Oct 09 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R6C8 is the only square in row 6 that can be <3>
R6C2 is the only square in row 6 that can be <7>
R7C5 is the only square in row 7 that can be <2>
R6C5 can only be <5>
R6C1 can only be <4>
R6C9 can only be <2>
R3C7 is the only square in row 3 that can be <2>
R4C2 is the only square in row 4 that can be <2>
R7C2 is the only square in row 7 that can be <3>
R8C8 is the only square in row 8 that can be <1>
R8C3 is the only square in row 8 that can be <4>
R9C4 is the only square in row 9 that can be <3>
R8C2 is the only square in column 2 that can be <6>
R8C4 can only be <8>
R8C7 can only be <7>
R8C5 can only be <9>
R8C6 can only be <5>
R5C8 is the only square in row 5 that can be <7>
R5C9 is the only square in row 5 that can be <4>
R3C3 is the only square in column 3 that can be <7>
Squares R9C5 and R9C6 in row 9 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.
R9C9 - removing <6> from <568> leaving <58>
Squares R1C5<167>, R4C5<16> and R9C5<67> in column 5 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <167>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C5 - removing <16> from <1468> leaving <48>
Squares R1C1 and R1C9 in row 1 and R9C1 and R9C9 in row 9 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in columns 1 and 9 can be removed.
R5C1 - removing <5> from <1589> leaving <189>
Squares R4C1 and R4C9 in row 4 and R9C1 and R9C9 in row 9 form a Simple X-Wing pattern on possibility <8>. All other instances of this possibility in columns 1 and 9 can be removed.
R5C1 - removing <8> from <189> leaving <19>
Squares R9C5, R9C6, R1C5 and R1C6 form a Type-4 Unique Rectangle on <67>.
R1C5 - removing <6> from <167> leaving <17>
R1C6 - removing <6> from <679> leaving <79>
Squares R9C9 (XY), R1C9 (XZ) and R7C7 (YZ) form an XY-Wing pattern on <6>. All squares that are buddies of both the XZ and YZ squares cannot be <6>.
R2C7 - removing <6> from <69> leaving <9>
R3C8 can only be <4>
R3C5 can only be <8>
R3C2 can only be <9>
R2C5 can only be <4>
R1C6 is the only square in row 1 that can be <9>
R1C5 is the only square in row 1 that can be <7>
R9C5 can only be <6>
R9C6 can only be <7>
R4C5 can only be <1>
R5C1 is the only square in row 5 that can be <9>
R4C1 can only be <8>
R4C9 can only be <6>
R9C1 can only be <5>
R5C2 can only be <5>
R4C8 can only be <9>
R1C9 can only be <5>
R5C7 can only be <8>
R5C3 can only be <1>
R2C2 can only be <8>
R7C7 can only be <6>
R7C8 can only be <5>
R7C3 can only be <8>
R2C8 can only be <6>
R9C9 can only be <8>
R1C1 can only be <1>
R1C4 can only be <6>
R5C4 can only be <2>
R2C6 can only be <2>
R2C3 can only be <5>
R2C4 can only be <1>
R5C6 can only be <6>
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