Oct 27 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C9 can only be <3>
R6C6 can only be <8>
R9C5 can only be <9>
R9C9 can only be <5>
R1C1 can only be <4>
R5C6 can only be <2>
R9C1 can only be <7>
R1C5 can only be <7>
R4C6 can only be <7>
R6C7 is the only square in column 7 that can be <1>
R5C5 is the only square in row 5 that can be <1>
R4C7 is the only square in column 7 that can be <3>
R4C4 can only be <9>
R4C8 is the only square in row 4 that can be <2>
R5C9 is the only square in column 9 that can be <8>
Squares R2C5 and R3C5 in column 5 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.
R6C5 - removing <34> from <3456> leaving <56>
Squares R5C8 and R6C8 in column 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <59>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C8 - removing <9> from <149> leaving <14>
Intersection of column 1 with block 7. The value <6> only appears in one or more of squares R7C1, R8C1 and R9C1 of column 1. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R8C2 - removing <6> from <468> leaving <48>
Intersection of column 2 with block 4. The values <56> only appears in one or more of squares R4C2, R5C2 and R6C2 of column 2. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain these values.
R4C3 - removing <5> from <58> leaving <8>
R5C1 - removing <5> from <359> leaving <39>
R6C3 - removing <5> from <459> leaving <49>
Squares R4C2, R4C5, R6C2 and R6C5 form a Type-1 Unique Rectangle on <56>.
R6C2 - removing <56> from <3456> leaving <34>
R6C5 is the only square in row 6 that can be <6>
R4C5 can only be <5>
R4C2 can only be <6>
R6C8 is the only square in row 6 that can be <5>
R5C8 can only be <9>
R5C1 can only be <3>
R5C4 can only be <4>
R6C2 can only be <4>
R5C2 can only be <5>
R6C4 can only be <3>
R6C3 can only be <9>
R8C2 can only be <8>
R3C3 can only be <5>
R8C1 can only be <6>
R8C5 can only be <2>
R2C2 can only be <3>
R7C5 can only be <8>
R2C5 can only be <4>
R2C8 can only be <1>
R3C5 can only be <3>
R2C9 can only be <9>
R8C8 can only be <4>
R2C1 can only be <8>
R3C9 can only be <2>
R3C1 can only be <9>
R7C3 can only be <4>
R3C7 can only be <4>
R7C9 can only be <6>
R7C7 can only be <2>
R7C1 can only be <5>
R8C9 can only be <1>
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