Mar 12 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C8 is the only square in row 1 that can be <5>
R1C4 is the only square in row 1 that can be <8>
R2C2 is the only square in row 2 that can be <4>
R2C1 is the only square in row 2 that can be <5>
R5C6 is the only square in row 5 that can be <6>
R7C1 is the only square in row 7 that can be <6>
R9C2 is the only square in row 9 that can be <1>
R9C4 is the only square in row 9 that can be <5>
R6C5 is the only square in row 6 that can be <5>
R7C9 is the only square in row 7 that can be <5>
Squares R2C8 and R9C8 in column 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <89>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R8C8 - removing <89> from <389> leaving <3>
Intersection of row 3 with block 3. The value <1> only appears in one or more of squares R3C7, R3C8 and R3C9 of row 3. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R2C9 - removing <1> from <178> leaving <78>
Intersection of column 7 with block 9. The value <4> only appears in one or more of squares R7C7, R8C7 and R9C7 of column 7. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R8C9 - removing <4> from <478> leaving <78>
Squares R2C9 and R8C9 in column 9 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 column.
R3C9 - removing <7> from <137> leaving <13>
Intersection of row 8 with block 8. The values <24> only appears in one or more of squares R8C4, R8C5 and R8C6 of row 8. These squares are the ones that intersect with block 8. Thus, the other (non-intersecting) squares of block 8 cannot contain these values.
R9C6 - removing <4> from <479> leaving <79>
Squares R7C5 and R9C6 in block 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <79>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R8C4 - removing <79> from <2479> leaving <24>
R8C6 - removing <79> from <2479> leaving <24>
Intersection of row 8 with block 7. The value <9> only appears in one or more of squares R8C1, R8C2 and R8C3 of row 8. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R7C3 - removing <9> from <49> leaving <4>
R9C3 - removing <9> from <489> leaving <48>
R9C3 can only be <8>
R9C8 can only be <9>
R9C6 can only be <7>
R2C8 can only be <8>
R7C7 can only be <7>
R2C9 can only be <7>
R8C9 can only be <8>
R7C5 can only be <9>
R9C7 can only be <4>
R1C2 is the only square in row 1 that can be <7>
R8C2 can only be <9>
R8C1 can only be <7>
R3C5 is the only square in row 3 that can be <7>
R5C5 is the only square in row 5 that can be <8>
R4C5 can only be <2>
R4C8 can only be <6>
R5C4 can only be <1>
R4C2 can only be <3>
R6C8 can only be <2>
R5C7 can only be <3>
R2C4 can only be <9>
R5C3 can only be <2>
R1C7 can only be <9>
R6C9 can only be <4>
R6C1 can only be <9>
R4C9 can only be <1>
R1C6 can only be <2>
R3C7 can only be <1>
R2C6 can only be <1>
R4C4 can only be <4>
R6C4 can only be <7>
R3C9 can only be <3>
R6C2 can only be <6>
R4C6 can only be <9>
R8C4 can only be <2>
R4C1 can only be <8>
R6C6 can only be <3>
R1C3 can only be <3>
R3C3 can only be <9>
R3C1 can only be <2>
R8C6 can only be <4>
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