Oct 14 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C5 can only be <2>
R1C5 can only be <1>
R1C6 can only be <2>
R9C5 can only be <7>
R1C4 can only be <5>
R1C1 can only be <6>
R3C4 can only be <9>
R3C6 can only be <7>
R2C6 can only be <3>
R1C2 can only be <8>
R1C3 can only be <4>
R5C2 can only be <6>
R5C6 can only be <4>
R5C8 can only be <5>
R5C4 can only be <3>
R5C3 can only be <8>
R5C7 can only be <9>
R2C8 can only be <2>
R2C1 can only be <5>
R3C8 can only be <8>
R4C1 is the only square in row 4 that can be <3>
R6C3 is the only square in row 6 that can be <5>
R7C9 is the only square in row 7 that can be <3>
R7C7 is the only square in row 7 that can be <8>
R9C4 is the only square in row 9 that can be <4>
Squares R3C3 and R4C3 in column 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <12>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R7C3 - removing <12> from <1279> leaving <79>
Intersection of row 7 with block 7. The value <7> only appears in one or more of squares R7C1, R7C2 and R7C3 of row 7. 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 <7> from <1279> leaving <129>
Intersection of row 7 with block 8. The value <6> only appears in one or more of squares R7C4, R7C5 and R7C6 of row 7. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain this value.
R9C6 - removing <6> from <169> leaving <19>
Intersection of row 9 with block 9. The values <26> only appears in one or more of squares R9C7, R9C8 and R9C9 of row 9. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain these values.
R8C7 - removing <2> from <257> leaving <57>
R8C9 - removing <2> from <259> leaving <59>
Squares R2C2, R2C3, R7C2 and R7C3 form a Type-1 Unique Rectangle on <79>.
R7C2 - removing <79> from <1279> leaving <12>
R7C3 is the only square in row 7 that can be <7>
R2C3 can only be <9>
R2C2 can only be <7>
R7C6 is the only square in row 7 that can be <9>
R9C6 can only be <1>
R9C8 can only be <6>
R6C6 can only be <6>
R8C4 can only be <2>
R9C7 can only be <2>
R4C8 can only be <7>
R8C8 can only be <1>
R4C4 can only be <1>
R7C4 can only be <6>
R8C2 can only be <9>
R9C9 can only be <9>
R4C7 can only be <6>
R6C7 can only be <4>
R8C9 can only be <5>
R4C3 can only be <2>
R6C9 can only be <2>
R3C7 can only be <5>
R6C2 can only be <1>
R8C7 can only be <7>
R3C9 can only be <4>
R3C3 can only be <1>
R7C2 can only be <2>
R7C1 can only be <1>
R3C1 can only be <2>
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