Oct 11 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C6 can only be <2>
R4C1 can only be <1>
R5C5 can only be <1>
R9C4 can only be <9>
R9C6 can only be <1>
R4C9 can only be <3>
R6C1 can only be <7>
R6C9 can only be <1>
R7C1 can only be <2>
R7C5 can only be <3>
R9C5 can only be <2>
R1C4 can only be <5>
R8C5 can only be <5>
R1C3 is the only square in row 1 that can be <3>
R3C1 is the only square in row 3 that can be <5>
R3C5 is the only square in row 3 that can be <6>
R7C8 is the only square in row 7 that can be <1>
R2C7 is the only square in row 2 that can be <1>
R2C8 is the only square in row 2 that can be <2>
R5C7 is the only square in row 5 that can be <2>
R8C3 is the only square in row 8 that can be <1>
R8C8 is the only square in row 8 that can be <9>
Squares R8C2 and R9C1 in block 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <48>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R9C3 - removing <8> from <678> leaving <67>
Intersection of row 2 with block 1. The value <8> only appears in one or more of squares R2C1, R2C2 and R2C3 of row 2. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R1C1 - removing <8> from <489> leaving <49>
Squares R3C2, R3C8 and R3C9 in row 3, R5C8 and R5C9 in row 5 and R7C2 and R7C9 in row 7 form a Swordfish pattern on possibility <7>. All other instances of this possibility in columns 2, 8 and 9 can be removed.
R1C9 - removing <7> from <4789> leaving <489>
R2C2 - removing <7> from <789> leaving <89>
R9C9 - removing <7> from <4678> leaving <468>
Squares R5C8, R5C9, R3C8 and R3C9 form a Type-1 Unique Rectangle on <47>.
R3C9 - removing <47> from <479> leaving <9>
Squares R1C1 (XY), R9C1 (XZ) and R2C2 (YZ) form an XY-Wing pattern on <8>. All squares that are buddies of both the XZ and YZ squares cannot be <8>.
R8C2 - removing <8> from <48> leaving <4>
R8C7 can only be <8>
R3C2 can only be <7>
R9C1 can only be <8>
R5C1 can only be <9>
R3C8 can only be <4>
R7C2 can only be <6>
R2C3 can only be <8>
R5C8 can only be <7>
R1C7 can only be <7>
R1C9 can only be <8>
R1C1 can only be <4>
R5C9 can only be <4>
R9C9 can only be <6>
R7C9 can only be <7>
R5C2 can only be <8>
R9C3 can only be <7>
R9C7 can only be <4>
R1C5 can only be <9>
R2C2 can only be <9>
R5C3 can only be <6>
R2C5 can only be <7>
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