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Sep 26 - Hard

Puzzle Copyright © Kevin Stone

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## Reasoning

R8C5 can only be <4>

R7C4 is the only square in row 7 that can be <2>

R7C1 is the only square in row 7 that can be <4>

R4C3 is the only square in row 4 that can be <4>

R7C2 is the only square in row 7 that can be <3>

R7C6 is the only square in row 7 that can be <5>

R2C6 can only be <9>

R9C7 is the only square in row 9 that can be <2>

R9C2 is the only square in column 2 that can be <1>

R8C1 can only be <9>

R9C3 can only be <7>

R9C8 is the only square in row 9 that can be <9>

R2C5 is the only square in column 5 that can be <2>

R2C1 can only be <6>

R8C6 is the only square in column 6 that can be <7>

R8C4 is the only square in block 8 that can be <1>

R8C9 can only be <6>

R3C8 is the only square in row 3 that can be <6>

R6C7 is the only square in row 6 that can be <6>

Squares R6C3 and R6C5 in row 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <58>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.

R6C1 - removing <8> from <138> leaving <13>

R6C9 - removing <58> from <1358> leaving <13>

Squares R4C5 and R6C5 in block 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <58>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.

R5C4 - removing <58> from <4568> leaving <46>

R5C6 - removing <8> from <468> leaving <46>

Intersection of row 4 with block 6. The value <9> only appears in one or more of squares R4C7, R4C8 and R4C9 of row 4. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain this value.

R5C7 - removing <9> from <39> leaving <3>

R5C9 - removing <9> from <35789> leaving <3578>

R6C9 can only be <1>

R6C1 can only be <3>

R7C9 can only be <7>

R4C7 can only be <9>

R7C8 can only be <1>

R1C7 can only be <1>

R1C8 can only be <5>

R1C2 can only be <9>

R5C8 can only be <7>

R2C9 can only be <3>

R3C9 can only be <9>

R2C4 can only be <5>

R1C3 can only be <8>

R1C6 can only be <4>

R6C3 can only be <5>

R3C1 can only be <2>

R1C4 can only be <3>

R5C6 can only be <6>

R3C4 can only be <8>

R3C2 can only be <5>

R5C1 can only be <8>

R5C2 can only be <2>

R3C6 can only be <1>

R9C4 can only be <6>

R5C9 can only be <5>

R4C1 can only be <1>

R5C4 can only be <4>

R9C6 can only be <8>

R5C3 can only be <9>

R4C9 can only be <8>

R6C5 can only be <8>

R4C5 can only be <5>

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