R2C9 can only be <5>

R2C3 can only be <1>

R4C3 can only be <9>

R2C4 can only be <4>

R6C6 can only be <6>

R4C1 can only be <1>

R7C3 can only be <3>

R6C4 can only be <7>

R7C1 can only be <9>

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