Aug 15 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R3C9 can only be <9>
R3C1 is the only square in row 3 that can be <5>
R7C5 is the only square in row 7 that can be <5>
R5C4 is the only square in row 5 that can be <5>
R9C2 is the only square in row 9 that can be <5>
R9C6 is the only square in row 9 that can be <9>
R6C5 is the only square in row 6 that can be <9>
R5C2 is the only square in row 5 that can be <9>
R6C4 is the only square in row 6 that can be <4>
R1C7 is the only square in row 1 that can be <4>
R3C7 can only be <7>
R3C3 can only be <2>
R3C5 can only be <4>
R1C4 is the only square in row 1 that can be <2>
R6C9 is the only square in row 6 that can be <2>
R5C5 is the only square in row 5 that can be <2>
R8C8 is the only square in row 8 that can be <2>
R9C8 is the only square in column 8 that can be <7>
Intersection of row 5 with block 6. The value <6> only appears in one or more of squares R5C7, R5C8 and R5C9 of row 5. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain this value.
R4C9 - removing <6> from <136> leaving <13>
Intersection of column 2 with block 1. The value <7> only appears in one or more of squares R1C2, R2C2 and R3C2 of column 2. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R1C3 - removing <7> from <178> leaving <18>
R2C1 - removing <7> from <1678> leaving <168>
R7C3 is the only square in column 3 that can be <7>
Intersection of column 8 with block 3. The value <8> only appears in one or more of squares R1C8, R2C8 and R3C8 of column 8. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R2C9 - removing <8> from <368> leaving <36>
Squares R5C3 and R9C3 in column 3 and R5C7 and R9C7 in column 7 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in rows 5 and 9 can be removed.
R5C6 - removing <3> from <138> leaving <18>
R5C8 - removing <3> from <36> leaving <6>
R1C8 can only be <8>
R1C3 can only be <1>
R2C8 can only be <3>
R2C9 can only be <6>
R1C6 can only be <7>
R9C3 can only be <3>
R2C1 can only be <8>
R1C2 can only be <6>
R6C6 can only be <3>
R2C5 can only be <1>
R2C2 can only be <7>
R8C5 can only be <6>
R6C1 can only be <7>
R8C2 can only be <8>
R4C5 can only be <7>
R9C4 can only be <1>
R5C3 can only be <8>
R8C1 can only be <1>
R9C7 can only be <6>
R4C4 can only be <6>
R7C7 can only be <1>
R4C1 can only be <3>
R5C6 can only be <1>
R5C7 can only be <3>
R4C6 can only be <8>
R4C9 can only be <1>
R7C1 can only be <6>
R7C9 can only be <8>
R8C9 can only be <3>
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