Sep 28 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C7 can only be <4>
R5C1 can only be <4>
R4C3 can only be <5>
R6C3 can only be <7>
R3C3 is the only square in row 3 that can be <4>
R5C4 is the only square in row 5 that can be <6>
R5C6 is the only square in row 5 that can be <7>
R6C6 is the only square in row 6 that can be <5>
R7C4 is the only square in row 7 that can be <4>
R6C4 can only be <1>
R6C7 can only be <8>
R5C5 can only be <8>
R6C5 can only be <4>
R5C9 can only be <1>
R8C2 is the only square in column 2 that can be <7>
R8C7 is the only square in row 8 that can be <2>
R1C3 is the only square in column 3 that can be <6>
Squares R1C5 and R1C7 in row 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <13>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R1C1 - removing <3> from <235> leaving <25>
Squares R1C1 and R9C1 in column 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <25>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R3C1 - removing <2> from <238> leaving <38>
R7C1 - removing <25> from <2358> leaving <38>
Squares R1C7 and R2C7 in column 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <13>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R3C7 - removing <13> from <1367> leaving <67>
R7C7 - removing <1> from <169> leaving <69>
R9C7 - removing <1> from <179> leaving <79>
Squares R1C7 and R2C7 in block 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <13>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R2C8 - removing <1> from <158> leaving <58>
R3C8 - removing <1> from <168> leaving <68>
Squares R1C1<25>, R2C2<15> and R3C2<12> in block 1 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <125>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R2C3 - removing <1> from <138> leaving <38>
Intersection of column 3 with block 7. The values <19> only appears in one or more of squares R7C3, R8C3 and R9C3 of column 3. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain these values.
R7C2 - removing <1> from <125> leaving <25>
Squares R1C1 and R1C9 in row 1 and R9C1 and R9C9 in row 9 form a Simple X-Wing pattern on possibility <5>. All other instances of this possibility in columns 1 and 9 can be removed.
R7C9 - removing <5> from <58> leaving <8>
R7C1 can only be <3>
R8C8 can only be <1>
R8C3 can only be <8>
R3C1 can only be <8>
R2C3 can only be <3>
R2C7 can only be <1>
R2C2 can only be <5>
R1C7 can only be <3>
R3C8 can only be <6>
R3C7 can only be <7>
R7C8 can only be <5>
R7C2 can only be <2>
R2C8 can only be <8>
R9C9 can only be <7>
R9C7 can only be <9>
R3C9 can only be <2>
R1C5 can only be <1>
R1C1 can only be <2>
R3C2 can only be <1>
R1C9 can only be <5>
R7C6 can only be <1>
R9C1 can only be <5>
R7C3 can only be <9>
R3C6 can only be <9>
R9C5 can only be <2>
R4C5 can only be <3>
R9C3 can only be <1>
R7C7 can only be <6>
R3C4 can only be <3>
R4C6 can only be <2>
R4C4 can only be <9>
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