Feb 08 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C4 can only be <6>
R8C6 can only be <6>
R5C4 can only be <4>
R8C4 can only be <7>
R8C5 can only be <5>
R5C6 can only be <2>
R5C3 can only be <9>
R2C6 can only be <1>
R7C5 can only be <9>
R2C5 can only be <2>
R6C3 can only be <4>
R4C3 can only be <2>
R3C5 can only be <3>
R1C1 is the only square in row 1 that can be <3>
R5C9 is the only square in row 5 that can be <3>
R6C9 is the only square in row 6 that can be <9>
R8C8 is the only square in row 8 that can be <3>
Intersection of column 2 with block 1. The value <1> only appears in one or more of squares R1C2, R2C2 and R3C2 of column 2. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R3C1 - removing <1> from <12789> leaving <2789>
Intersection of column 2 with block 7. The values <56> only appears in one or more of squares R7C2, R8C2 and R9C2 of column 2. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain these values.
R7C1 - removing <56> from <245678> leaving <2478>
R9C1 - removing <56> from <5679> leaving <79>
Intersection of block 6 with column 7. The value <5> only appears in one or more of squares R4C7, R5C7 and R6C7 of block 6. These squares are the ones that intersect with column 7. Thus, the other (non-intersecting) squares of column 7 cannot contain this value.
R7C7 - removing <5> from <45678> leaving <4678>
Squares R7C1<2478>, R7C3<78>, R8C1<248> and R8C2<24> in block 7 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <2478>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C2 - removing <24> from <2456> leaving <56>
R9C1 - removing <7> from <79> leaving <9>
R9C9 is the only square in row 9 that can be <7>
R2C1 is the only square in row 2 that can be <7>
R3C3 can only be <8>
R3C1 can only be <2>
R7C3 can only be <7>
R3C7 is the only square in row 3 that can be <7>
R7C9 is the only square in row 7 that can be <2>
R8C2 is the only square in row 8 that can be <2>
R1C9 is the only square in column 9 that can be <5>
R1C8 can only be <4>
R1C2 can only be <1>
R2C9 can only be <8>
R2C8 can only be <9>
R8C9 can only be <4>
R8C1 can only be <8>
R4C9 can only be <6>
R3C2 can only be <9>
R2C2 can only be <4>
R3C8 can only be <6>
R3C9 can only be <1>
R9C8 can only be <5>
R4C1 can only be <1>
R6C7 can only be <5>
R5C7 can only be <8>
R7C1 can only be <4>
R9C2 can only be <6>
R7C8 can only be <8>
R4C5 can only be <8>
R6C1 can only be <6>
R4C7 can only be <4>
R5C5 can only be <6>
R5C1 can only be <5>
R6C5 can only be <1>
R7C7 can only be <6>
R7C2 can only be <5>
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