Oct 31 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C4 can only be <5>
R9C9 can only be <2>
R3C3 is the only square in row 3 that can be <9>
R3C2 is the only square in row 3 that can be <1>
Intersection of row 3 with block 3. The values <24> only appears in one or more of squares R3C7, R3C8 and R3C9 of row 3. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain these values.
R2C7 - removing <4> from <34568> leaving <3568>
R2C8 - removing <4> from <456> leaving <56>
Intersection of block 2 with row 3. The value <6> only appears in one or more of squares R3C4, R3C5 and R3C6 of block 2. These squares are the ones that intersect with row 3. Thus, the other (non-intersecting) squares of row 3 cannot contain this value.
R3C1 - removing <6> from <5678> leaving <578>
R3C7 - removing <6> from <2345678> leaving <234578>
R3C8 - removing <6> from <24567> leaving <2457>
R3C9 - removing <6> from <368> leaving <38>
Squares R3C4<68>, R3C6<36> and R3C9<38> in row 3 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <368>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R3C1 - removing <8> from <578> leaving <57>
R3C5 - removing <38> from <358> leaving <5>
R3C7 - removing <38> from <234578> leaving <2457>
R3C1 can only be <7>
R9C1 can only be <5>
R1C7 is the only square in row 1 that can be <7>
R9C7 can only be <4>
R9C3 can only be <7>
R3C7 can only be <2>
R3C8 can only be <4>
R1C3 is the only square in row 1 that can be <5>
R5C2 is the only square in row 5 that can be <5>
R7C2 is the only square in column 2 that can be <2>
R5C8 is the only square in column 8 that can be <2>
Intersection of block 4 with column 3. The values <238> only appears in one or more of squares R4C3, R5C3 and R6C3 of block 4. These squares are the ones that intersect with column 3. Thus, the other (non-intersecting) squares of column 3 cannot contain these values.
R2C3 - removing <8> from <468> leaving <46>
R7C3 - removing <8> from <1468> leaving <146>
R8C3 - removing <8> from <1468> leaving <146>
Intersection of block 6 with column 7. The values <169> only appears in one or more of squares R4C7, R5C7 and R6C7 of block 6. These squares are the ones that intersect with column 7. Thus, the other (non-intersecting) squares of column 7 cannot contain these values.
R2C7 - removing <6> from <3568> leaving <358>
R7C7 - removing <6> from <3568> leaving <358>
R8C7 - removing <6> from <68> leaving <8>
R8C2 can only be <4>
R2C2 can only be <8>
R2C5 can only be <3>
R1C1 can only be <6>
R2C7 can only be <5>
R3C6 can only be <6>
R2C8 can only be <6>
R7C7 can only be <3>
R2C3 can only be <4>
R8C8 can only be <7>
R1C9 can only be <8>
R3C4 can only be <8>
R7C9 can only be <6>
R7C1 can only be <8>
R7C3 can only be <1>
R8C5 can only be <1>
R7C8 can only be <5>
R3C9 can only be <3>
R7C6 can only be <9>
R8C3 can only be <6>
R5C6 can only be <3>
R4C5 can only be <9>
R4C7 can only be <1>
R6C7 can only be <6>
R5C3 can only be <8>
R4C6 can only be <2>
R6C4 can only be <4>
R5C7 can only be <9>
R4C3 can only be <3>
R6C6 can only be <1>
R5C5 can only be <7>
R6C3 can only be <2>
R5C4 can only be <6>
R7C5 can only be <4>
R6C5 can only be <8>
R7C4 can only be <7>
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