Jul 19 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C4 can only be <3>
R7C3 can only be <7>
R1C6 can only be <1>
R1C2 can only be <7>
R1C8 can only be <5>
R3C3 is the only square in row 3 that can be <5>
R8C3 can only be <1>
R3C2 is the only square in row 3 that can be <2>
R2C3 can only be <9>
R5C3 can only be <2>
R5C6 is the only square in row 5 that can be <6>
R6C8 is the only square in row 6 that can be <6>
R8C8 is the only square in row 8 that can be <2>
R8C1 is the only square in row 8 that can be <5>
R9C2 is the only square in row 9 that can be <6>
R2C2 can only be <1>
R2C1 can only be <6>
R4C2 is the only square in column 2 that can be <4>
R6C2 is the only square in column 2 that can be <9>
Squares R4C9 and R6C9 in column 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <57>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C9 - removing <7> from <478> leaving <48>
R8C9 - removing <7> from <478> leaving <48>
Squares R4C9 and R6C9 in block 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <57>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R4C8 - removing <7> from <179> leaving <19>
Intersection of row 7 with block 9. The value <9> only appears in one or more of squares R7C7, R7C8 and R7C9 of row 7. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R8C7 - removing <9> from <3789> leaving <378>
Intersection of row 9 with block 8. The value <8> only appears in one or more of squares R9C4, R9C5 and R9C6 of row 9. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain this value.
R7C5 - removing <8> from <348> leaving <34>
R8C4 - removing <8> from <4789> leaving <479>
R8C6 - removing <8> from <3489> leaving <349>
Intersection of column 5 with block 5. The values <17> only appears in one or more of squares R4C5, R5C5 and R6C5 of column 5. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain these values.
R4C4 - removing <7> from <5789> leaving <589>
R6C4 - removing <7> from <2578> leaving <258>
Squares R2C9<48>, R3C7<18> and R3C8<14> in block 3 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <148>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R2C7 - removing <8> from <378> leaving <37>
R2C8 - removing <4> from <347> leaving <37>
Squares R2C8 and R9C8 in column 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <37>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R7C8 - removing <3> from <349> leaving <49>
Squares R3C5 and R3C8 in row 3 and R7C5 and R7C8 in row 7 form a Simple X-Wing pattern on possibility <4>. All other instances of this possibility in columns 5 and 8 can be removed.
R5C5 - removing <4> from <14> leaving <1>
R5C7 can only be <9>
R5C4 can only be <4>
R4C8 can only be <1>
R4C1 can only be <8>
R3C8 can only be <4>
R3C5 can only be <8>
R7C8 can only be <9>
R2C9 can only be <8>
R6C1 can only be <1>
R2C4 can only be <2>
R8C9 can only be <4>
R3C7 can only be <1>
R6C5 can only be <7>
R6C9 can only be <5>
R4C5 can only be <3>
R4C9 can only be <7>
R2C6 can only be <4>
R6C4 can only be <8>
R4C6 can only be <9>
R7C5 can only be <4>
R4C4 can only be <5>
R8C6 can only be <3>
R6C6 can only be <2>
R9C4 can only be <7>
R8C2 can only be <8>
R9C6 can only be <8>
R9C8 can only be <3>
R8C4 can only be <9>
R2C8 can only be <7>
R7C7 can only be <8>
R2C7 can only be <3>
R7C2 can only be <3>
R8C7 can only be <7>
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