Sep 22 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C4 can only be <7>
R5C3 can only be <6>
R8C2 can only be <4>
R8C8 can only be <8>
R8C1 can only be <2>
R8C9 can only be <6>
R1C9 is the only square in row 1 that can be <2>
R2C2 is the only square in row 2 that can be <3>
R1C6 is the only square in row 1 that can be <3>
R3C1 is the only square in row 3 that can be <6>
R5C4 is the only square in row 5 that can be <2>
R9C7 is the only square in column 7 that can be <3>
R9C9 is the only square in row 9 that can be <4>
Squares R4C1 and R6C1 in column 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <49>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C1 - removing <49> from <45789> leaving <578>
R2C1 - removing <9> from <589> leaving <58>
R7C1 - removing <9> from <15789> leaving <1578>
R9C1 - removing <9> from <15789> leaving <1578>
R2C8 is the only square in row 2 that can be <9>
Squares R3C5 and R5C5 in column 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 column.
R6C5 - removing <5> from <3459> leaving <349>
R7C5 - removing <8> from <89> leaving <9>
Squares R9C4 and R9C6 in row 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <68>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R9C1 - removing <8> from <1578> leaving <157>
R9C3 - removing <8> from <789> leaving <79>
Intersection of row 9 with block 7. The values <79> only appears in one or more of squares R9C1, R9C2 and R9C3 of row 9. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain these values.
R7C1 - removing <7> from <1578> leaving <158>
R7C3 - removing <7> from <78> leaving <8>
Squares R1C2 and R9C2 in column 2 and R1C8 and R9C8 in column 8 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in rows 1 and 9 can be removed.
R1C1 - removing <5> from <578> leaving <78>
R9C1 - removing <5> from <157> leaving <17>
R1C4 - removing <5> from <58> leaving <8>
R1C7 - removing <5> from <1457> leaving <147>
R1C1 can only be <7>
R9C4 can only be <6>
R3C5 can only be <5>
R5C5 can only be <8>
R5C6 can only be <1>
R5C7 can only be <5>
R4C6 can only be <9>
R6C9 can only be <3>
R6C5 can only be <4>
R4C9 can only be <1>
R9C6 can only be <8>
R6C4 can only be <5>
R9C1 can only be <1>
R3C3 can only be <4>
R3C7 can only be <7>
R1C3 can only be <9>
R3C9 can only be <8>
R7C7 can only be <1>
R2C9 can only be <5>
R4C1 can only be <4>
R6C6 can only be <6>
R6C1 can only be <9>
R4C5 can only be <3>
R7C1 can only be <5>
R1C7 can only be <4>
R9C8 can only be <5>
R9C2 can only be <9>
R1C8 can only be <1>
R7C9 can only be <7>
R1C2 can only be <5>
R9C3 can only be <7>
R2C1 can only be <8>
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