Jun 06 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C8 can only be <2>
R3C8 is the only square in row 3 that can be <7>
R3C1 is the only square in row 3 that can be <8>
R1C9 is the only square in row 1 that can be <8>
R5C5 is the only square in row 5 that can be <8>
R6C5 is the only square in row 6 that can be <7>
R6C3 is the only square in row 6 that can be <9>
R8C2 is the only square in row 8 that can be <8>
R9C7 is the only square in row 9 that can be <9>
R4C8 is the only square in row 4 that can be <9>
R7C5 is the only square in row 7 that can be <9>
R4C5 is the only square in column 5 that can be <1>
R2C6 is the only square in block 2 that can be <6>
R2C5 is the only square in row 2 that can be <2>
R8C5 can only be <5>
R8C4 can only be <2>
R3C5 can only be <3>
R3C4 can only be <5>
R6C4 can only be <6>
R7C6 can only be <3>
R4C4 can only be <3>
R6C2 is the only square in block 4 that can be <5>
R4C9 is the only square in column 9 that can be <5>
Squares R2C8 and R3C7 in block 3 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.
R2C7 - removing <14> from <1345> leaving <35>
Intersection of column 1 with block 4. The value <1> only appears in one or more of squares R4C1, R5C1 and R6C1 of column 1. These squares are the ones that intersect with block 4. Thus, the other (non-intersecting) squares of block 4 cannot contain this value.
R5C2 - removing <1> from <146> leaving <46>
Intersection of column 3 with block 7. The values <27> only appears in one or more of squares R7C3, R8C3 and R9C3 of column 3. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain these values.
R9C1 - removing <2> from <234> leaving <34>
Squares R9C1 and R9C2 in row 9 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 row.
R9C3 - removing <4> from <247> leaving <27>
R9C9 - removing <4> from <247> leaving <27>
Squares R9C1 and R9C2 in block 7 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 block.
R8C3 - removing <4> from <146> leaving <16>
Squares R7C2 and R8C3 in block 7 form a simple naked pair. These 2 squares both contain the 2 possibilities <16>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C3 - removing <16> from <1267> leaving <27>
Intersection of column 3 with block 1. The values <45> only appears in one or more of squares R1C3, R2C3 and R3C3 of column 3. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain these values.
R2C2 - removing <4> from <134> leaving <13>
Intersection of column 9 with block 6. The value <4> only appears in one or more of squares R4C9, R5C9 and R6C9 of column 9. These squares are the ones that intersect with block 6. Thus, the other (non-intersecting) squares of block 6 cannot contain this value.
R4C7 - removing <4> from <246> leaving <26>
R5C8 - removing <4> from <146> leaving <16>
Squares R9C3, R9C9, R7C3 and R7C9 form a Type-1 Unique Rectangle on <27>.
R7C9 - removing <27> from <127> leaving <1>
R7C2 can only be <6>
R7C7 can only be <2>
R5C2 can only be <4>
R8C3 can only be <1>
R7C3 can only be <7>
R4C7 can only be <6>
R9C9 can only be <7>
R3C3 can only be <4>
R9C3 can only be <2>
R3C7 can only be <1>
R2C3 can only be <5>
R2C8 can only be <4>
R8C7 can only be <4>
R5C8 can only be <1>
R5C9 can only be <2>
R9C2 can only be <3>
R4C1 can only be <2>
R5C1 can only be <6>
R6C9 can only be <4>
R6C6 can only be <2>
R8C8 can only be <6>
R9C1 can only be <4>
R2C2 can only be <1>
R2C7 can only be <3>
R1C3 can only be <6>
R1C7 can only be <5>
R4C6 can only be <4>
R6C1 can only be <1>
R1C1 can only be <3>
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