Mar 10 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C2 is the only square in row 1 that can be <7>
R4C2 is the only square in row 4 that can be <3>
R4C9 is the only square in row 4 that can be <2>
R6C2 is the only square in row 6 that can be <2>
R8C5 is the only square in row 8 that can be <2>
R2C7 is the only square in row 2 that can be <2>
R3C6 is the only square in row 3 that can be <2>
R8C3 is the only square in row 8 that can be <7>
R5C1 is the only square in row 5 that can be <7>
R7C5 is the only square in row 7 that can be <7>
R6C1 is the only square in column 1 that can be <5>
R6C9 can only be <4>
R1C5 is the only square in column 5 that can be <1>
R1C6 can only be <8>
R9C6 can only be <9>
R7C6 can only be <1>
R3C4 is the only square in column 4 that can be <9>
R1C4 is the only square in column 4 that can be <4>
R1C8 can only be <3>
R9C5 is the only square in column 5 that can be <8>
R9C8 can only be <4>
R9C2 can only be <6>
R9C4 can only be <3>
R7C4 can only be <6>
R7C9 is the only square in row 7 that can be <3>
R3C7 is the only square in column 7 that can be <4>
Squares R4C8 and R6C8 in column 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <69>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R5C8 - removing <69> from <15689> leaving <158>
R8C8 - removing <9> from <189> leaving <18>
Squares R4C8 and R6C8 in block 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <69>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R5C7 - removing <9> from <189> leaving <18>
Intersection of block 4 with row 5. The value <9> only appears in one or more of squares R5C1, R5C2 and R5C3 of block 4. These squares are the ones that intersect with row 5. Thus, the other (non-intersecting) squares of row 5 cannot contain this value.
R5C5 - removing <9> from <469> leaving <46>
Squares R6C5, R6C8, R4C5 and R4C8 form a Type-1 Unique Rectangle on <69>.
R4C5 - removing <69> from <469> leaving <4>
R4C1 can only be <6>
R5C5 can only be <6>
R6C5 can only be <9>
R6C8 can only be <6>
R4C8 can only be <9>
R3C1 can only be <8>
R3C9 can only be <5>
R7C1 can only be <4>
R2C2 can only be <4>
R3C5 can only be <3>
R5C9 can only be <8>
R2C8 can only be <8>
R5C7 can only be <1>
R7C3 can only be <9>
R7C7 can only be <8>
R5C3 can only be <4>
R8C2 can only be <8>
R8C8 can only be <1>
R8C7 can only be <9>
R5C8 can only be <5>
R2C3 can only be <3>
R5C2 can only be <9>
R2C5 can only be <5>
R3C3 can only be <6>
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