Dec 19 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C3 can only be <1>
R8C3 can only be <9>
R2C3 can only be <3>
R7C2 can only be <2>
R7C8 can only be <7>
R7C5 can only be <9>
R3C5 can only be <1>
R1C5 can only be <7>
R1C8 is the only square in row 1 that can be <5>
R5C6 is the only square in row 5 that can be <6>
R6C4 is the only square in row 6 that can be <1>
R6C6 is the only square in row 6 that can be <5>
R2C6 can only be <9>
R2C4 can only be <5>
R5C7 is the only square in row 5 that can be <5>
R8C9 is the only square in row 8 that can be <3>
R8C1 is the only square in row 8 that can be <4>
R9C2 is the only square in row 9 that can be <5>
R2C9 is the only square in column 9 that can be <4>
Squares R1C1 and R9C1 in column 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <16>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C1 - removing <1> from <178> leaving <78>
Squares R5C5 and R9C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <28>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R4C5 - removing <8> from <348> leaving <34>
R6C5 - removing <8> from <348> leaving <34>
Squares R3C8<89>, R4C8<489> and R6C8<48> in column 8 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <489>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C8 - removing <8> from <128> leaving <12>
R8C8 - removing <8> from <1268> leaving <126>
R9C8 - removing <8> from <1268> leaving <126>
Squares R8C4<27>, R8C6<78> and R8C7<28> in row 8 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <278>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R8C8 - removing <2> from <126> leaving <16>
Squares R2C2 and R2C8 in row 2 and R8C2 and R8C8 in row 8 form a Simple X-Wing pattern on possibility <1>. All other instances of this possibility in columns 2 and 8 can be removed.
R1C2 - removing <1> from <169> leaving <69>
R9C8 - removing <1> from <126> leaving <26>
Squares R3C2 and R3C8 in row 3 and R6C2 and R6C8 in row 6 form a Simple X-Wing pattern on possibility <8>. All other instances of this possibility in columns 2 and 8 can be removed.
R2C2 - removing <8> from <178> leaving <17>
R4C2 - removing <8> from <378> leaving <37>
R4C8 - removing <8> from <489> leaving <49>
R4C6 is the only square in row 4 that can be <8>
R8C6 can only be <7>
R5C5 can only be <2>
R9C5 can only be <8>
R8C4 can only be <2>
R9C9 can only be <1>
R9C1 can only be <6>
R1C9 can only be <9>
R8C8 can only be <6>
R1C2 can only be <6>
R5C9 can only be <8>
R3C8 can only be <8>
R3C2 can only be <9>
R6C8 can only be <4>
R2C7 can only be <2>
R5C1 can only be <7>
R6C5 can only be <3>
R4C8 can only be <9>
R8C7 can only be <8>
R8C2 can only be <1>
R9C8 can only be <2>
R1C1 can only be <1>
R2C8 can only be <1>
R2C2 can only be <7>
R2C1 can only be <8>
R4C2 can only be <3>
R4C5 can only be <4>
R6C2 can only be <8>
R4C4 can only be <7>
R5C4 can only be <9>
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