Sep 08 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C1 can only be <4>
R5C9 can only be <1>
R6C4 can only be <2>
R5C6 can only be <8>
R5C4 can only be <9>
R6C6 can only be <7>
R6C5 can only be <6>
R5C5 can only be <5>
R1C4 can only be <3>
R1C6 can only be <2>
R9C6 can only be <4>
R9C4 can only be <1>
R4C6 can only be <3>
R4C4 can only be <4>
R4C5 can only be <1>
R1C3 is the only square in row 1 that can be <5>
R2C7 is the only square in row 2 that can be <1>
R2C1 is the only square in row 2 that can be <3>
R3C7 is the only square in row 3 that can be <3>
R7C8 is the only square in row 7 that can be <1>
R8C5 is the only square in row 8 that can be <3>
R7C2 is the only square in row 7 that can be <3>
R7C3 is the only square in row 7 that can be <4>
R2C5 is the only square in row 2 that can be <4>
R3C2 is the only square in row 3 that can be <4>
R8C7 is the only square in row 8 that can be <5>
R9C3 is the only square in column 3 that can be <9>
Squares R2C9 and R8C9 in column 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <27>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R3C9 - removing <27> from <2679> leaving <69>
R7C9 - removing <2> from <269> leaving <69>
Intersection of row 1 with block 3. The value <8> only appears in one or more of squares R1C7, R1C8 and R1C9 of row 1. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R3C8 - removing <8> from <268> leaving <26>
Intersection of row 8 with block 7. The value <8> only appears in one or more of squares R8C1, R8C2 and R8C3 of row 8. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R7C1 - removing <8> from <268> leaving <26>
Squares R1C2 and R1C8 in row 1 and R9C2 and R9C8 in row 9 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in columns 2 and 8 can be removed.
R3C8 - removing <6> from <26> leaving <2>
R2C9 can only be <7>
R2C3 can only be <2>
R8C9 can only be <2>
R8C1 can only be <8>
R8C3 can only be <7>
R3C1 can only be <6>
R3C3 can only be <8>
R9C2 can only be <6>
R9C8 can only be <8>
R1C2 can only be <7>
R7C1 can only be <2>
R9C5 can only be <2>
R9C7 can only be <7>
R1C8 can only be <6>
R7C7 can only be <9>
R1C5 can only be <9>
R1C7 can only be <8>
R3C5 can only be <7>
R3C9 can only be <9>
R7C9 can only be <6>
R7C5 can only be <8>
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