Jul 09 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C7 can only be <1>
R7C6 can only be <6>
R6C7 can only be <7>
R2C8 is the only square in row 2 that can be <6>
R4C6 is the only square in row 4 that can be <5>
R5C5 is the only square in row 5 that can be <7>
R5C4 is the only square in row 5 that can be <8>
R6C5 is the only square in row 6 that can be <6>
R8C5 is the only square in row 8 that can be <2>
R4C4 is the only square in row 4 that can be <2>
R3C4 can only be <9>
R3C6 can only be <2>
R6C4 can only be <1>
R7C4 can only be <4>
R9C5 can only be <1>
R8C2 is the only square in row 8 that can be <6>
R9C8 is the only square in row 9 that can be <7>
R3C9 is the only square in row 3 that can be <7>
R4C5 is the only square in column 5 that can be <4>
R4C3 can only be <3>
R6C3 can only be <9>
R6C6 can only be <3>
R9C3 can only be <4>
R5C6 can only be <9>
Squares R3C1 and R5C1 in column 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <14>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C1 - removing <1> from <1359> leaving <359>
R7C1 - removing <1> from <135> leaving <35>
R8C1 - removing <1> from <139> leaving <39>
Squares R7C1<35>, R8C1<39> and R9C2<59> in block 7 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <359>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C2 - removing <35> from <1358> leaving <18>
Intersection of column 2 with block 1. The value <3> 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.
R2C1 - removing <3> from <359> leaving <59>
Squares R3C2<148>, R5C2<14> and R7C2<18> in column 2 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 column.
R1C2 - removing <48> from <3458> leaving <35>
R2C2 - removing <18> from <13589> leaving <359>
Intersection of row 1 with block 3. The value <4> only appears in one or more of squares R1C7, R1C8 and R1C9 of row 1. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R3C8 - removing <4> from <148> leaving <18>
Squares R2C1<59>, R2C2<359>, R2C5<38> and R2C7<58> in row 2 form a comprehensive naked quad. These 4 squares can only contain the 4 possibilities <3589>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R2C3 - removing <8> from <128> leaving <12>
R2C9 - removing <5> from <125> leaving <12>
R7C9 is the only square in column 9 that can be <5>
R7C1 can only be <3>
R9C7 can only be <9>
R9C2 can only be <5>
R8C1 can only be <9>
R2C1 can only be <5>
R1C2 can only be <3>
R1C5 can only be <8>
R2C2 can only be <9>
R1C3 can only be <2>
R2C5 can only be <3>
R2C7 can only be <8>
R8C7 can only be <4>
R3C8 can only be <1>
R3C1 can only be <4>
R7C8 can only be <8>
R2C9 can only be <2>
R7C2 can only be <1>
R8C8 can only be <3>
R1C7 can only be <5>
R8C9 can only be <1>
R5C8 can only be <2>
R8C3 can only be <8>
R1C8 can only be <4>
R2C3 can only be <1>
R5C9 can only be <3>
R3C2 can only be <8>
R5C1 can only be <1>
R5C2 can only be <4>
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