Oct 19 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C7 can only be <5>
R3C9 can only be <8>
R5C5 can only be <5>
R3C5 can only be <2>
R1C9 can only be <6>
R2C8 can only be <4>
R8C8 can only be <6>
R3C1 can only be <1>
R2C4 is the only square in row 2 that can be <5>
R4C9 is the only square in row 4 that can be <5>
R5C1 is the only square in row 5 that can be <6>
R8C4 is the only square in row 8 that can be <4>
R6C9 is the only square in column 9 that can be <3>
Squares R5C7 and R5C9 in row 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <47>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R5C2 - removing <7> from <178> leaving <18>
Squares R9C3 and R9C4 in row 9 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 row.
R9C1 - removing <8> from <348> leaving <34>
R9C5 - removing <8> from <36789> leaving <3679>
R9C6 - removing <1> from <1679> leaving <679>
Intersection of row 8 with block 8. The value <7> only appears in one or more of squares R8C4, R8C5 and R8C6 of row 8. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain this value.
R9C5 - removing <7> from <3679> leaving <369>
R9C6 - removing <7> from <679> leaving <69>
Squares R4C1<38>, R7C1<48> and R9C1<34> in column 1 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <348>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C1 - removing <8> from <278> leaving <27>
Squares R5C7, R5C9, R9C7 and R9C9 form a Type-1 Unique Rectangle on <47>.
R9C9 - removing <47> from <479> leaving <9>
R9C6 can only be <6>
R7C9 can only be <4>
R7C1 can only be <8>
R5C9 can only be <7>
R9C7 can only be <7>
R9C5 can only be <3>
R2C6 can only be <7>
R5C7 can only be <4>
R2C2 can only be <8>
R8C6 can only be <1>
R7C5 can only be <9>
R4C1 can only be <3>
R9C3 can only be <1>
R1C5 can only be <8>
R8C2 can only be <3>
R1C6 can only be <9>
R9C4 can only be <8>
R1C4 can only be <1>
R9C1 can only be <4>
R8C5 can only be <7>
R1C3 can only be <2>
R2C5 can only be <6>
R5C2 can only be <1>
R4C2 can only be <9>
R4C8 can only be <8>
R6C2 can only be <7>
R5C8 can only be <2>
R5C3 can only be <8>
R6C8 can only be <9>
R6C1 can only be <2>
R1C1 can only be <7>
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