Jan 23 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C4 can only be <7>
R5C7 can only be <8>
R6C3 can only be <4>
R7C4 can only be <6>
R7C5 can only be <8>
R4C6 can only be <9>
R4C7 can only be <4>
R6C4 can only be <1>
R6C6 can only be <8>
R3C6 can only be <7>
R4C3 can only be <2>
R5C5 can only be <3>
R5C8 can only be <2>
R6C7 can only be <7>
R3C4 can only be <5>
R7C6 can only be <2>
R8C5 can only be <7>
R1C2 is the only square in row 1 that can be <2>
R2C2 is the only square in row 2 that can be <7>
R8C9 is the only square in row 8 that can be <2>
R9C8 is the only square in row 9 that can be <7>
Squares R3C1 and R3C5 in row 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <19>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R3C2 - removing <9> from <689> leaving <68>
R3C8 - removing <1> from <148> leaving <48>
R3C9 - removing <9> from <469> leaving <46>
Squares R7C2 and R7C9 in row 7 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 row.
R7C1 - removing <9> from <139> leaving <13>
R7C8 - removing <4> from <134> leaving <13>
Intersection of column 1 with block 1. The value <9> only appears in one or more of squares R1C1, R2C1 and R3C1 of column 1. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R1C3 - removing <9> from <159> leaving <15>
R2C3 - removing <9> from <15689> leaving <1568>
R1C7 is the only square in row 1 that can be <9>
R2C9 can only be <6>
R3C9 can only be <4>
R3C8 can only be <8>
R7C9 can only be <9>
R7C2 can only be <4>
R3C2 can only be <6>
R9C2 can only be <9>
R5C2 can only be <5>
R5C3 can only be <9>
R8C2 can only be <8>
R2C3 is the only square in row 2 that can be <8>
R8C8 is the only square in row 8 that can be <4>
Squares R3C1, R3C5, R2C1 and R2C5 form a Type-1 Unique Rectangle on <19>.
R2C1 - removing <19> from <159> leaving <5>
R8C1 can only be <3>
R1C3 can only be <1>
R8C7 can only be <6>
R7C1 can only be <1>
R8C3 can only be <5>
R9C7 can only be <1>
R9C3 can only be <6>
R2C7 can only be <3>
R7C8 can only be <3>
R1C8 can only be <5>
R3C1 can only be <9>
R2C8 can only be <1>
R2C5 can only be <9>
R3C5 can only be <1>
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