Jul 06 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C7 can only be <9>
R1C2 is the only square in row 1 that can be <2>
R1C8 is the only square in row 1 that can be <6>
R4C1 is the only square in row 4 that can be <2>
R5C2 is the only square in row 5 that can be <9>
R6C5 is the only square in row 6 that can be <3>
R2C9 is the only square in row 2 that can be <3>
R7C3 is the only square in row 7 that can be <5>
R3C6 is the only square in row 3 that can be <5>
R2C1 is the only square in row 2 that can be <5>
R8C5 is the only square in row 8 that can be <9>
R9C8 is the only square in row 9 that can be <5>
R7C7 is the only square in column 7 that can be <1>
Squares R8C8 and R8C9 in row 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <78>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R8C2 - removing <8> from <148> leaving <14>
R9C2 is the only square in column 2 that can be <8>
Intersection of row 1 with block 2. The values <348> only appears in one or more of squares R1C4, R1C5 and R1C6 of row 1. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain these values.
R2C5 - removing <4> from <147> leaving <17>
R3C4 - removing <4> from <147> leaving <17>
Intersection of row 6 with block 6. The value <7> only appears in one or more of squares R6C7, R6C8 and R6C9 of row 6. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain this value.
R5C8 - removing <7> from <478> leaving <48>
R5C9 - removing <7> from <5678> leaving <568>
Squares R3C4<17>, R5C4<178> and R7C4<78> in column 4 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <178>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R1C4 - removing <8> from <348> leaving <34>
R9C4 - removing <1> from <134> leaving <34>
Squares R3C3 and R6C3 in column 3 and R3C7 and R6C7 in column 7 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in rows 3 and 6 can be removed.
R6C1 - removing <4> from <46> leaving <6>
R5C9 is the only square in row 5 that can be <6>
R5C5 is the only square in row 5 that can be <5>
R4C9 is the only square in row 4 that can be <5>
R2C5 is the only square in column 5 that can be <7>
R2C8 can only be <4>
R3C4 can only be <1>
R2C2 can only be <1>
R5C8 can only be <8>
R3C7 can only be <7>
R3C3 can only be <4>
R6C7 can only be <4>
R5C4 can only be <7>
R8C8 can only be <7>
R6C9 can only be <7>
R6C3 can only be <8>
R8C9 can only be <8>
R8C2 can only be <4>
R5C6 can only be <1>
R7C4 can only be <8>
R5C1 can only be <4>
R9C6 can only be <3>
R4C5 can only be <8>
R4C3 can only be <1>
R7C6 can only be <7>
R8C1 can only be <1>
R9C4 can only be <4>
R1C6 can only be <8>
R1C5 can only be <4>
R9C5 can only be <1>
R1C4 can only be <3>
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