Jul 10 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C1 can only be <4>
R1C9 can only be <1>
R3C7 can only be <6>
R5C5 can only be <8>
R1C6 can only be <2>
R2C8 can only be <7>
R4C8 can only be <8>
R6C2 is the only square in row 6 that can be <8>
R7C5 is the only square in row 7 that can be <2>
R7C4 is the only square in row 7 that can be <4>
R2C4 can only be <6>
R2C5 is the only square in row 2 that can be <4>
R7C6 is the only square in row 7 that can be <7>
R3C4 is the only square in row 3 that can be <7>
R3C6 is the only square in row 3 that can be <8>
R9C4 is the only square in row 9 that can be <8>
R9C5 is the only square in row 9 that can be <3>
R1C5 can only be <9>
R8C4 can only be <9>
R1C4 can only be <3>
R9C1 is the only square in row 9 that can be <9>
Squares R6C1 and R6C9 in row 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <56>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R6C3 - removing <5> from <1345> leaving <134>
R6C7 - removing <5> from <345> leaving <34>
R6C8 - removing <6> from <136> leaving <13>
Squares R6C9 and R9C9 in column 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <56>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R4C9 - removing <5> from <579> leaving <79>
R5C9 - removing <6> from <679> leaving <79>
Intersection of column 1 with block 4. The values <567> only appears in one or more of squares R4C1, R5C1 and R6C1 of column 1. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain these values.
R4C2 - removing <5> from <25> leaving <2>
R4C3 - removing <5> from <459> leaving <49>
R5C7 is the only square in row 5 that can be <2>
Squares R2C2 and R8C5 form a remote naked pair. <15> can be removed from any square that is common to their groups.
R8C2 - removing <5> from <35> leaving <3>
R8C8 can only be <6>
R5C2 can only be <1>
R7C3 can only be <5>
R9C9 can only be <5>
R9C6 can only be <6>
R6C9 can only be <6>
R7C7 can only be <3>
R5C8 can only be <3>
R2C2 can only be <5>
R5C3 can only be <9>
R6C8 can only be <1>
R6C7 can only be <4>
R6C3 can only be <3>
R4C7 can only be <5>
R6C1 can only be <5>
R3C3 can only be <1>
R2C6 can only be <1>
R8C6 can only be <5>
R3C5 can only be <5>
R8C5 can only be <1>
R4C1 can only be <7>
R5C9 can only be <7>
R4C3 can only be <4>
R5C1 can only be <6>
R4C9 can only be <9>
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