Aug 29 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C3 is the only square in row 2 that can be <7>
R3C1 can only be <9>
R7C1 can only be <1>
R4C1 can only be <6>
R6C1 can only be <7>
R3C9 is the only square in row 3 that can be <7>
R4C3 is the only square in row 4 that can be <8>
R5C3 is the only square in row 5 that can be <3>
R5C7 is the only square in row 5 that can be <6>
R6C9 is the only square in row 6 that can be <3>
R7C4 is the only square in row 7 that can be <3>
R7C8 is the only square in row 7 that can be <8>
R3C6 is the only square in row 3 that can be <8>
R2C7 is the only square in row 2 that can be <8>
R8C4 is the only square in row 8 that can be <6>
R3C5 is the only square in row 3 that can be <6>
R9C6 is the only square in row 9 that can be <7>
Squares R2C4 and R2C6 in block 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <15>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R1C4 - removing <5> from <2459> leaving <249>
R1C6 - removing <5> from <2459> leaving <249>
R3C4 - removing <5> from <245> leaving <24>
Intersection of row 5 with block 5. The values <125> only appears in one or more of squares R5C4, R5C5 and R5C6 of row 5. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain these values.
R4C5 - removing <15> from <1459> leaving <49>
R6C5 - removing <15> from <1459> leaving <49>
R5C5 is the only square in column 5 that can be <1>
R7C5 is the only square in column 5 that can be <5>
Intersection of column 4 with block 2. The value <4> only appears in one or more of squares R1C4, R2C4 and R3C4 of column 4. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
R1C6 - removing <4> from <249> leaving <29>
Intersection of column 8 with block 6. The value <1> 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.
R4C7 - removing <1> from <12459> leaving <2459>
R6C7 - removing <1> from <12459> leaving <2459>
Squares R6C2<125>, R6C3<25> and R6C8<125> in row 6 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <125>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R6C7 - removing <25> from <2459> leaving <49>
Squares R6C5, R6C7, R4C5 and R4C7 form a Type-1 Unique Rectangle on <49>.
R4C7 - removing <49> from <2459> leaving <25>
R4C5 is the only square in row 4 that can be <4>
R6C5 can only be <9>
R6C7 can only be <4>
R4C9 is the only square in row 4 that can be <9>
R7C9 can only be <2>
R7C2 can only be <4>
R7C6 can only be <9>
R3C2 can only be <5>
R8C3 can only be <9>
R1C6 can only be <2>
R9C4 can only be <1>
R8C7 can only be <1>
R9C3 can only be <2>
R8C6 can only be <4>
R9C7 can only be <9>
R6C3 can only be <5>
R2C4 can only be <5>
R1C7 can only be <5>
R5C6 can only be <5>
R3C4 can only be <4>
R1C3 can only be <4>
R4C7 can only be <2>
R3C8 can only be <2>
R2C6 can only be <1>
R5C4 can only be <2>
R1C4 can only be <9>
R4C2 can only be <1>
R6C8 can only be <1>
R6C2 can only be <2>
R4C8 can only be <5>
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