Aug 27 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R8C8 is the only square in row 8 that can be <5>
R2C7 is the only square in column 7 that can be <3>
Intersection of row 5 with block 6. The value <1> only appears in one or more of squares R5C7, R5C8 and R5C9 of row 5. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain this value.
R4C8 - removing <1> from <1346> leaving <346>
R4C9 - removing <1> from <16> leaving <6>
R6C9 can only be <9>
R6C6 is the only square in row 6 that can be <6>
Squares R1C4 and R1C6 in row 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <47>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R1C2 - removing <47> from <4678> leaving <68>
R1C8 - removing <47> from <4678> leaving <68>
Squares R1C4 and R1C6 in block 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <47>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R2C4 - removing <47> from <2457> leaving <25>
R2C6 - removing <47> from <2479> leaving <29>
Squares R2C6 and R9C6 in column 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <29>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R8C6 - removing <29> from <1279> leaving <17>
Intersection of row 7 with block 7. The value <7> only appears in one or more of squares R7C1, R7C2 and R7C3 of row 7. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R8C1 - removing <7> from <347> leaving <34>
R8C2 - removing <7> from <234679> leaving <23469>
R8C3 - removing <7> from <2467> leaving <246>
Squares R6C1 and R8C1 in column 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <34>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C1 - removing <4> from <457> leaving <57>
R4C1 - removing <34> from <3457> leaving <57>
Intersection of row 7 with block 9. The value <1> only appears in one or more of squares R7C7, R7C8 and R7C9 of row 7. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R8C7 - removing <1> from <126> leaving <26>
R8C9 - removing <1> from <18> leaving <8>
R2C9 can only be <1>
R3C2 is the only square in row 3 that can be <1>
R3C5 is the only square in row 3 that can be <5>
R5C5 can only be <8>
R2C4 can only be <2>
R6C4 can only be <4>
R6C1 can only be <3>
R1C4 can only be <7>
R4C6 can only be <1>
R1C6 can only be <4>
R2C6 can only be <9>
R8C4 can only be <1>
R9C4 can only be <8>
R2C5 can only be <6>
R9C6 can only be <2>
R4C4 can only be <5>
R8C6 can only be <7>
R6C8 can only be <2>
R8C1 can only be <4>
R6C2 can only be <8>
R4C1 can only be <7>
R1C2 can only be <6>
R1C8 can only be <8>
R9C2 can only be <9>
R4C2 can only be <4>
R2C1 can only be <5>
R4C8 can only be <3>
R5C3 can only be <2>
R5C2 can only be <5>
R7C3 can only be <7>
R8C3 can only be <6>
R3C3 can only be <4>
R8C7 can only be <2>
R7C7 can only be <1>
R9C8 can only be <6>
R8C2 can only be <3>
R2C2 can only be <7>
R2C8 can only be <4>
R2C3 can only be <8>
R3C8 can only be <7>
R5C8 can only be <1>
R3C7 can only be <6>
R5C7 can only be <4>
R7C8 can only be <9>
R7C5 can only be <3>
R8C5 can only be <9>
R7C2 can only be <2>
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