Aug 08 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R4C2 is the only square in row 4 that can be <2>
R7C1 is the only square in column 1 that can be <7>
R5C7 is the only square in column 7 that can be <6>
Squares R7C2 and R7C9 in row 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <59>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R7C5 - removing <59> from <2589> leaving <28>
R7C8 - removing <59> from <2589> leaving <28>
Squares R4C8 and R4C9 in block 6 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 block.
R5C8 - removing <14> from <1457> leaving <57>
Intersection of row 3 with block 3. The value <7> 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.
R2C7 - removing <7> from <179> leaving <19>
R2C8 - removing <7> from <1479> leaving <149>
R8C7 is the only square in column 7 that can be <7>
Intersection of row 6 with block 6. The values <79> only appears in one or more of squares R6C7, R6C8 and R6C9 of row 6. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain these values.
R5C8 - removing <7> from <57> leaving <5>
Squares R4C5<68>, R5C5<38> and R6C5<36> in column 5 form a comprehensive naked triplet. These 3 squares can only contain the 3 possibilities <368>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C5 - removing <3> from <1359> leaving <159>
R3C5 - removing <3> from <123> leaving <12>
R7C5 - removing <8> from <28> leaving <2>
R8C5 - removing <38> from <23589> leaving <259>
R7C8 can only be <8>
R3C5 can only be <1>
R3C8 is the only square in row 3 that can be <2>
R8C8 can only be <9>
R8C5 can only be <5>
R6C8 can only be <7>
R7C9 can only be <5>
R6C9 can only be <9>
R7C2 can only be <9>
R9C9 can only be <1>
R8C2 can only be <4>
R8C3 can only be <2>
R2C5 can only be <9>
R9C4 can only be <4>
R9C6 can only be <9>
R8C6 can only be <3>
R9C7 can only be <2>
R1C9 can only be <3>
R4C9 can only be <4>
R1C4 can only be <5>
R1C6 can only be <2>
R2C7 can only be <1>
R2C8 can only be <4>
R1C7 can only be <9>
R4C8 can only be <1>
R3C9 can only be <7>
R3C2 can only be <3>
R8C4 can only be <8>
R2C6 can only be <7>
R1C1 can only be <8>
R2C4 can only be <3>
R5C6 can only be <4>
R3C1 can only be <4>
R5C2 can only be <1>
R5C3 can only be <8>
R5C5 can only be <3>
R1C3 can only be <1>
R4C1 can only be <6>
R5C4 can only be <7>
R6C5 can only be <6>
R6C2 can only be <5>
R4C5 can only be <8>
R9C1 can only be <5>
R6C1 can only be <3>
R2C2 can only be <6>
R9C3 can only be <6>
R2C3 can only be <5>
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