 Jan 25 - Super Hard

## Reasoning

R8C2 can only be <1>

R7C2 can only be <7>

R2C5 is the only square in row 2 that can be <8>

R1C7 is the only square in row 1 that can be <8>

R3C3 is the only square in row 3 that can be <7>

R1C9 is the only square in row 1 that can be <7>

R4C6 is the only square in row 4 that can be <8>

R4C5 is the only square in row 4 that can be <7>

R5C5 is the only square in row 5 that can be <6>

R6C1 is the only square in row 6 that can be <1>

R4C7 is the only square in row 4 that can be <1>

R6C3 is the only square in row 6 that can be <8>

R9C6 is the only square in row 9 that can be <7>

R9C2 is the only square in row 9 that can be <8>

R9C1 is the only square in row 9 that can be <3>

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

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

Squares R7C6 and R7C7 in row 7 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 row.

R7C3 - removing <49> from <469> leaving <6>

R7C5 - removing <49> from <1459> leaving <15>

R7C8 - removing <4> from <1456> leaving <156>

Intersection of block 4 with row 5. The value <2> only appears in one or more of squares R5C1, R5C2 and R5C3 of block 4. These squares are the ones that intersect with row 5. Thus, the other (non-intersecting) squares of row 5 cannot contain this value.

R5C8 - removing <2> from <245> leaving <45>

Intersection of block 6 with column 9. The value <2> only appears in one or more of squares R4C9, R5C9 and R6C9 of block 6. These squares are the ones that intersect with column 9. Thus, the other (non-intersecting) squares of column 9 cannot contain this value.

R8C9 - removing <2> from <249> leaving <49>

R9C9 - removing <2> from <24569> leaving <4569>

R8C5 is the only square in row 8 that can be <2>

Squares R7C7 and R8C9 in block 9 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 block.

R9C7 - removing <49> from <249> leaving <2>

R9C8 - removing <4> from <12456> leaving <1256>

R9C9 - removing <49> from <4569> leaving <56>

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

R1C1 - removing <9> from <569> leaving <56>

Squares R3C7 (XY), R3C4 (XZ) and R2C9 (YZ) form an XY-Wing pattern on <6>. All squares that are buddies of both the XZ and YZ squares cannot be <6>.

R3C8 - removing <6> from <246> leaving <24>

R3C4 is the only square in row 3 that can be <6>

Squares R5C8 (XY), R3C8 (XZ) and R5C2 (YZ) form an XY-Wing pattern on <2>. All squares that are buddies of both the XZ and YZ squares cannot be <2>.

R3C2 - removing <2> from <23> leaving <3>

R3C8 is the only square in row 3 that can be <2>

Squares R3C5 and R7C6 form a remote naked pair. <49> can be removed from any square that is common to their groups.

R1C6 - removing <49> from <349> leaving <3>

R9C5 - removing <49> from <1459> leaving <15>

R6C6 can only be <4>

R7C6 can only be <9>

R7C7 can only be <4>

R3C7 can only be <9>

R8C9 can only be <9>

R8C1 can only be <4>

R2C9 can only be <6>

R2C1 can only be <9>

R9C9 can only be <5>

R1C8 can only be <4>

R3C5 can only be <4>

R4C1 can only be <5>

R9C3 can only be <9>

R1C3 can only be <2>

R9C5 can only be <1>

R6C9 can only be <2>

R7C8 can only be <1>

R1C2 can only be <5>

R5C3 can only be <4>

R1C4 can only be <1>

R5C8 can only be <5>

R4C4 can only be <2>

R1C1 can only be <6>

R5C2 can only be <2>

R4C9 can only be <4>

R6C4 can only be <5>

R6C5 can only be <3>

R7C5 can only be <5>

R9C8 can only be <6>

R9C4 can only be <4>

R1C5 can only be <9>

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