Jan 13 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R6C8 can only be <3>
R6C7 can only be <7>
R2C8 is the only square in row 2 that can be <2>
R8C9 is the only square in row 8 that can be <3>
R3C9 can only be <1>
R2C9 can only be <5>
R5C9 can only be <8>
R7C9 can only be <7>
R7C4 can only be <5>
R1C2 is the only square in row 1 that can be <5>
R5C8 is the only square in row 5 that can be <5>
R9C7 is the only square in row 9 that can be <5>
R6C3 is the only square in column 3 that can be <2>
R6C5 can only be <8>
R6C2 can only be <1>
R2C1 is the only square in row 2 that can be <1>
R7C3 is the only square in row 7 that can be <1>
R7C1 is the only square in row 7 that can be <4>
R7C7 is the only square in column 7 that can be <2>
R7C6 can only be <6>
R3C1 is the only square in row 3 that can be <6>
R2C5 is the only square in row 2 that can be <6>
R4C7 is the only square in column 7 that can be <6>
R4C8 can only be <9>
R1C8 can only be <4>
Intersection of row 9 with block 7. The value <8> only appears in one or more of squares R9C1, R9C2 and R9C3 of row 9. 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 <8> from <6789> leaving <679>
Intersection of column 3 with block 1. The value <9> only appears in one or more of squares R1C3, R2C3 and R3C3 of column 3. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R2C2 - removing <9> from <479> leaving <47>
R2C4 is the only square in row 2 that can be <9>
Intersection of column 5 with block 5. The value <4> only appears in one or more of squares R4C5, R5C5 and R6C5 of column 5. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain this value.
R5C6 - removing <4> from <247> leaving <27>
Squares R5C1 and R8C1 in column 1 and R5C4 and R8C4 in column 4 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in rows 5 and 8 can be removed.
R5C2 - removing <7> from <479> leaving <49>
R8C2 - removing <7> from <679> leaving <69>
R5C5 - removing <7> from <2347> leaving <234>
R8C5 - removing <7> from <127> leaving <12>
R5C6 - removing <7> from <27> leaving <2>
R8C6 - removing <7> from <278> leaving <28>
R8C6 can only be <8>
R8C4 can only be <7>
R3C6 can only be <4>
R3C3 can only be <9>
R2C6 can only be <7>
R8C1 can only be <9>
R5C4 can only be <3>
R9C5 can only be <1>
R9C8 can only be <6>
R8C5 can only be <2>
R8C8 can only be <1>
R2C2 can only be <4>
R1C5 can only be <3>
R3C7 can only be <3>
R1C3 can only be <7>
R3C4 can only be <8>
R1C7 can only be <9>
R5C5 can only be <4>
R5C2 can only be <9>
R4C5 can only be <7>
R8C2 can only be <6>
R5C1 can only be <7>
R9C3 can only be <8>
R4C2 can only be <8>
R9C2 can only be <7>
R4C3 can only be <4>
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