Aug 30 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C8 is the only square in row 1 that can be <2>
R2C2 is the only square in row 2 that can be <9>
R1C7 is the only square in row 1 that can be <9>
R2C1 is the only square in row 2 that can be <5>
R5C1 can only be <8>
R5C8 can only be <7>
R5C9 can only be <5>
R5C2 can only be <6>
R5C6 can only be <1>
R4C3 can only be <5>
R5C4 can only be <9>
R5C5 can only be <3>
R6C3 can only be <3>
R1C3 is the only square in row 1 that can be <6>
R2C9 is the only square in row 2 that can be <6>
R3C4 is the only square in row 3 that can be <1>
R3C7 is the only square in row 3 that can be <3>
R3C6 is the only square in row 3 that can be <6>
R4C5 is the only square in row 4 that can be <2>
R4C4 is the only square in row 4 that can be <6>
R7C3 is the only square in row 7 that can be <2>
R8C8 is the only square in row 8 that can be <3>
Squares R1C5 and R2C5 in column 5 form a simple naked pair. These 2 squares both contain the 2 possibilities <48>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R6C5 - removing <48> from <4578> leaving <57>
R8C5 - removing <8> from <1578> leaving <157>
R9C5 - removing <8> from <1578> leaving <157>
Squares R4C7 and R6C7 in column 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <48>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R7C7 - removing <48> from <1458> leaving <15>
R9C7 - removing <48> from <1458> leaving <15>
Intersection of block 8 with row 7. The value <8> only appears in one or more of squares R7C4, R7C5 and R7C6 of block 8. These squares are the ones that intersect with row 7. Thus, the other (non-intersecting) squares of row 7 cannot contain this value.
R7C9 - removing <8> from <478> leaving <47>
Squares R4C6, R4C7, R6C6 and R6C7 form a Type-1 Unique Rectangle on <48>.
R6C6 - removing <48> from <478> leaving <7>
R6C5 can only be <5>
R7C6 can only be <8>
R7C4 can only be <5>
R4C6 can only be <4>
R4C7 can only be <8>
R6C7 can only be <4>
R6C4 can only be <8>
R7C7 can only be <1>
R9C7 can only be <5>
R8C2 is the only square in row 8 that can be <5>
R8C9 is the only square in row 8 that can be <8>
R3C9 can only be <4>
R9C8 can only be <4>
R9C2 can only be <8>
R2C8 can only be <8>
R7C9 can only be <7>
R2C5 can only be <4>
R3C1 can only be <7>
R7C1 can only be <4>
R9C3 can only be <7>
R1C2 can only be <4>
R9C5 can only be <1>
R3C3 can only be <8>
R8C1 can only be <1>
R8C5 can only be <7>
R1C5 can only be <8>
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