Jul 22 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C8 is the only square in row 1 that can be <3>
R1C3 is the only square in row 1 that can be <7>
R6C3 is the only square in row 6 that can be <1>
R6C4 is the only square in row 6 that can be <5>
R5C3 is the only square in column 3 that can be <3>
R3C4 is the only square in column 4 that can be <7>
R3C9 can only be <9>
R3C7 can only be <5>
R3C3 can only be <6>
R8C5 is the only square in column 5 that can be <3>
R8C8 is the only square in column 8 that can be <5>
Squares R8C2 and R9C2 in column 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <19>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C2 - removing <19> from <189> leaving <8>
R2C2 - removing <9> from <459> leaving <45>
R4C2 - removing <9> from <4689> leaving <468>
R5C2 - removing <9> from <45689> leaving <4568>
Squares R8C2 and R9C2 in block 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <19>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R8C3 - removing <9> from <29> leaving <2>
Intersection of row 6 with block 6. The values <346> only appears in one or more of squares R6C7, R6C8 and R6C9 of row 6. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain these values.
R4C7 - removing <4> from <2489> leaving <289>
R5C7 - removing <4> from <24789> leaving <2789>
R5C8 - removing <46> from <2467> leaving <27>
R5C9 - removing <6> from <267> leaving <27>
R6C8 is the only square in column 8 that can be <4>
R6C7 can only be <3>
R6C9 can only be <6>
R9C9 is the only square in row 9 that can be <3>
R9C8 is the only square in column 8 that can be <6>
R9C4 can only be <9>
R9C2 can only be <1>
R8C4 can only be <4>
R8C7 can only be <1>
R5C4 can only be <6>
R8C2 can only be <9>
R9C7 can only be <2>
R2C7 can only be <7>
R7C9 can only be <7>
R2C8 can only be <2>
R7C7 can only be <4>
R5C8 can only be <7>
R5C9 can only be <2>
R4C6 is the only square in row 4 that can be <2>
R7C6 can only be <6>
R7C5 can only be <2>
R2C5 is the only square in row 2 that can be <6>
R4C2 is the only square in row 4 that can be <6>
R4C1 is the only square in row 4 that can be <4>
R3C1 can only be <1>
R5C2 can only be <5>
R2C2 can only be <4>
R2C6 can only be <9>
R2C3 can only be <5>
R1C6 can only be <1>
R3C5 can only be <4>
R1C1 can only be <9>
R5C5 can only be <1>
R5C6 can only be <4>
R5C1 can only be <8>
R7C3 can only be <8>
R5C7 can only be <9>
R7C1 can only be <5>
R4C3 can only be <9>
R4C7 can only be <8>
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