Oct 10 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C8 can only be <5>
R8C9 can only be <9>
R9C2 can only be <6>
R8C1 can only be <7>
R7C3 can only be <2>
R7C7 can only be <7>
R9C8 can only be <2>
R9C4 can only be <7>
R9C6 can only be <8>
R1C6 is the only square in row 1 that can be <7>
R6C7 is the only square in row 6 that can be <2>
R7C6 is the only square in row 7 that can be <1>
Squares R1C4 and R7C4 in column 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <34>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C4 - removing <34> from <2349> leaving <29>
R3C4 - removing <4> from <4569> leaving <569>
R5C4 - removing <34> from <346> leaving <6>
Squares R2C6 and R5C6 in column 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <34>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R3C6 - removing <4> from <456> leaving <56>
Squares R1C4 and R2C6 in block 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <34>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R2C5 - removing <34> from <2348> leaving <28>
R3C5 - removing <4> from <4568> leaving <568>
Intersection of block 5 with column 5. The values <57> only appears in one or more of squares R4C5, R5C5 and R6C5 of block 5. These squares are the ones that intersect with column 5. Thus, the other (non-intersecting) squares of column 5 cannot contain these values.
R3C5 - removing <5> from <568> leaving <68>
R8C5 - removing <5> from <256> leaving <26>
Squares R1C2 and R5C6 form a remote naked pair. <34> can be removed from any square that is common to their groups.
R5C2 - removing <34> from <348> leaving <8>
R6C9 is the only square in row 6 that can be <8>
R2C9 can only be <4>
R2C6 can only be <3>
R4C9 can only be <3>
R3C7 can only be <8>
R3C5 can only be <6>
R2C1 can only be <9>
R5C6 can only be <4>
R1C4 can only be <4>
R3C6 can only be <5>
R8C5 can only be <2>
R3C4 can only be <9>
R8C6 can only be <6>
R5C7 can only be <1>
R4C7 can only be <4>
R8C4 can only be <5>
R2C5 can only be <8>
R1C2 can only be <3>
R7C4 can only be <3>
R2C4 can only be <2>
R4C1 can only be <6>
R3C3 can only be <4>
R6C3 can only be <7>
R6C1 can only be <3>
R4C2 can only be <5>
R6C5 can only be <5>
R6C8 can only be <6>
R5C3 can only be <9>
R6C2 can only be <4>
R4C5 can only be <7>
R7C5 can only be <4>
R4C8 can only be <9>
R5C5 can only be <3>
R4C3 can only be <1>
R5C8 can only be <7>
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