Oct 12 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C9 is the only square in row 1 that can be <8>
R1C2 is the only square in row 1 that can be <9>
R1C1 is the only square in row 1 that can be <2>
R3C9 is the only square in row 3 that can be <2>
R4C5 is the only square in row 4 that can be <9>
R5C5 is the only square in row 5 that can be <2>
R9C2 is the only square in row 9 that can be <2>
R9C9 is the only square in row 9 that can be <9>
Intersection of row 3 with block 1. The value <5> only appears in one or more of squares R3C1, R3C2 and R3C3 of row 3. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R1C3 - removing <5> from <357> leaving <37>
R2C1 - removing <5> from <13567> leaving <1367>
R2C2 - removing <5> from <156> leaving <16>
Intersection of row 2 with block 3. The value <5> only appears in one or more of squares R2C7, R2C8 and R2C9 of row 2. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R1C8 - removing <5> from <4567> leaving <467>
Intersection of column 5 with block 2. The values <67> only appears in one or more of squares R1C5, R2C5 and R3C5 of column 5. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain these values.
R1C4 - removing <6> from <356> leaving <35>
R1C6 - removing <7> from <357> leaving <35>
Squares R1C4 and R1C6 in row 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <35>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R1C3 - removing <3> from <37> leaving <7>
R5C3 is the only square in column 3 that can be <3>
R4C1 can only be <1>
R5C2 can only be <5>
R6C1 can only be <8>
R5C4 is the only square in row 5 that can be <8>
R9C3 is the only square in row 9 that can be <8>
R7C5 is the only square in row 7 that can be <8>
R2C1 is the only square in column 1 that can be <3>
R4C4 is the only square in column 4 that can be <6>
R9C7 is the only square in column 7 that can be <3>
R9C4 can only be <1>
R9C6 can only be <4>
R8C5 can only be <3>
R6C5 can only be <4>
Squares R1C7 and R1C8 in block 3 form a simple naked pair. These 2 squares both contain the 2 possibilities <46>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R2C8 - removing <6> from <1567> leaving <157>
R2C9 - removing <6> from <1567> leaving <157>
R3C7 - removing <6> from <167> leaving <17>
R8C9 is the only square in column 9 that can be <6>
R8C2 can only be <1>
R9C8 can only be <7>
R9C1 can only be <6>
R2C2 can only be <6>
R7C3 can only be <5>
R3C1 can only be <5>
R2C5 can only be <7>
R3C5 can only be <6>
R3C3 can only be <1>
R8C1 can only be <4>
R3C7 can only be <7>
R7C9 can only be <1>
R7C7 can only be <4>
R2C9 can only be <5>
R6C9 can only be <3>
R8C8 can only be <5>
R7C1 can only be <7>
R2C8 can only be <1>
R5C8 can only be <6>
R5C7 can only be <1>
R1C8 can only be <4>
R6C4 can only be <5>
R4C9 can only be <7>
R1C7 can only be <6>
R4C6 can only be <3>
R5C6 can only be <7>
R6C6 can only be <1>
R1C4 can only be <3>
R1C6 can only be <5>
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