Jan 30 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R3C4 is the only square in row 3 that can be <4>
R4C8 is the only square in row 4 that can be <5>
R5C5 is the only square in row 5 that can be <2>
Squares R4C5 and R4C6 in row 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <37>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R4C2 - removing <37> from <3479> leaving <49>
R4C3 - removing <7> from <479> leaving <49>
Squares R4C2 and R4C3 in block 4 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.
R5C2 - removing <4> from <3478> leaving <378>
R5C3 - removing <4> from <1478> leaving <178>
R6C2 - removing <9> from <789> leaving <78>
Squares R4C5 and R4C6 in block 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <37>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R6C4 - removing <7> from <678> leaving <68>
R6C5 - removing <7> from <678> leaving <68>
R4C5 is the only square in column 5 that can be <7>
R4C6 can only be <3>
Squares R6C4 and R6C5 in row 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <68>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R6C2 - removing <8> from <78> leaving <7>
R6C8 - removing <6> from <169> leaving <19>
R5C7 is the only square in row 5 that can be <7>
R5C8 is the only square in row 5 that can be <4>
R5C9 is the only square in row 5 that can be <6>
R9C2 is the only square in row 9 that can be <4>
R4C2 can only be <9>
R4C3 can only be <4>
R8C7 is the only square in row 8 that can be <4>
R9C8 is the only square in row 9 that can be <2>
R3C7 is the only square in row 3 that can be <2>
R7C2 is the only square in row 7 that can be <2>
R2C2 is the only square in column 2 that can be <5>
R3C3 is the only square in column 3 that can be <7>
R1C8 is the only square in column 8 that can be <6>
Intersection of column 6 with block 8. The values <56> only appears in one or more of squares R7C6, R8C6 and R9C6 of column 6. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain these values.
R7C4 - removing <6> from <3679> leaving <379>
R8C5 - removing <6> from <368> leaving <38>
Squares R6C4, R6C5, R2C4 and R2C5 form a Type-2 Unique Rectangle on <68>.
R1C4 - removing <3> from <378> leaving <78>
R2C1 - removing <3> from <1389> leaving <189>
R2C7 - removing <3> from <139> leaving <19>
R1C2 is the only square in row 1 that can be <3>
R5C2 can only be <8>
R5C3 can only be <1>
R5C1 can only be <3>
R3C8 is the only square in row 3 that can be <3>
R8C8 can only be <9>
R8C9 can only be <5>
R6C8 can only be <1>
R7C9 can only be <1>
R6C7 can only be <9>
R7C7 can only be <3>
R1C9 can only be <8>
R1C4 can only be <7>
R3C9 can only be <9>
R2C7 can only be <1>
R1C6 can only be <1>
R7C4 can only be <9>
R3C6 can only be <8>
R3C1 can only be <1>
R8C6 can only be <6>
R9C6 can only be <5>
R7C1 can only be <5>
R7C3 can only be <6>
R9C4 can only be <8>
R8C3 can only be <8>
R6C4 can only be <6>
R8C5 can only be <3>
R9C1 can only be <9>
R7C6 can only be <7>
R6C5 can only be <8>
R2C4 can only be <3>
R2C3 can only be <9>
R2C5 can only be <6>
R2C1 can only be <8>
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