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Sep 26 - Very Hard

Puzzle Copyright © Kevin Stone

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## Reasoning

R2C8 can only be <4>

R2C2 is the only square in row 2 that can be <5>

R4C6 is the only square in row 4 that can be <3>

R4C5 is the only square in row 4 that can be <4>

R5C1 is the only square in row 5 that can be <4>

R5C4 is the only square in row 5 that can be <5>

R7C7 is the only square in row 7 that can be <4>

R8C2 is the only square in row 8 that can be <8>

R9C3 is the only square in row 9 that can be <5>

R3C1 is the only square in column 1 that can be <2>

R5C9 is the only square in column 9 that can be <2>

R4C3 is the only square in row 4 that can be <2>

R6C5 is the only square in row 6 that can be <2>

R6C7 is the only square in block 6 that can be <8>

Squares R3C7 and R4C7 in column 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <17>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.

R1C7 - removing <17> from <1237> leaving <23>

Squares R1C2 and R5C2 in column 2, R5C5 and R8C5 in column 5 and R1C8, R5C8 and R8C8 in column 8 form a Swordfish pattern on possibility <7>. All other instances of this possibility in rows 1, 5 and 8 can be removed.

R1C3 - removing <7> from <78> leaving <8>

R8C9 - removing <7> from <67> leaving <6>

R1C5 can only be <1>

R3C7 is the only square in row 3 that can be <1>

R4C7 can only be <7>

R4C4 can only be <1>

R5C8 can only be <1>

R8C1 is the only square in row 8 that can be <1>

R7C6 is the only square in row 7 that can be <1>

Intersection of block 7 with row 7. The value <9> only appears in one or more of squares R7C1, R7C2 and R7C3 of block 7. These squares are the ones that intersect with row 7. Thus, the other (non-intersecting) squares of row 7 cannot contain this value.

R7C4 - removing <9> from <679> leaving <67>

Intersection of block 8 with column 5. The value <9> only appears in one or more of squares R7C5, R8C5 and R9C5 of block 8. These squares are the ones that intersect with column 5. Thus, the other (non-intersecting) squares of column 5 cannot contain this value.

R2C5 - removing <9> from <89> leaving <8>

R2C9 can only be <3>

R2C1 can only be <9>

R7C9 can only be <7>

R1C7 can only be <2>

R7C4 can only be <6>

R3C9 can only be <8>

R8C8 can only be <9>

R8C5 can only be <7>

R9C8 can only be <2>

R9C7 can only be <3>

R1C8 can only be <7>

R1C2 can only be <3>

R7C1 can only be <3>

R3C3 can only be <7>

R6C3 can only be <6>

R6C6 can only be <9>

R7C3 can only be <9>

R5C2 can only be <7>

R6C4 can only be <7>

R3C6 can only be <6>

R9C2 can only be <6>

R3C4 can only be <9>

R9C5 can only be <9>

R5C5 can only be <6>

R5C6 can only be <8>

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