Jul 04 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R8C1 is the only square in column 1 that can be <3>
R5C6 is the only square in column 6 that can be <3>
R1C8 is the only square in column 8 that can be <9>
Squares R9C2 and R9C5 in row 9 form a simple naked pair. These 2 squares both contain the 2 possibilities <15>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R9C3 - removing <15> from <158> leaving <8>
R9C7 - removing <15> from <13578> leaving <378>
R9C8 - removing <5> from <3578> leaving <378>
R3C1 is the only square in row 3 that can be <8>
Squares R8C3 and R9C2 in block 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <15>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C1 - removing <5> from <569> leaving <69>
R7C2 - removing <15> from <12569> leaving <269>
R7C3 - removing <15> from <1259> leaving <29>
Intersection of row 4 with block 5. The value <1> only appears in one or more of squares R4C4, R4C5 and R4C6 of row 4. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain this value.
R5C4 - removing <1> from <159> leaving <59>
R5C5 - removing <1> from <12567> leaving <2567>
Squares R5C1 and R5C4 in row 5 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.
R5C3 - removing <59> from <259> leaving <2>
R5C5 - removing <5> from <2567> leaving <267>
R7C3 can only be <9>
R7C1 can only be <6>
R7C2 can only be <2>
R2C1 is the only square in row 2 that can be <9>
R5C1 can only be <5>
R5C4 can only be <9>
R6C2 can only be <4>
R1C2 can only be <5>
R4C2 can only be <9>
R9C2 can only be <1>
R9C5 can only be <5>
R3C2 can only be <6>
R8C3 can only be <5>
R3C3 is the only square in row 3 that can be <1>
R4C8 is the only square in column 8 that can be <6>
R5C5 is the only square in row 5 that can be <6>
R6C5 is the only square in column 5 that can be <7>
R6C8 can only be <8>
R6C4 can only be <5>
R7C8 can only be <5>
R3C8 can only be <3>
R9C8 can only be <7>
R6C6 can only be <2>
R2C4 can only be <4>
R9C7 can only be <3>
R2C3 can only be <7>
R2C6 can only be <5>
R1C5 can only be <3>
R3C5 can only be <2>
R3C9 can only be <4>
R3C7 can only be <5>
R7C9 can only be <1>
R1C7 can only be <7>
R7C5 can only be <4>
R5C9 can only be <7>
R8C9 can only be <6>
R1C3 can only be <4>
R2C7 can only be <6>
R5C7 can only be <1>
R2C9 can only be <2>
R7C7 can only be <8>
R4C5 can only be <1>
R8C6 can only be <8>
R8C7 can only be <4>
R8C4 can only be <1>
R4C6 can only be <4>
R4C4 can only be <8>
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