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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