Jan 17 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C9 can only be <5>
R5C6 can only be <1>
R6C9 can only be <9>
R9C6 can only be <8>
R6C5 can only be <8>
R1C5 can only be <7>
R6C1 can only be <1>
R9C4 can only be <2>
R1C6 can only be <4>
R1C4 can only be <8>
R3C5 can only be <1>
R4C5 can only be <2>
R4C1 can only be <7>
R5C5 can only be <5>
R5C4 can only be <7>
R1C2 is the only square in row 1 that can be <5>
R3C7 is the only square in row 3 that can be <3>
R7C3 is the only square in row 7 that can be <3>
R8C3 is the only square in row 8 that can be <1>
R8C7 is the only square in row 8 that can be <5>
R9C8 is the only square in row 9 that can be <1>
R7C2 is the only square in column 2 that can be <2>
R8C1 can only be <8>
R8C9 can only be <2>
R1C8 is the only square in column 8 that can be <2>
Intersection of row 7 with block 9. The values <78> only appears in one or more of squares R7C7, R7C8 and R7C9 of row 7. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain these values.
R9C7 - removing <7> from <479> leaving <49>
Squares R7C8 and R9C7 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.
R7C7 - removing <49> from <4789> leaving <78>
R7C9 - removing <4> from <478> leaving <78>
Squares R1C7<69>, R5C7<46> and R9C7<49> in column 7 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 column.
R2C7 - removing <4> from <478> leaving <78>
Squares R7C7, R7C9, R2C7 and R2C9 form a Type-1 Unique Rectangle on <78>.
R2C9 - removing <78> from <478> leaving <4>
R2C1 can only be <2>
R5C9 can only be <6>
R3C8 can only be <9>
R7C8 can only be <4>
R1C7 can only be <6>
R5C7 can only be <4>
R7C1 can only be <6>
R9C7 can only be <9>
R9C5 can only be <6>
R1C3 can only be <9>
R5C1 can only be <9>
R5C3 can only be <2>
R7C5 can only be <9>
R3C1 can only be <4>
R9C3 can only be <7>
R9C2 can only be <4>
R2C3 can only be <8>
R2C7 can only be <7>
R3C3 can only be <6>
R7C7 can only be <8>
R3C9 can only be <8>
R3C2 can only be <7>
R7C9 can only be <7>
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