Mar 08 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C5 can only be <2>
R2C6 can only be <5>
R8C4 can only be <4>
R2C5 can only be <9>
R5C5 can only be <3>
R2C4 can only be <6>
R5C6 can only be <4>
R5C4 can only be <2>
R8C6 can only be <3>
R6C7 is the only square in row 6 that can be <3>
R1C9 is the only square in row 1 that can be <3>
R7C2 is the only square in row 7 that can be <3>
Intersection of row 1 with block 1. The value <5> only appears in one or more of squares R1C1, R1C2 and R1C3 of row 1. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R3C1 - removing <5> from <568> leaving <68>
R3C2 - removing <5> from <2589> leaving <289>
R3C3 - removing <5> from <2569> leaving <269>
Intersection of column 2 with block 4. The value <5> 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 this value.
R5C1 - removing <5> from <5678> leaving <678>
R5C3 - removing <5> from <15679> leaving <1679>
R6C3 - removing <5> from <456> leaving <46>
Intersection of column 9 with block 9. The value <4> only appears in one or more of squares R7C9, R8C9 and R9C9 of column 9. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R7C7 - removing <4> from <1489> leaving <189>
R7C8 - removing <4> from <1478> leaving <178>
R9C7 - removing <4> from <124> leaving <12>
Squares R2C2 and R2C8 in row 2 and R8C2 and R8C8 in row 8 form a Simple X-Wing pattern on possibility <2>. All other instances of this possibility in columns 2 and 8 can be removed.
R3C2 - removing <2> from <289> leaving <89>
R3C8 - removing <2> from <1256> leaving <156>
R4C8 - removing <2> from <248> leaving <48>
R4C7 is the only square in row 4 that can be <2>
R9C7 can only be <1>
R9C5 can only be <7>
R3C7 can only be <6>
R3C1 can only be <8>
R1C7 can only be <4>
R8C5 can only be <1>
R2C8 can only be <2>
R2C2 can only be <4>
R8C8 can only be <7>
R3C9 can only be <5>
R3C2 can only be <9>
R3C3 can only be <2>
R3C8 can only be <1>
R5C9 can only be <9>
R5C7 can only be <8>
R7C9 can only be <4>
R7C1 can only be <7>
R9C9 can only be <2>
R8C2 can only be <2>
R7C8 can only be <8>
R4C2 can only be <8>
R6C2 can only be <5>
R4C8 can only be <4>
R4C3 can only be <9>
R7C7 can only be <9>
R6C8 can only be <6>
R5C2 can only be <1>
R6C3 can only be <4>
R5C8 can only be <5>
R7C3 can only be <1>
R5C1 can only be <6>
R5C3 can only be <7>
R1C1 can only be <5>
R9C3 can only be <5>
R9C1 can only be <4>
R1C3 can only be <6>
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