Oct 16 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C3 can only be <7>
R5C5 can only be <9>
R3C3 can only be <4>
R1C1 is the only square in row 1 that can be <6>
R1C5 is the only square in row 1 that can be <8>
R2C5 is the only square in row 2 that can be <4>
R6C1 is the only square in row 6 that can be <4>
R7C5 is the only square in row 7 that can be <3>
R7C1 is the only square in row 7 that can be <7>
R8C2 is the only square in row 8 that can be <8>
R5C2 can only be <3>
R2C2 can only be <5>
R4C1 can only be <1>
R3C1 can only be <3>
R5C1 can only be <8>
R9C1 can only be <5>
R5C3 can only be <2>
R2C6 is the only square in row 2 that can be <3>
R4C9 is the only square in row 4 that can be <3>
R1C7 is the only square in row 1 that can be <3>
R9C9 is the only square in row 9 that can be <8>
Intersection of row 3 with block 3. The value <9> 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 this value.
R1C9 - removing <9> from <259> leaving <25>
Intersection of row 7 with block 9. The value <2> only appears in one or more of squares R7C7, R7C8 and R7C9 of row 7. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R9C7 - removing <2> from <269> leaving <69>
R7C7 is the only square in column 7 that can be <2>
Squares R2C8<27>, R4C8<79> and R6C8<279> in column 8 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <279>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R8C8 - removing <9> from <169> leaving <16>
Intersection of row 8 with block 8. The values <59> only appears in one or more of squares R8C4, R8C5 and R8C6 of row 8. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain these values.
R9C4 - removing <9> from <2679> leaving <267>
R9C6 - removing <9> from <29> leaving <2>
Intersection of column 8 with block 6. The value <9> only appears in one or more of squares R4C8, R5C8 and R6C8 of column 8. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain this value.
R6C9 - removing <9> from <279> leaving <27>
Squares R4C2, R4C8, R6C2 and R6C8 form a Type-1 Unique Rectangle on <79>.
R6C8 - removing <79> from <279> leaving <2>
R6C9 can only be <7>
R2C8 can only be <7>
R6C2 can only be <9>
R4C8 can only be <9>
R2C4 can only be <2>
R4C2 can only be <7>
R1C4 can only be <9>
R1C6 can only be <5>
R8C4 can only be <6>
R1C9 can only be <2>
R8C6 can only be <9>
R3C5 can only be <7>
R9C5 can only be <1>
R8C8 can only be <1>
R9C4 can only be <7>
R8C5 can only be <5>
R5C8 can only be <6>
R7C9 can only be <9>
R9C3 can only be <9>
R5C7 can only be <5>
R7C3 can only be <1>
R3C9 can only be <5>
R9C7 can only be <6>
R3C7 can only be <9>
R5C9 can only be <1>
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