Jan 06 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C6 can only be <3>
R5C5 can only be <9>
R8C7 can only be <2>
R1C3 can only be <7>
R1C7 can only be <8>
R1C4 can only be <5>
R8C6 can only be <7>
R4C3 is the only square in row 4 that can be <5>
R7C6 is the only square in row 7 that can be <2>
R7C8 is the only square in row 7 that can be <5>
Squares R7C5 and R8C4 in block 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <18>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C4 - removing <18> from <1348> leaving <34>
Squares R2C4<49>, R2C6<469> and R3C6<469> in block 2 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <469>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R3C4 - removing <49> from <1489> leaving <18>
Squares R2C3<346>, R5C3<34> and R9C3<46> in column 3 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <346>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R6C3 - removing <3> from <138> leaving <18>
Squares R2C3 and R2C7 in row 2 and R5C3 and R5C7 in row 5 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in columns 3 and 7 can be removed.
R6C7 - removing <3> from <1369> leaving <169>
R9C7 - removing <3> from <36> leaving <6>
R9C3 can only be <4>
R7C9 can only be <3>
R7C4 can only be <4>
R3C9 can only be <7>
R9C6 can only be <9>
R5C3 can only be <3>
R7C2 can only be <1>
R9C4 can only be <3>
R4C9 can only be <2>
R6C9 can only be <6>
R5C7 can only be <4>
R2C3 can only be <6>
R7C5 can only be <8>
R4C2 can only be <4>
R6C2 can only be <2>
R8C3 can only be <8>
R2C4 can only be <9>
R7C1 can only be <6>
R3C5 can only be <1>
R8C4 can only be <1>
R6C3 can only be <1>
R3C4 can only be <8>
R2C6 can only be <4>
R3C1 can only be <4>
R2C7 can only be <3>
R3C6 can only be <6>
R3C8 can only be <9>
R3C2 can only be <3>
R4C1 can only be <9>
R4C8 can only be <7>
R6C8 can only be <3>
R4C7 can only be <1>
R6C1 can only be <8>
R6C7 can only be <9>
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